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'41 . 1. 1 :41» 13%.1‘31‘1341144‘1‘“ .11. 1.12411:- mews IIIAIY University This is to certify that the thesis entitled THE VON THUHEN MODEL APPLIED IN AN ARCHIPELAGO CONTEXT: A HYPOTHETICAL ANALYSIS presented by CHARLES S . JOHNSTON has been accepted towards fulfillment of the requirements for —MA—SJ‘-ER$—degree in max— Dr. David J. Campbell Major professor Date November 18, 1985 0.7639 MS U is an Affirmative Action/Equal Opportunity Institution MSU RETURNING MATERIALS: Place in book drop to usRARlEs remove this checkout from 4—3—— your record. FINES will be charged if‘book is returned after the date stamped below. » ‘ '9”, NW 15’ “‘80; 300 A310 H JUL T522200? THE VON THUNEN MODEL APPLIED IN AN ARCHIPELAGO CONTEXT: A HYPOTHETICAL ANALYSIS By Charles S. Johnston A THESIS Submitted to [Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF ARTS Department of Geography 1985 ABSTRACT THE VON THUNEN MODEL APPLIED IN AN ARCHIPELAGO CONTEXT: A HYPOTHETICAL ANALYSIS By Charles S. Johnston The Thunen model demonstrates the role of distance in creating zones of agricultural production. The spatial context is the "Isolated State;" comprised of a central "Town," a "uniform plain," and a surrounding "wildernessd' In this thesis the context has been changed to an "Isolated Archipelagod' This introduced new spatial features unique to islands: discontiguity, finite areal constraints, pattern and shape. The nature of the analysis was graphical and diagnammatic to enable visualization of the effects of these features. A static analysis demonstrated the effects on location of production when demand originated at a coastal."PortJ' This also created new conditions for ring formation. A partial equilibrium analysis showed the spatial effects resulting from change in demand, supply) transport and the number of markets. IDiscontiguity, areal constraints and pattern were found to be important features in determining production at a given site. Shape proved to be of little consequence. DEDICATION This thesis took me a long time to complete. Months longer than it should have. Certain stages were especially painful and at times I wondered if I would ever get through. .But I have, finally, as this bound document testifies. So to those students who find themselves in a similar situation; plodding along, wondering where their next burst of motivation will come from, I would.now like to dedicate this thesis. Persevere and you will finish, even if there isn't any light at the end of the tunnel right now. Good Luck! ii ACKNOWIEDGEMEINTS I would like to thank the members of my graduate committee for the help and guidance they gave me. .First and foremost, my advisor, In» David Campbell, deserves more thanks than I can put on a word processor for his nearly eternal patience. I would never have finished without his continual support and good advice. Thanks also are due to Dr. Bruce Pigozzi for the technical assistance he gave me as I struggled through all those tedious economics readings. They may be good science, but are they for real? Dr. Richard Groop, my "third reader," deserves thanks for sacrificing several fine summer days to ‘wade through the final drafts This enabled me to get out of East Lansing on time. In addition, a special thanks goes to Gustave Rylander, my friend and colleague, for doing far more than what I expected to turn my left-handed scribbles into nicely finished graphs and diagrams. Gus". if you ever make it to Hawaii, iiflll be my shout! iii TABLE OF CONTENTS Page DEDICATION ii ACKNOWLEDGEMENTS iii LIST OF FIGURES vii Chapter I. INTRODUCTION 1 Objectives 4 Theoretical Background 5 Thunen's Descriptive Model 5 The Twentieth Century Normative Model 9 Spatial Properties of Archipelagos 14 Research Questions and Hypotheses 20 Methodology 21 Factors of.Model Construction 21 The Analysis 25 II. THE ISOLATED ARCHIPELAGO MODEL AND THE STATIC ANALYSIS 28 The Model 28 Spatial Features 28 Physical Features 28 Transport Features 29 Economic Features 30 Assumptions of Rationality 30 iv TABLE OF CONTENTS (Continued) Chapter The Static Analysis A Comparison of Locations of Demand: Town vs Port The Two-Island Case: Initial Discontiguity and Distance Relationships The Two Product Case Multiple Products Conditions for Ring Formation New Conditions for Ring Formation in Archipelagos Summary III. THE PARTIAL EQUILIBRIUM ANALYSIS Demand and Supply Relationships Analysis of Change in Demand Demand at a Point Location Demand at an Areal Location Analysis of Change in Supply FUrther Modifications Modification of Transport Assumptions ' Multiple Markets NonePerfect Elasticities of Supply'Factors Uniform Fertility Summary Page 32 32 34 37 39 43 49 55 57 57 58 65 67 72 72 83 88 9O 9O TABLE OF CONTENTS (Concluded) Chapter IV. TOWARDS TESTING THE ISOLATED ARCHIPELAGO MODEL Testing the Archipelago Model Brookfield's Analysis of Agricultural Zones in the South Pacific Comparison of Brookfield's werk with the Isolated Archipelago Suggestions for Further Research Endnotes BIBLIOGRAPHY: VON THUNEN LITERATURE OTHER REFERENCES CITED vi Page 93 93 98 100 103 104 105 108 11. 12. 13. 14. 15. LIST OF FIGURES Depiction of the Rent Surface for Islands Comparison of the Rent Surface: Town versus Port The Effect of Discontiguity in the One Crop Case The Effects of Discontiguity: Vertical Perspective The Two Crop Case: Town versus Port The Effects of Discontiguity in the Two Crop Case The Multiple Crop Case - 1 The Multiple Crop Case - 2 Dunn's Three Conditions for Ring Formation The Effects of Discontiguity When Transport Rates are Identical for Two Crops Conditions for Ring Formation: Considerations of Isolation and Island Size Conditions for Ring Formation: Consideration of Break of Bulk Points Conditions for Ring Formation: Consideration of Shape Several Influences on Ring Formation Spatial Changes in Production Resulting from an Increase in Demand: the One Crop Case Page 22 31 33 35 36 38 40 41 43 45 48 5O 52 54 59 Figure 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. LIST OF FIGURES (Concluded) Spatial Changes in Production Resulting from an Increase in Demand: a Three Crop Situation on the Port-Island Spatial Changes in Production Resulting from an Increase in Demand: a Three Crop, Three Island Situation Spatial Changes in Production Resulting from a Yield Increasing Innovation Spatial Changes in Production Resulting from a Yield Increasing Innovation Occurring Under Conditions of Constant Demand Increases in Potential Range of Crop Production Resulting from a Sea Transport Innovation Zonal Effects Resulting from Island Pattern: Isolated versus Clustered Zonal Effects Resulting from a Linear Pattern of Islands Zonal Patterns of Crop Production in Fiji Crop Zonation in Tonga The Copra Export Zone in the Gilbert and Ellice Islands Zonation in a Multiple Market Archipelago - Four Possibilities Hypothetical Sets of Transport Costs from Port-4 to Port-1 viii Page 62 64 71 74 76 78 79 81 82 84 88 Chapter One: Introduction For geographers modeling an agricultural situation, the use of the ideas of Thunen has become d2 rigueur. Living in the early 19th century, Thunen produced "the world's first econometric model" (Hall, 1966). Published in 1826 as The Isolated State, Thunen's model was a well developed hypothetical construct where physical, transport, human and economic variables occurring in the real world were designated as parameters. This enabled him to determine the effect of distance, measured by the cost of transport, on crop type and intensity of crop production. Because the model has proven so versatile, subsequent researchers have been able to study it from many approaches. It has been updated to fulfill the more rigorous expectations of late 20th century science, modified through relaxation of key assumptions to show the operation of forces in addition to distance, and tested for accuracy by case studies focusing on widely divergent types of farming systems . The Isolated State model had three fundamental spatial characteristics. A point located at the center represented the 'Town,’ which was the source of all demand for agricultural products. A physically homogeneous surface, the 'uniform plain,‘ led away from the Town in all directions. Finally, an uncultivated 'wilderness' formed a circumference around the town at the distance where cost of transport made production prohibitively expensive. This wilderness isolated the state from the rest of the world. Under these idealized spatial conditions, distance as measured by 1 2 cost of transport from the farm to the market would cause concentric rings of agricultural production to come into existence. Thunen then modified the uniform conditions on this plain to bring the model closer to reality. By including a second town and a navigable river, for example, he showed that the production 'rings' would be distorted by creating "inhomogeneous" (Beckmann, 1968) physical conditions. The present research will focus on a physical modification of the uniform plain. An analysis will be made of a landform commonly found in.the physical world.but not yet fully examined in the literature — the archipelago. Archipelagos, or groups of islands, are quite numerous in the world's oceans. Huxley (1962), for example, described the geography of ninety-nine distinct island groups, surely a number far smaller than the actual total. He labelled as archipelagos those island groups containing only two islands (Guadeloupe), as well as those containing hundreds (FijiL This thesis will be based on abstracted forms that highlight the major similarities and differences between an.archipelago and the Thunen model. One shared characteristic is isolation. Archipelagos are disconnected from major land surfaces by the ocean, a wilderness in the truest sense. However, the islands in each archipelago do compose the 'state' in an extremely discontiguous form. This discontiguity of the land area affects the zones of production because the possibility of farming is abruptly ended at the edge of each island. Discontiguity also produces three new spatial characteristics. The amount of land available for production is reduced by the inclusion of water; patterns of islands are produced, and each island has a unique shape. These sub—features will have 3 different effects upon the zones of production in the archipelago model, which will hereafter be referred to as the "Isolated Archipelago". Though modification of assumptions is a standard.exercise in.a Thunenian study, analysis of the effects of the above spatial features has not been done to any depth. The inclusion of the effects of water transport was done by Thunen himself (Hall, 1966), as well as by others (Dunn, 1954; Peet, 1969). Dunn (1954) and Feet (1969) also looked at how areal changes affected the production surface in the uniform pfladru The research in the literature that comes closest to this thesis ‘was done by Couper (1967) and Brookfield (1969). Couper looked at the location of agricultural production in three South Pacific archipelagos and.noted that Thunenrtype rings did exist in two of them. However, because Couperls research focused on practical location of transport facilities, he stopped short of examining the existence of these rings from a theoretical standpoint. His research will be reinterpreted in this study in terms of the island.fpatternd Brookfield (1969) studied Pacific towns as market places. He concluded that from a Thunenian standpoint a three—ring system had emerged. lkn;all rings surrounded every Port that was studied because of the wide variety of cultural and economic conditions that existed. Brookfieldhs conclusions will be described in Chapter Four, then used to compare the results obtained from the idealized research done on archipelagos in Chapters Two and Three of this thesis. 4 Objectives The problem to be considered by this thesis is how the zonation of agricultural production will be modified by the spatial properties of archipelagos. To show these effects variations of the Thunen model will be constructed and analyzed, and some of the assumptions will be relaxed. The first objective will be to develop the model of the Isolated Archipelago. Though some features of Thunen's original design continue to be workable, others pertain to conditions no longer relevant. Today, the Thunen model contains several categories of assumptions which have been adapted to fit modern circumstances whenever necessary. These include spatial assumptions that articulate geometric features of the model; physical assumptions that describe the land surface; transport assumptions that point out the costs and conditions of travel; economic assumptions that describe the model of perfect competition and the nature of the agricultural commodities involved; and human assumptions about the economic character of the farmers. These assumptions will be elaborated to produce archipelago models that are sufficiently flexible to undergo a systematic analysis . The second objective will be to analyze these models representing the Isolated Archipelago. The most comprehensive modern method of analysis was formulated by Dunn (1954). This involved first developing a 'static' model where the economy is in complete equilibrium. Then a partial equilibrium analysis is conducted, where one or more assumptions are systematically relaxed. Static and partial equilibrium analyses may be conducted on a wide variety of 5 economic models. In a Thunenian agricultural model the partial equilibrium analysis takes two forms. First, demand at the Town is altered to show supply changes (and thus changes in the rent surface) in the uniform plain. Secondly, conditions of spatial uniformity are relaxed to show how variation over the plain produces ring distortion. The sequence of activities in Dunn's (1954) analysis will be combined with alternative forms of archipelagos to show how the nature of this distortion might vary. The emphasis will be on modification of transport and market place assumptions. Theoretical Background Thunen' 5 Descriptive Model Thunen's model, though "extraordinarily well developed," (Hall, 1966) was designed as an example for others living during the first half of the nineteenth century. As these conditions have now largely disappeared from the agricultural communities of the developed world, newer, normative elements have been introduced to the model to make it "independent of time and culture" (Visser, 1982). Nevertheless, as many of the fundamental concepts of the model have not changed, it remains of value to begin by describing Thunen's original model, his theories and his results. The Isolated State Thunen established the guidelines for his model in his famous first chapter: "Hypotheses." The spatial properties of the model - the Town, the uniform plain and the wilderness, were stated. The function of the Town was to buy the agricultural surplus produced in the plain and to supply the farmers with manufactured goods. Thunen 6 further assumed that all produce was taken to the Town on horse-drawn wagons via the most direct route; a transport method appropriate for the time. These conditions created a situation where the only non-uniform cost to the farmer was the transport cost to take a crop to the market. This cost would by definition increase with distance from the Town. The spatial result was that those farmers living near the Town received a greater profit from the same yield than farmers living further away, because their transport costs were lower. This locational advantage Thunen referred to as "land rent" (Hall, 1966). Crop and Intensity Theories As noted by Horvath (1969) , Thunen conceived of two theories that would determine the location of a crop within the larger farming system. Location was a function of either the type of crop being considered or the degree of intensity of inputs which were used in the cultivation of the crop. These theories were not mutually exclusive - in his Isolated State, Thunen considered that both would be operating simultaneously. Thunen's crop theory was based upon his understanding of the relationship between the nature of a crop in relation to the type of transport system. Certain perishable crops, for example, would spoil too quickly or were too fragile to withstand a long journey. Other crops were too bulky in relation to their value to pay the cost of transport from a farm located from the market. On the other hand, some crops were simply not valuble enough to be grown near the market. These would be pushed to more distant locations by crops that could 7 produce more profit per land area. Crop locations based on these types of considerations constituted Thunen's crop type theory. Thunen was also well aware that the same crop was grown using different methods in different areas of Europe. Each method used a certain amount of inputs, and produced a correspondingly high or low yield. Thunen developed this input-output relationship for wheat. He showed that in the area of the wheat zone closest to the market it would be necessary to utilize more inputs to increase yields so as to maximize income. Tran8port costs for inputs and outputs would, however, eventually make this method less profitable than a less- intensive method. This concept is now referred to as marginal productivity: Dickinson, 1969. The result was that at a certain distance from the market, farming methods would change. Thus, within the zone of production for a crop, there was the further possibility of having different methods of production. This concept has been called Thunen's theory of intensity. The Spatial Result - Ring Formation Thunen's theories of crop type and intensity operated simultaneously in an agricultural system consisting of several products. He showed that as distance decreased from the wilderness to the Town, the varying transport costs reduced each crops' marginal product at a different rate. The land use at a location was determined by whatever type of crop or intensity of inputs to production could produce the highest rent. The result, on the uniform plain, was a set of six concentric rings. These are described below: 8 (1) {Market gardening and milk production. These activities were quite perishable and had high transport costs. They also had high yields per unit of land and so were very profitable. They were grown near the market, but the high rent they yielded declined quickly over a short distance because their marginal productivity was reduced by transport costs. (2) .Forest products. In the early 19th century, wood was in great demand as a fuel and building material. It was very bulky and costly to transport but it also yielded rather large amounts per land area with low production costs. lIt could therefore outbid other farming activities for land. (3), (4) and (5) Wheat production. Thunen divided the production of this crop into three rings of declining intensity. The most intensive method, which produced the highestlyields by also had the highest production costs, was innermost; the most extensive method was furthest away. (6) The last ring was livestock ranching. Land was used very extensively but production costs were correSpondingly low. Additionally, the cattle could walk to market, keeping transport costs down. ‘Besides meat, products derived from live animals, such as butter and wool, were produced in this ring. Alcohol made from grain, and industrial crops of the time, such as flax and oil seeds, were also produced there. At the outer edge, at the distance where rent for all products became zero, the wilderness outside the Isolated State began. The Twentieth Century Normative Model Writing over one hundred years later, Dunn (1954) was the first to convert Thunen's model to a normative form. Now over thirty years old itself, Dunn's work remains valuable to a certain degree. It has, however, been made more precise by subsequent researchers, who built upon the foundations it provided. The contemporary normative model is thus built—up from the following categories of assumptions: Spatial Features Thunen's original conception of a Town, plain and wilderness continues to form the initial geometry of the Isolated State. The function of each feature, as a source of demand, source of supply, or creator of a condition of economic isolation, respectively, has not changed. Physical Features The uniform plain concept has likewise sustained the rigours of scientific investigation. It remains virtually unchanged in most analyses. The surface of the land then, continues to be completely uniform in its physical characteristics: the topography is completely flat and the soil is everywhere of the same fertility. This in turn provides identical yields across the plain for any given crop, provided it is grown with equal intensity of inputs (Found, 1971). The economic result is that every unit of land on each island has the same income—producing potential for a given crop. The amount of rent received by the farmer will depend only on distance to market, not physical qualities of the land at the farm location. 10 Transport Features In normative revisions of the model the method of transport is now generally unspecified (Dunn, 1954; Found, 1971; Alonso, 1974). Distance from the farm to the market is considered simply as an economic cost. This cost may be linear (Huff, 1981; Day and Tinney, 1969; Cromley, 1982; Garrison and Marble, 1957; Bannister, 1977; O'Sullivan and Ralston, 1980; Jones, 1978; Stevens, 1961; Beckmann, 1968), or non-linear (Katzman, 1974; Visser, 1982; Beckmann, 1972; Jones, McGuire and Witte, 1978) depending on the explicit research topic being done. Non-linear transport costs are represented by a function rather than a variable. However costs are calculated, the assumption made by Thunen that farmers would take the straight—line distance to the Town is still usually followed. The concept that creates this capability is now referred to as an "undifferentiated transport network" (Beckmann, 1968). Economic Features Thunen assumed that economic activities operating in his Isolated State would be constrained by the parameters of perfect competition. This is a fully developed model in economics, containing a set of concepts describing the market interactions between buyers and sellers (Mansfield, 1983). The following represent some of the major characteristics of the model. Agricultural products are homogeneous; this eliminates any preference regarding from which farmer they are bought (Due, 1956). There is no 'friction' among factors of production (labor and capital); this gives them perfect mobility and divisibility (Beckmann, 1968; Robinson, 1971), as well as free entry 11 and exit from the market (Amache, 1983). Prices at the market are completely fixed on the basis of supply and demand. There are a large number of sellers and buyers, but there is no government or other agency that is capable of manipulating the economy (Due, 1956; Hall, 1966). These prices, and the state of the entire market, are considered to be stable. This enables the buyers and sellers of the produce to maximize income. In a spatial model, certain additional properties of the economy must be articulated regarding the costs of production for crops. It is generally assumed that all costs of inputs to production are uniform over the land surface (Dunn, 1954; Found, 1971; Jones, 1978). These input factors exist in sufficient supply at all locations; ie., their supply is infinitely elastic (Dunn, 1954; Beckmann, 1972). This condition allows the further assumption, already mentioned in relation to physical properties, that all returns from production are uniform (Found, 1971) and constant in scale (Beckmann, 1972; Katzman, 1974). Jones (1978, 1979) has elaborated the supply and demand characteristics of the perfectly competitive agricultural economy. Demand characteristics are that the products are 'substitutes,' that is, demand for one crop reduces the demand for another. This also means that demand for this product is negatively related to its own price - the more price rises the less of it will be bought. As a substitute, however, demand for a product is positively related to the price of the other commodities. Demand is also positively related to the aggregate income. If the total income for society rises, demand will rise. The products themselves are implicitly designated as necessities, though with the exception of Huff's (1981) research on 12 the effects of introduction of a luxury good, this is never recognized. With regard to supply, for any of the products in the economy the quantity that is produced will be a positive function of the price. If the price of a product rises, more of it will come on the market for sale. ‘When the price for a product reflects the situation where the amount demanded and the amounts supplied are identical, a state of equilibrium is said to have been reached. In the typical sequence of development of the Thunen model, this condition is taken as the starting point. Homo Oeconomicus An assumption made by Thunen was that farming was done "absolutely rationally" (Hall, 1966). This was based upon a conception of human character that has been labeled "homo oeconomicus" (Vickrey, 1964). Such a creature is in possession of "perfect information" (Garrison and Marble, 1957) or "perfect knowledge" (de Souza and Foust, 1979) regarding the state of the market and relevant production technology. Farmers utilized this information for the sole purpose of optimizing their income (de Souza and Foust, 1979). Katzman (1974) has defined this more in line with modern economic concepts by noting that farmers "equate factor payments to marginal revenue products" when making decisions. This concept of man is widely employed in the literature because it allows an analysis to be conducted at the level of the 'industry' rather than the 'firm' (Dunn, 1954). This is important because it 13 permits the assumption that all farmers located the same distance from the market will choose to grow the second crop. Overall, when the above set of assumptions is operative, the Isolated State is said to be in "spatial equilibrium" (Visser, 1982). This condition forms the geographical basis for the static model that is the typical starting point for analysis. Rent Calculations in the Normative Model An "explicit distance function," which would maximize the rent for land at any known distance from the market, was first developed by Dunn (1954). When solved for all crops the function would produce concentric land use zones when an economy is in equilibrium. This function is now well known: R=E(p- a)- Efk where: R = rent per unit of land E = yield per unit of land market price per unit of commodity *6 II a = production cost per unit of commodity f transport rate per unit of distance per unit of each commodity k = distance With the assumptions of the model and method of calculation articulated, Dunn went on to analyze economic maximization solutions for the uniform plain in the cases of static and partial equilibrium. This method will be utilized for the archipelago case in Chapters Two and Three. 14 Spatial Properties _o_f_‘ Archipelagos The uniform plain Thunen created has been useful in many types of analysis done subsequently on his model. As the vast majority of the land surface of the world is continental (though not topographically uniform) this concept may very often be appropriate as a beginning assumption. However, features of archipelagos may perhaps represent the most different alternative to the spatial characteristics of the Isolated State model that can be found on the physical surface of the planet. The breaking up of the uniform plain surface into islands potentially adds infinite complexity to any model of an archipelago. This complexity must be reduced to a meaningfully small number of variations to show the most salient differences between the models. For the Isolated Archipelago model, the complicating factors are discontiguity and variation in area, pattern and shape. Discontiguity of the Land Surface Discontiguity is the most important of the four properties being considered here. Pattern, shape and areal considerations emerge from the break—up of the uniform plain into a surface composed of land and water. Discontiguity produced by water also creates several new conditions in the model. The first condition is that the transport system will be bimodal, and that land tranSport will have different rate structures than sea transport. These different rates would change the theoretical route from farm to market in an undifferentiated bimodal network. The preferred route would now theoretically become that for which the total economic costs were lowest, rather than the route having the 15 shortest straight-line distance (Dtmn, 1954; Chisholm, 1962). By being more expensive, land transport routes would tend to go straight toward the nearest dock-site along the water; they would not take the straightest distance overland in the exact direction of the Town. Once the product was loaded onto a ship the reverse would be more nearly the case. When transported by water a product could be brought straight to the Port. This surface represents a form that "is frictionally uniform to transport" (Couper, 1969) -- ie., it comes very close to Thunen's assumption of being undifferentiated. Projected into any archipelago model, a second effect of discontiguity due to water should be to increase the crop—zone width. Thunen himself noted that because water transport was cheaper per unit distance than land transport, the effect of the introduction of a river or canal would be to elongate the inner rings of production (Hall, 1966). Only certain bulky crops could benefit from this change in mode of transport, because crops that needed to be sold quickly would not stay fresh on the longer, in terms of time, water journey. When models were otherwise equal, the lower sea transport rates in the Isolated Archipelago would increase the distance from the Town (Port) that would bring a positive rent for a given crop or level of intensity beyond what the economically viable distance was on the uniform plain. Thus, this characteristic of archipelagos should theoretically serve to expand the zones of production. Peet's (1969) study of the expansion of commercial agriculture in the 19th century around the London market took note that when demand rose: "agricultural lands would bulge out along lines of low spatial resistance." Because sea transport costs were cheaper than 16 land transport costs, areas supplying London followed the shipping lines. Thus, as demand expanded hinterlands of the Baltic Sea, the Black Sea, and the Great Lakes all had their turn as suppliers; Australia finally emerged as a major supplier by the early 20th century. Political and economic relationships, Peet noted, could also create spatial resistance. Colonies, for example, would trade with the mother country, no matter what the ratio of profits to costs was. Countries with developed markets of their own would lure production away from the world market. The resulting spatial pattern, according to Peet, was one of a dominant world market, centered around.London, ‘with.large areas of supply located in scattered areas all over the ‘world. 'This situation could be interpreted as a macro-scale archipelago: one 'Port,' encompassing several nations where demand is located, and areas of suppLy on several continental-sized.lislandsfl A third condition created by discontiguity relates to the ability of the produce to be transferred from land onto boats. Locations where this occurs are known.as "break-of bulk" points (de Souza and Foust, 1979). In an undifferentiated network no discussion of this feature was needed. In an island context it becomes relevant. If the entire shoreline of an island permitted docking of boats and transference of produce, the break-of—bulkzfipoint"would become a line. IHowever, coastal topography is very often too extreme for this to occur; Islands may end abruptly at cliffs, or swamps may extend miles inland from the shore. The water may be too shallow to allow docking for suitably large ships, or extensive shoals or reefs may prevent a ship from even approaching. Unsheltered coast lines usually lack protection from storms. .As a result of these physical features, 17 suitable breakpof-bulk points may be rather rare along the shore, and 'lines' are even more unusual. A final condition caused by discontiguity involves the altering of the location of the Town. In the Isolated State it was located in the center of the uniform plain by definition. In the Isolated Archipelago, where an island may not even exist at the center, this location would be unlikely; .A second factor is that the lower cost of water transport would provide greater accessibility for outer islands and would make a location on the shore of’an.island more advantageous than in the interior. Thus, in the Isolated Archipelago, the Town 'will more than likely be at a different location than it is assumed to be in the Isolated State. Areal.limitations The areal features of archipelagos differ dramatically from the circular Isolated State. Total agricultural production for the Isolated State was found by multiplying;yields times the area of a circle. For an Isolated Archipelago, if the radius is considered to be half the straight-line distance from the two most distant islands, the total land area would always be less (usually much less) than this because of the large expanses of water. It has been noted that the size of the Town is a function of the area of the region supplying it 'with agricultural surplus (Peet, 1969). The larger the region, the greater the growth potential. Stated from the demand perspective: the larger the Town, the greater the potential for a larger set of rings of production to emerge. For archipelagos, therefore, the greater the land-area to water-area ratio, the greater the potential for a large 18 Port and more complicated agricultural pattern to develop. In the Isolated State model it is also implicitly assumed that the supply area will.rise or fall as demand in the Town changes. 'When demand rises, for example, production could become more intensive, the ‘wilderness boundary could shift outward, or both. In an archipelago this latter change has definite limitations. IProduction would gradually extend from islands near the Town.to those further away. Once it reached the outermost island, no further expansion could take place because no further production area exists. Thus, if demand rose, the effect would be an increase in intensity in the inner rings after the production surface has reached the outermost island. This intensity change, however, would be complicated.by'discontiguity; .A method employing a particular level of inputs could be cut short well before its marginal productivity fell too low, because the most distant point on the island had been reached. For archipelagos of different areal extent, then, the zonation of agricultural production could vary. Island Pattern Pattern is perhaps the most diverse property for it includes the number of islands within the archipelago, their relationship (in terms of distance) to each other, and the location of the Town with respect to the other islands. .As noted in the introduction, the term archipelago has been used to refer to two-island groups or groups containing hundreds of islands. 'With every new island the effects of pattern on production are compounded. A glance at maps of the archipelagos of the Pacific Ocean shows 19 that the location of these islands with respect to each other follows no universal pattern. Some archipelagos, however, may be in lines of various types. The Hawaiian Islands form a long curve, for example. In Vanuatu the 'line' splits into two to form a rough °Y° shape. In New Caledonia, a single long, narrow island represents one line, while three smaller, non-linear islands (the Loyalty Islands) running parallel form a second 'line.‘ The pattern for most archipelagos is not usually as distinctive as in this linear case. Islands may be clustered near each other, widely separated, or both. This, in turn, complicates aspects of production. Outer islands may themselves be isolated states because boats travel there so infrequently. Clustered islands, on the other hand, may hardly feel the effects of discontiguity. Island Shape This factor represents a fourth distinct spatial property. An island that is nearly linear in shape will potentially have a very different rent surface from islands that are more circular or rectangular. This will be further modified by the break-of-bulk situation . Results Caused by the Spatial Features of Archipelagos By changing the uniform plain to an archipelago, several changes have been made in the production surface. Discontiguity altered the transport system to where at least two forms would normally be required for all locations not on the island where the Port was located. The distance from farm to market might easily be something longer than the most direct route. The Town or Port would no longer 20 be located in the center of the archipelago 'state.‘ The smaller land area of an archipelago would limit the potential production area, which might tend to keep the Port smaller than the Town when both the Isolated Archipelago and the Isolated State had 'radii' of equal length. The elimination of production beyond the outer island would create changes in intensity that would not occur on the uniform plain. Variations in pattern may highlight or negate the effects of discontiguity. Islands may be completely isolated within a group, or if clustered, the combined areas may reduce the effects of the intervening water surface. Finally, the shape of an island may radically modify the production pattern on its surface. Research Questions and Hypotheses The flexibility of the Thunen model and the amount of research that has utilized it have produced conclusions that are considerably more liberal than originally conceived. It is now well known that the concentric ring arrangement will only rarely be approached in the real-world, and that any a pgio_r_i_ change of assumptions in the theoretical research will modify the resulting spatial arrangement. The main research question of this thesis asks how the zonal pattern of production would be modified when an archipelago is substituted for a uniform plain. The expected overall result is that any zonal patterns on islands exist as a function of the distance decay created by the increase in transport costs. Patterns from farm to market will continue to be zonal but will be highly modified by the four spatial features distinct to archipelagos - discontiguity, areal variation, shape and pattern. In addition, variations between land 21 and sea transport costs and the nature of the 'exchange surface' between them as represented by the 'break-of—bulk' points will cause further modification in the zonal arrangement. Methodology Factors o_f Model Construction The major purpose of this thesis is to construct an alternative form of a familiar model, then analyze it. An expedient method of doing the former is to update the model through discussion of the previous research. Doing the latter will also utilize the analysis methods of previous researchers, both in terms of technique and sequence, in order to show how the spatial properties of the archipelagos would cause modification. Spatial Representation of the Rent Surface on Archipelagos As noted, the definition of archipelago is unspecific and includes many forms of island groups. What shape then, best represents all spatial forms? The answer would seem to be that no one shape does permit a complete analysis under either static or partial equilibrium conditions. The rent surface is bound to be modified by the four spatial features under consideration. Island pattern, for example, may be determined by relative island position. This matters little when island shape is being considered. Necessarily, then a variety of models of island groups must be chosen to elucidate the spatial surface properties under consideration. The rent surface can be shown graphically or diagrammatically, as in Figure 1. In the graph at the bottom of the figure, the amount of rent at the Town is shown on the y-axis, while the distance from the 22 Town is shown on the x—axis. The rent curve for each crop slopes downward at a different rate. land transport costs have a steeper rate of decline over distance than sea transport costs, so the curves representing them will have correspondingly steeper slopes on the graphs. In the diagram at the top, two circular islands (idealized 'maps') are shown. In this case the isorent lines represent the distance to where there is a change in production - ie., a new zone. o 0 a: high rent crop \\ b: middle rent crop \ c: low rent crop ‘~l \ Island 2 w: wilderness k3: mar in of pro uction of crop a FP: furthest point Island 1 ~~~ ~§ ‘— AAAAAAA - I - VVVVVVVV'VVV Figure 1. Depiction of the Rent Surface for Islands The effects of discontiguity are portrayable by either of these methods. Pattern, shape and area considerations can only be shown easily by using diagrams. Therefore, the 'map' format at the top will be used when these properties are being examined. For simplicity, 23 islands will always be considered circular, unless specific examples of 'shape' are being discussed. When an island has a Port, it will be necessary to find the most distant location away from this Port on the island. This will represent the last unit of land available for production. Beyond, the sea represents the wilderness. This point can be found by drawing a line from the Port through the center of the circle to the line of circumference on the other side (this line equals the diameter of the circle). Conventionally, this point will be referred to as the "furthest point," or the "FP" in the analysis. Normative Combinations of Thunen's Crop Type and Intensity Theories Since Thunen's crop sequence did not occur universally, modification has been necessary. His specific crop sequence has been abstracted to a numerical sequence by Dunn (1954). To show concentricity, Dunn used an arbitrary "multiple—product" graph showing the sequence of five crops (the graph in Figure 1 represented a three crop system). Dunn later went on to note that an assumption of a single crop per ring was unrealistic for any typical farming system in a region. For example, there were cases where more than one product could be produced as a result of the same processes and in fixed proportions (such as wool and mutton). The most profitable output remained where the marginal cost of the "composite unit" equalled the combined price. The ability to produce two products has the advantagous result of producing more rent than one product alone. This, in turn, may bring a spatial comparative advantage over another crop or crop combination. 24 Taking this one step further; it could be possible to produce more than one crop on a unit of land during the year. The question then becomes how much of each to produce? The answer lies in separate analyses of the marginal costs of each product. With regard to rent, the amount produced will again be a combination of all crops that can be grown on the unit of land. With this refinement made explicit, it has been recognized that a set of crops may be labeled arbitrarily, and that each designation may represent a single crop or a combination of crops. Within the sequence any given designation could theoretically be equated with either a lone crop or a combination of them, depending upon the farming system being considered. This abstract method will be employed here; zones representing specific crop types, different levels of intensity, or a combination of the two will be identified by an alphabetical sequence. Letter 'a' will represent that crop, crop combination or method which has the highest rent value per unit of land. Each letter following will represent crops that are sequentially lower in rent—earning capability. The letter 'w' will represent 'wilderness;' an area where no land rent is being earned. The Transport System In the uniform plain Thunen assumed all produce would be brought to market on horse—drawn wagons, a concept humourously inappropriate in an archipelago. Normative modifications specify that transport costs are measured per unit of distance, but leave the actual method undefined. The latter approach will be taken here. Be cause there are two surfaces, the analysis will be complicated by use of two modes of 25 transport - land and sea. To show the effects of the spatial properties being examined, these modes may be assigned a variety of rates as necessary. 'When a dual mode of transport is utilized a third cost factor is terminal costs at the breakeof—bulk points. Initially, it will be assumed that these costs do not exist; that the produce will immediately be transferred from land onto a boat at no extra charge. This will reduce the model to a condition where the only cost for transport to market is borne to overcome distance. IHowever, a choice between competing economic assumptions must be made as to where to locate these breakeof—bulk points. The direct—line, least—distance to market assumption states that the produce will be taken via the shortest distance from the farm to the Port, no matter what the combined land and sea transport costs are. The assumption of least- cost access to the market requires the farmer to take the crop to the sea via the shortest route, in order to take advantage of the cheaper water transport rates. In this thesis, for the sake of simplicity, a modification of the.former will be assumed. There will be an initial assumption of only one break-of—bulk point on each island. This point will be located on the unit of land that is closest to the Port. Crops will be brought there overland, even if this land journey is longer. The Analysis The sequence of activities to be conducted in the analysis of the archipelago model follows the traditional research in the literature. This sequence was mentioned in the introduction: 26 (1) The model will be developed and analyzed in the static case. Its development will necessitate inclusion of many of the normative modifications that have been made since WW II. A more current, comprehensive form of the Isolated State will emerge. This version will then be placed in the context of an archipelago to show how the distinctive spatial properties of this landform will modify the results obtained in the uniform plain. A static analysis is conducted on an economy that is set in a state of total equilibrium (Awh, 1976). It has arrived at this state by assumption; there is no necessity to subject it to the changes required to produce equilibrium (Vickrey, 1964). Dewey (197 5) has noted that static models are the most common type because they are the easiest to construct and alter and have the greatest predictive ability. Dunn (1954) worked through the most complete version of the static analysis. His sequence of steps will be repeated for the Isolated Archipelago model. (2a) Partial equilibrium — demand and supply modifications. In this section the work of those authors who have altered these two features of the economy will be discussed. Analysis of change in demand will preceed analysis of change in supply. The former will involve raising the demand at the Port to see the spatial effects on the zones of supply. Analysis of change in supply will involve reversing the procedure. (2b) Partial equilibrium - spatial modifications to the Isolated Archipelago. In this section the categories of assumptions inherent in the model will be modified so that they are no longer spatially uniform. The intent of this section is to bring the model closer to 27 the actual physical and economic conditions under which residents of archipelagos live. Throughout this section of the analysis the spatial properties of archipelagos will be emphasized to show their effect. They will be introduced as variations in the model of the archipelago under examination. Not all properties will be examined for all modifications of assumptions, as this would lead to extensive redundancy. When the partial equilibrium analysis has been concluded it is hoped that the salient differences between an archipelago and a uniform plain will have been shown. Chapter Two: The Isolatederohipela 0 Model and the Static Analysis TheiMbdel Thunen's (Hall, 1966) and Dunn's (1954) models have been used as the starting point for much of the subsequent research analysis on agricultural location theory. In this chapter the appropriate features of the models of various writers will be combined to produce the Isolated Archipelago model. Spatial Features The Isolated Archipelago will initially have one center of demand. The location.of this Town within its boundaries will vary depending on the location of islands and the spatial property being considered. Initially, comparisons between an interior Town and coastal Port will be made. .As the analysis progresses, only a Port location will be assumed. Islands will exist in varying numbers, and will also vary in size, relative position.(pattern) and shape. The simplest version of the model will include only one island. If the location of the Town is further assumed to be central, this model comes very close to being identical to the conventional Isolated State. The only real difference is that the wilderness boundary on an island may not expand, while this is possible on a land-based model. Physical Features As this thesis focuses on spatial rather than physical properties of archipelagos, it is not necessary to tamper with the concept of the 28 29 uniform plain. Let the surface of every island, then, be considered completely uniform in topography and soil characteristics. The soil is everywhere of the same fertility; this in turn provides identical yields for any given crop, at any given intensity (Found 1971). Economically, each unit of land on each island will have the same income-producing potential for a given crop. The amount of rent received by the farmer will depend on transport costs, not soil properties. Transport Features The system of transport will be by ship for the inter—island trade. The rate charged will be assumed to be linear (Found, 1971), constant over time and unique to each crop (Dunn, 1954; Bannister, 1977). As Couper (1968):noted, the assumption that all locations have direct access to the Town is approached closely in an archipelago, where the sea surface permits straight-line crossings from any outer island to the Port. In addition, it will be assumed that the supply of sea transport is perfectly elastic» This provides the farmer with the ability to go from any island to the Port whenever necessary. Jones (1979) has shown that the supply of transport facilities may be assumed to be perfectly elastic. 'With respect to land transport, the undifferentiated network conditions discussed in the methodology will apply for all island surfaces. However, because of discontiguity, the produce must first be taken to the break—of—bulk points on outer islands. As noted in the methodology, there will initially be only one of these per island, and it will be located at the point on the island nearest the Port. 30 The assumption of an infinitely elastic supply of sea transport removes the necessity of including terminal costs. There will in fact be only two transport costs, land and sea, both of which are linear. This allows for explicit consideration of the role of distance. At the break-of—bulk point it will be assumed there is a 'Pier,' from which produce will be transferred to ships at no charge to farmers. It will initially be assumed that there is no demand for products at this Pier. 'When the relaxation of the single Town. assumption.is discussed, Piers will.be assumed to have become additional Towns. EconomicIFeatures The economy in the Isolated Archipelago will be modeled.under assumptions of perfect competition. .As stated in the introductory chapter, this includes the following characteristics: (1) Homogeneous agricultural products. (2) Perfect mobility and divisibility of factors of production. (3) Fixed prices for agricultural products. (4) Many buyers and sellers. (5) No government intervention in the economy. Additionally, spatial equilibrium features include an infinitely elastic supply of inputs to production, which are available at uniform prices. Assumptions 3): Rationality Finally, let it be assumed that all farmers are economizers. They make perfectly rational decisions based on perfect information regarding all elements involved in the production process. 31 Area of Positive Rent w: Wildefness PP: furthest 90““ P o r t Effect of Effect of Transport Costs Transport Costs Rent AAAAAAAAAAAAA Figure 2. Comparison of the Rent Surface: Town versus Port 32 The Static Analysis Before proceeding with the static analysis of the Isolated Archipelago, an introductory comparison will now be made between the Isolated State and this new form of the model. The assumptions regarding the nature of the new model have now been made explicit. The intent of this first section is to show the basic differences between a centrally located Town and a coastal Port regarding location of agricultural production. A Comparison 2: Locations g Demand: Town E Port Figure 2 compares the rent surface on two different islands of equal size in the one crop case. In the island to the left (Figure 2a) the Town is centrally located; on the island to the right (Figure 2b) the location has been changed to a port on the coast. In this example the crop has the same rent value at both market places, the islands are both circular, and transport costs on land are equal on both islands. When the two figures are compared it can be seen that the rent line changes because the location of demand has shifted from the center of the island to the coast. With a centrally located Town, the rent decreased equally in all directions, and was reduced to zero at all points along the shore. From the Port, rent decreases would be circular except that the shore cuts off production. land at the shore is able to 'bid' as much rent as any interior point located the same distance away from the Port. However, because land transport costs are equal, much of the interior of the Port-island is now beyond the distance where production is profitable. Transport costs will be 33 FP: Furthesf Point Town A#.. F? FP """"""" ISLAND 1 lSLAND 2 F‘x‘ “‘ “‘ ‘ FP Port ' " Pier FP ~~““~ “‘~“ “‘ FP Port - Pier FP Figure 3. The Effect of Discontiguity in the One Crop Case 34 dealt with more fully throughout this thesis; they are mentioned here to show that for a Port-market, higher land transport costs may give coastal, outer island locations an advantage over interior locations on the Port—island. The Two—Island Case: Initial Discontiguity and Distance Relationships In Figure 3 the role of discontiguity is examined. In each of the three diagrams, Islands -1 and.-2 compose a two—island archipelago. Distance is the only variable. In Figure 3a, the level of demand at the Town.and the slope of land transport rates are assumed.to be just sufficient to bring all the land on the island into production. Because the Town is centrally located, there is no importing of any produce from the second island. The result of a shift in location from Town.to Port is shown.by comparing Figure 3a with Figure 3b. li;can be seen that because land transport rates have been held equal to those on Island-1, production can.nOW'extend.only halfway into the island (the same case as in Figure 1h». The remainder of the land lies beyond the spatial margin of profitability; However, because sea transport is cheaper, land on Island-2 now brings positive rent from production. In comparing Figure 3b with Figure 3c the effect of discontiguity is made more clear. Both island groups are assumed to have equal transport rates Ch%, the negative slopes of the marginal rent lines are equal). ‘When the two islands are separated by a larger expanse of water (Figure 3c) it becomes apparent that sea distance has reduced the ability of land on Island—2 to bring rent. This is because the higher sea transport cost from Pier to Port has reduced the distance 35 Area of Production Surface ISLAND 1 ISLAND 2 {5:22; Port Pier Figure 4. The Effects of Discontiguity: Vertical PerSpective 36 b Port Figure 5. The No Crop Case: Town versus Port 37 into the interior of Island-2 that production can take place. Higher land transportation rates quickly absorb the remainder of the land rent. A second less apparent effect of discontiguity is that because the amount of land able to produce rent is smaller on the archipelagos in both Figures 3b and 3c, the total supply of the crop from Islands -1 and -2 (based upon homogeneous yields) is also reduced. (The land area for all three archipelagos is assumed to be equal.) On Island—1, the area of supply has been reduced by nearly two-thirds. The area under production on Island-2 is dependent upon the intervening ocean distance separating it from the Port. This is shown from a vertical perspective in Figure 4. The reduction of rent producing area causes problems with unmet demand at the Port. This topic will be considered in Chapter Three. The Two Product Case In Figure 5, two single islands are shown; each has two crops, and each crop has a different rent potential at the market as well as a different land transport rate. In Figure 5a, where a central Town is again conceptualized, two land use rings will form around the Town and land use will change at the distance where the marginal costs per unit distance of crop-b become less than for crop—a. This case is very similar to the Isolated State of Dunn (1954). With a Port location, the distance on Island-1 where crop—b becomes more profitable remains the same as in Figure 5a. However, as in the one crop case, the area of production for both crops is reduced, and land beyond the profitable margin is idle. 38 Port Pier 'vvvvvvvvvv'vv'v'r Figure 6. The Effects of Discontiguity in the W0 Crop Case 39 When a second island is introduced, new rent relationships result in the two—crop case. The simplest example is shown in Figure 6. In Figure 6a, the land transport cost for crop—a is assumed to reduce rent to zero at the shore of Island-1. Hence, only'crop;b will be produced on Island-2. In Figure 6b, the Port location permits production of both crops on Islande2. In this particular figure, water transport is shown.to be somewhat more expensive for crop—a than for crop—b. However, distance is not sufficiently great for the larger rent earning ability of crop—a to be negated. The result is a zonation on Island-2 that reflects land use on Island—1. Crop—a occupies the land nearer the pier, but its greater land transport cost eventually reduces its marginal rent value below that of crop—b, which is then produced until its rent potential also declines to zero. After this point the land falls idle and becomes wilderness. In the second graph for the two crop, two island case (Figure 60), water transport rates are again differentiated and are assumed to be much greater for crop-a than for crop—b. In this case there is a high rate of distance decay for crop-a; a relatively low rate of decay for crop-b. Here, the rent—earning potential of crop—a is never greater than crop—b on Island-2. Consequently, only crop—b will be produced. Multiple.Products 'When several crops are placed into the Isolated Archipelago, the resulting spatial pattern may be virtually unchanged from the uniform plain conception, or it may be altered extensively by the relationship 4O A Q3 Pier P6rf v ISLAND 3 0 Pier ISLAND 2 ‘0. Pier Port ISLAND 1 0 V Figure 7. The Multiple Crop Case - 1 41 Pier Pier Port The Multiple Crop Case - 2 Figure 8. 42 between discontiguity and water transport costs. Figure 7a shows a two-island model where the production surface on Island-2 resembles that of the Port-Island. Crops —a through -d follow each other in zonal succession; the only difference being that a hypothetically greater ratio of water-land transports cost for crops —a and -b has shortened their production radius on Island-2 by a greater proportion than crop—c. Crop—d has its production area cut— off before rent is reduced to zero because the FP on Island—2 has been reached. Figure 7b, represents a three island, linear archipelago. Here the introduction of the third island effects production by enabling crop—d to be grown to the distance where combined land and sea transport costs do reduce rent to zero. The two cases shown.in.Figure 7 represent situations of similarity between the Isolated State and the Isolated Archipelago. Each crop on the Port-island reestablishes itself on the outer islands in the same order. Each is "bounded" (Garrison and Marble, 1957), meaning that it has an inner and outer distance of production. In between these distances it is the most profitable choices Outside this range other crops produce more rent. In Figure 8, a situation dissimilar to the Isolated State is shown. On the Port-island, assume the static crop zonation sequence exists. .Also assume water tranSport costs are sufficiently high for inner zone crops so that their rent is reduced to zero before Island-2 is reached. The effect of discontiguity is therefore to limit their (crops -a and -b) production to the Port—island. Crop—c becomes the highest rent crop capable of profitable production on Island-2. 43 Figure 9. Dunn's Three Conditions for Ring Formation (adapted from Dunn, 1954, p. 10, 12, 13) However, in the example shown, crop—d has exactly the same rent value at the Pier because of differential sea transport rates and discontiguity; Lower land transport costs on Island-2 then give crop» d a rent advantage over crop—c everywhere on the island. Finally, the outer margin for crop—d is reached and crop—e becomes the more profitable choice. As shown, its production continues to the end of the island. In this example, the conventional zonation (Figure 7) has been modified due to discontiguity. Conditions for Ring Formation Dunn (1954) specified three conditions for ring formation. The first two were that each crop would.have progressively lower rent values at the market place, but would also have less negatively steep 44 slopes, reflecting the ability to withstand progressively longer transport distances. A final condition was that the slopes of these transport functions must cross before the distance where zero-rent was reached (ie., in the first quadrant). Conditions -1 and -2 are shown in Figure 9a; condition-3 is shown in Figure 9b. It is obvious that Figure 9b applies to both the Isolated State and Archipelago. Crops must have marginal rent functions that cross in the first quadrant. Discontiguity in an archipelago context complicates Dunn's first condition (shown in Figure 9a). In the discussion of the two crop case, Figure 6b showed that crop-a could capture the inner zone behind the Pier on Island-2 when the relationship between discontiguity, transport cost and crop type permitted. Then the expected zonation sequence (crop-a, then crop-b) could also occur on Island-2. But in Figure 6c, changing the sea transport rate for crop-a made its marginal rent slope steeper and changed the outcome. As shown, the two islands were sufficiently discontiguous so that the rent for crop-a had become less than that for crop—b over the entire surface of Island—2. In an archipelago then, for ring formation to occur a necessary condition is that the marginal rent lines must cross at distances where land exists. If these lines cross over water, the crop with the lowest water transport rate would prevail on islands further away from the Port. In the uniform plain, if two crops have different rent potentials at the Town, but the same rate of decline due to identical transport costs, crop—a will always outbid crop-b (Dunn, 1954). This is shown in Figure 90. In the Isolated Archipelago, this is not necessarily the case because of the bimodal transport system. Figure 10 shows the 45 Port Pier Pier lSLAND‘l ISLAND 2 ISLAND 3 Figure 10. The Effects of Discontiguity When Transport Rates are Identical for Two Crops Port—island, a second island nearby, and a third island that is more distant. Discontiguity has necessitated that both land and sea transport are required to bring the crops to the Port from the outer islands. On Island-2, proximity to the Port has kept rent values quite high at the Pier. Then the differential rates for land transport between crops rapidly reduced the marginal rent for crop—a, and a distance was eventually reached where crop—b became more profitable. In this exampde, having identical sea transport rates for both crops was insufficient to counter the differential land transport rates, and zonation occurred. On Island-3, this was not the result. The greater distance between islands (ie., discontiguity) has reduced the rent for both 46 crops considerably. However, because the sea transport rates are assumed to be identical for the two crops, crop-a is still sufficiently profitable to be produced on Island-3. Crop—b is outbid completely. This is a similar result to that obtained by Dunn (1954) on the uniform plain (Figure 16c). What is unexpected is that this result has occurred on Island-3, located a greater distance away from the Port than Island-2, where zonation occurred. A greater expanse of water (discontiguity) has thus provided a higher rent crop with the opportunity to extend production to land that is too distant for production of a lower rent crop. This result is something of a reversal from the standard Thunenian conclusion, but a moment's thought easily shows that it is not unique to archipelagos. The situation is comparable to one described by Dunn (1954) for the uniform plain. The same result could be obtained where a differentiated transport network (consisting of two methods of tran8port that had different rates per unit of distance) existed. Farms located a great distance from the Town could grow high rent crops if the less expensive transport method were available nearby. Farms nearer to the Town that had to rely on the more expensive method would be forced to grow lower rent crops. The relationship between distance and type of production has now become a function of the economics of cost of transport. What is different between an archipelago and the uniform plain is the following: on the uniform plain the less expensive transport method could be theoretically extended radially, so that eventually all locations could benefit from it. Should this occur, an undifferentiated network would again have been produced and crop 4'7 zonation would be purely a function of distance. In the archipelago, the 'frictionless' quality of water has already created an undifferentiated sea transport network. IHowever, discontiguity of the land surface has created the necessity of a bimodal transport system. iEven.if this bimodal system was composed of two undifferentiated networks, whose total costs for each.crop at any distance were simply additive, the effect of discontiguity would be different from the unimodal system of the uniform plain. Thus, the result is that in specific cases, the overall effect of distance is necessarily reversed in an archipelago and a higher rent crop could be grown.further away than a lower rent crop. This analysis has been based entirely upon the assumption that both crops have identical sea transport rates. The question must be asked: is this merely a hypothetical construct, or a situation that could possibly occur? To answer, it is not necessary to go into a lengthy discussion of transport rates for different crpos. Crops —a and -b may be interpreted as being the same type, but grown under two methods of unequal intensity: Crop-a would therefore produce higher yields and would have a higher rent per unit of land than crop—b, (assuming that inputs to supply are infinitely elastic). In this example then, the more intensive production method would be exclusively utilized on Island—3, while there would be a change to a less intensive method of production at a certain distance into the interior of Island-2. ISLAND 4 ISLAND 5 ISLAND I Figure 11. ISLAND 2 and Island Size Conditions for Ring Formation: Considerations of Isolation 49 New Conditions for RingFormation‘in_Archipelagos In addition to the three characteristics described by Dunn, there are four additional conditions that must be made explicit for the archipelago. These occur because of the new spatial features of island groups: areal differences in islands, shape and pattern, and because of the need for break-of-bulk points to exist (resulting from discontiguity). Discussing pattern first, it is obvious that trade must exist between islands within the archipelago if ring formation is to occur. The undifferentiated transport network and.nniform plain permit the further assumption that all land in the uniform plain would produce some type of surplus that would be transported to the Towun For archipelagos this assumption cannot be maintained. Isolation of an island within the group becomes a distinct possibility, This is shown in Figure 11, where Island-2 has no sea route connnecting it to Island-1. If export conditions exist between islands, crop zonation may or may not occur depending on the area of the outer islands involved. For example, Island-3 in Figure 11 is assumed to represent any small island. Because of lack of area the entire surface is utilized for production of crop-a. This areal consideration is readily apparent; what is less so is the combined role of area and discontiguity. A comparison between Islands —3 and -4 in Figure 11 makes this combined role clearer. Island-3 has been positioned at a distance where, if it were of sufficient size, there would be a change in zones from crop -a to -b. This is shown on Island-4, which is large enough for all production 50 Ax ISLAND 3 ISLAND 2 ISLAND 4 Port 2\ ISLAND 1 Figure 12. Conditions for Ring Formation: Consideration of Break of Bulk Points 51 zones to emerge. CkIIsland-3 zones do not occur because of the bimodal transport cost relationship between the two crops; crop—a can outbid crop-b everywhere on the island. 'With islands then, where perfect supply of transport is assumed to exist, crop zones may be less rigidly related to distance than they are on the uniform plain. In this case, discontiguity and lack of areal extent can create a situation where an island produces different crops than if distance over contiguous agricultural space were the reality. In addition to smallness in area, shape and position may play a factor in zonation. An island that has a linear shape may lack any ring formation. TEhis obvious concept is exemplified by Island-5 in Figure 11. This island has a sufficient size for ring development to occur but it does not, because of its shape. If the island were positioned differently, however, or the break-of-bulk point was on an end rather than in the center, zonation could occur because land transport costs for the higher rent crop could be reduced to where an outer zone crop was profitable, before all production was ended at the shore. An important consideration as to how ring formation will occur is the breakeof-bulk situation on the island. There are three possibilities that represent extremes. In Figure 12 it can be seen that on Island—2, with only one transfer point, the ring formation resembles that of the Port-island. It is a reflection of Islande1, with the highest rent crop located at the Pier, and the lowest rent crop produced at the furthest distance away. On Island-3, with several break-of-bulk points, quite a different ring formation has emerged. The high rent crop extends inland from f Shape 53 all four Piers because the greatly cheaper sea transport rate has enabled production to extend entirely around the island. The remainder of the land is occupied by crop-b; the second highest in rent potential. This crop has four indifference lines, along which producers of crop—b may choose one of two Piers to ship from. Finally, Island-4 has a shoreline that allows transfer of produce everywhere along the perimeter. In this case, a formation occurs that is the reverse of Island-2. Crop-a will extend entirely around the island, and crop-b will occupy the interior. Figure 13 shows this relationship between break-of-bulk and ring formation applied to three idealized island shapes; the triangle, rectangle and square. For each shape, variation—1 has one break-of— bulk Pier; variation-2 has several of them and variation-3 has a surface that permits transfer everywhere (a break-of-bulk line). It can be seen that the general effect is to distort the zonation pattern in accordance with the overall shape of the island. Figure 14 illustrates several of the previously mentioned points. The Port-Island has a systematic progression of crops —a, -b, and —c. Island-2 is sufficiently small and close—by so that only crop—a is produced. On Island-3, crop-a also occupies the area closest to the Pier, but more expensive land transport insures a quick take-over by crop—b. An expanse of sea water completely inhibits crop-c on Island —4. Only crop-d, which is not capable of producing sufficient rent to be grown anywhere on the Port-island, can bear the long sea transport costs from this distant island. 54 \ \ ISLAND 4 \\ \ \ \ \ \ Figure 14. Several Influences on Ring Formation 55 Summary The static analysis for the Isolated Archipelago has produced some similarities and some differences with the uniform plain model. Changing the location from a central Town to a Port on the coast decreased the ability of interior locations to produce high rent crops. Conversely, this location facilitated the ability of other islands to enter the economy, by the utilization of less expensive sea transport. Discontiguity in the land surface had several additional effects. Although sea transport permitted outer islands to grow crops for the Port, the effect of distance was to reduce the area on these islands that could produce rent. This, in turn, reduced the total supply of the crops that would be available to the Port. In the two-crop case, discontiguity between islands complicated the production pattern by making zonation dependent upon the relationship between distance and sea transport costs. Either crop -a or -b might be produced at the Pier on Island-2, depending on their respective sea transport costs. For a multiple crop system, the effect of discontiguity was to inhibit the production of inner zone products on outer islands because of conditions of perishability or high sea transport costs. This situation was quite similar to the uniform plain. The conditions under which zones would exist were seen to be more complicated in the Isolated Archipelago. Discontiguity created the condition that the marginal rent lines for crops cross over other islands, not above water. Secondly, if sea transport costs were the same, such as when one crop was grown under two methods of unequal intensity, outer islands could have the advantage over interior 56 locations on inner islands. 'This was because the more intensive method could take differential advantage of cheaper sea transport rates. It was also shown that isolation might prohibit any trade at all; that the size of an island could either inhibit or facilitate zonation, and that a linear shape could inhibit zonation even if the island contained sufficient area to permit it. Finally, breakeof—bulk points would tend to alter zonation by complicating the direction that a farmer would send his produce over laukt This factor was complicated by both the shape of the island and the number of break-of-bulk points. Attention will now be turned to the partial equilibrium analysis. This will show further modification of zonation patterns by the systematic relaxation of assumptions. Chapter 3: The Partial.Ehuilibrium.Analysis In the static analysis just completed, the economy was considered in full equilibrium. Here, that assumption will not be maintained. In this partial equilibrium analysis, selected modifications will be introduced to show the subsequent spatial changes in the agricultural production zones of the Isolated Archipelago. These modifications have become standard (Dunn, 1954; Hall, 1966; Found, 1971; Alonso, 1974), and include: change in demand and supply, differentiated transportation networks, additional markets, nonsperfect elasticities of supply factors and non-uniform soil fertility, The effect of relaxing the spatially uniform nature of any of these assumptions is to reduce overall concentricity on the land surface. In the Isolated Archipelago, where concentricity has already been precluded by water, this quality will be even further reduced on the surfaces of islands. Demand.and.Supply'InterrelationShips The factors producing change in.demand are well known and include the:number of consumers in the market, their income level, their tastes and the level of other prices (Mansfield, 1983). Additionally, each crop has a demand curve showing how much of it consumers will buy at various prices. ILowered prices mean.greater quantities sold and vice versa. This represents a shift along the demand curve. An increase in demand occurs when there is a rightward shift of the curve; more of the product is being demanded at the same price. .A decrease in demand shifts the curve to the left. iPrice elasticity of demand reflects the reality that there may not be a one-to—one 57 58 relationship between change in price and quantity sold. Typically, agricultural products have elasticities of less than one, indicating that as a product price falls, demand will increase, but by a lesser amount. The supply curve for agricultural products is upwardly (positively) sloping to the right. The higher the price for the good, the more is produced. Increases and decreases in the supply curve occur in the same directions as for the demand curve. In the static analysis just completed the demand.and supply for all products was in equilibrium: the amounts of crops demanded and supplied were equal. This assumption will.now be relaxed to show how production in an archipelago will change in response to a demand change. 'This will be done by varying the assumed prices for crops sold at the Port; they may be raised or lowered independently or simultaneously: Changing the demand price will change the rent at the Port, which in turn will create spatial changes felt throughout the agricultural zones in the archipelago. The second analysis will involve changes in supply, Here the sequence of activities is reversed. Change is first felt in the production zones; the result is either a raising or lowering of the rent value at the Port, reflecting a new level of demand. Analysis of‘Changes in.Demand Although there are several potential causes of change in demand, in this first analysis all demand for surplus agricultural products exists only at a point, the Port—city. From a spatial standpoint this makes the specification of the reasons for change unnecessary. For the 59 Fher FP Port Figure 15. Spatial Changes in Production Resulting from an Increase in Demand: the One Crop Case 60 purposes of analysis of the spatial effects on production in the archipelago, it will simply be assumed that demand has changed. ' Demand at a Point Location In a uniform plain that produces only one crop, if an increase in demand occurred, price would rise and farmers would respond by bringing land beyond the old equilibrium margin into production (Hall, 1966; Dunn, 1954). This will, in turn, raise the rent at the Port. In Figure 15, the demand has been hypothetically increased (from [A1]) to the point where the market price [B1] just allows all land on the Port-island to be cultivated (rent equals zero at the furthest point from the Port). On Islands -2 and -3, the cheaper sea transport previously had allowed some production on each island at the old price [A2, A3]. As demand rose, the new, higher prices enabled more land to come under cultivation [B2, B3]. On Island-2, all land was cultivated, and because the island is smaller than the Port-island, yet also reasonably close-by, the rent on land at the FP from the Pier remained above zero [C2]. This represents a condition of shortage, which in a perfectly competitive economy will induce a further price rise for the crop [D1]. In response, farmers would intensify their production methods and/ or bring land into production beyond the new margin on Island-3. All land on Island-3 is eventually brought into production [D3], but there still remains a small amount of positive rent. Because no land is left anywhere in the archipelago, this rent would cause a further rise in price along the demand curve, rather than a rightward shift in it. The spatial solution would now of necessity be further increases in intensity. The equilibrium point 61 for the Isolated Archipelago would finally be reached when increases in intensity equalled the aggregate income levels available for the purchase of the crop. Peet (1969) has shown.that when such conditions exist as: (1) an increase in demand; (2) rising levels of production intensity on inner zone land; and.(3) vacant land at the margin of production, the economic climate may be right for the development of transport innovations. These would effectively allow production across discontiguous areas, such as water bodies, and would lessen transportation costs upon land. In an archipelago context (a micro- model in comparison with Peet's study of the expansion of the nineteenth century London wheat market) a sea transport innovation would enable crop production to expand to islands further away. Referring back to Figure 15, production would now be possible on,a hypothetical fourth island, formerly beyond the spatial margins of profitability. On the other hand, if the demand rose but no sea transport innovations were introduced, eventually all the land would be put into production on islands currently involved in the economy, (This was shown in Figure 15, when the rent surface expanded from A1 to B1.) 'When this occurred there would be a round of increases in.intensity as farmers attempted to maximize profits. These new price levels could induce transport innovations, permitting production to occur on islands previously not within the archipelago economy: By breaking up the land surface into islands, therefore, discontiguity may necessitate that a transport innovation occur before the factor of distance can be overcome and the natural expansion of zones can take 62 Original Equilibrium Price for Crop b Rises Spatial Adjustments: the New Equilibrium Figure 16. Spatial Changes in Production Resulting from an Increase in Demand: a Three Crop Situation on the Port—Island 63 place. In,a three-crop scenario, a complication arises if it is assumed that an.increase in demand for one of the crops causes a shortage of the other two. Initially, a price rise for a crop, say crop-b, would change the marginal rent for the farmer. This becomes especially critical near the inner and outer spatial margins of production, where a choice must be made between crop—b and either crops -a or -c. Farmers located near these margins, who had been producing the other crops, would.now find it more profitable to grow crop-b. Therefore, the first result of a rise in demand for one of the crops is that both the inner and outer margins of its production will change (Dunn, 1954). As this spatial change has produced a shortage of land for production of crops -b and -c, a second result would be a new round of price changes and spatial adjustments until equilibrium is again reached. This is shown for the Port—island in Figure 16. Because the increase in rent for crop—b will raise the rent for crop—c to a positive amount at the FP of the Port-island, a further equilibrium shift and increase in intensity would occur, producing spatial changes similar to that discussed in the one crop case. ‘When.additional islands are included in the multi—crop production surface, a demand increase may bring a new zonal variation. In the one crop case the increase in demand produced a positive rent value at the furthest point on Island~2 (refer to Fig. 15). 'When more than one crop is included in the system, but the demand increase is different for each crop, there would be a possibility that, because of the limited production area, one crop might completely outbid others on 64 New Equilibrium)» . Rise in Price of Crop b . Old Equilibrium p Figure 17. Spatial Changes in Production Resulting from an Increase in Demand: a Three Crop, Three Island Situation 65 that island. For those islands close to the Port this crop would more likely be an inner zone variety because farmers could take advantage of changes in intensity and their proximity to the high rent values at the Port. On islands further away outer zone products would more likely emerge because of differential transport advantages. Whenever a crop shortage caused by differential rises in demand occurred, the shifting of prices that followed could produce several fluctuations in type of crop production as farmers attempted to maximize their returns. An example of this process is shown for a three-crop scenario in Figure 17. Here, the rent value of crop—b is assumed to increase dramatically to the same amount as crop-a; this eliminates all production of crop—c in Island-2. Then shortage causes price readjustments to occur and crop-c is able to reestablish itself on Island-2. In the terminology of economics, when supply and demand changes go through several cycles, the graphical result is known as a "cobweb." In an archipelago numbering several islands, with a random pattern, this graphical feature could resemble "spatial cobwebbing" as the zone of production for a crop jumped from island to island. Demand at Q Areal location The assumption that all demand originates at a point has been modified by several researchers (Chisholm, 1962; Peet, 1969; Lozano, 1968; Belding, 1981; Muller, 1973). Kellerman (1977), for example, altered the Thunen model to fit actual conditions prevailing in the U.S.A. - a country with large urban areas where produce is bought from nation—wide supply regions. He developed a macro-model which 66 identified three sizes of markets: local, metropolitan and megalopolitan. Using an "index of net income/ acre" as a surrogate for land rent, his regression analysis showed that the megalopolitan market continued to account for most of the variance in the data. It therefore could continue to be seen as the most important market. Chisholm (1962) has considered the relationship between demand as a point versus an areal location in a more general sense. He noted that conurbations such as London or Tokyo are too large to be considered "mere points (unless) a sufficiently sizeable section of the world, or the whole globe, is taken into account. Even the largest conurbations then dwindle into insignificant little blobs." In an archipelago, under what situations could demand be considered to exist at an areal, rather than a point location, as has been assumed so far? It would seem to be the case that for the majority of archipelagos, the assumption of a point location is more accurate than for a continuous land-mass model. Although many islands are quite extensive, they 'dwindle' when compared to the immensity of the surrounding ocean. For example, the South Pacific archipelago nation of Vanuatu forms a narrow 'Y' in shape, from north to south. This 'broken line' of islands extends roughly 850 km in length. If 425 km is then assumed to be a radius, the area of the 'circular state' would be 567,450 Square kilometers. The actual land area of the archipelago is 12,280 square kilometers (Quantin, 1972). Thus, the land surface of Vanuatu composes just over two percent of the area of a circular Isolated State having the same length. It can be seen that discontiguity due to water plays a major role in limiting the space where agriculture could exist. Farms, at this point in time, 67 can only exist on land, so they too may only be located at a relatively small number of places, with respect to the entire 'circular state.‘ For archipelagos then, it could be considered more appropriate to conclude that supply also comes from point locations; the islands are merely dots on the ocean surface. This landform thus represents the opposite of the Isolated State for this feature of the model. There is a further possibility - that each island is a center of demand. This is considered in the section on Multiple Markets. Analysis of Change in Supply Supply variations come about because of two widely recognized reasons; change in technology or change in input prices (Mansfield, 1983). The result from either cause would be a complicated sequence of areal changes in the surface of production. Dunn (1954) noted that a change in production technology could produce a supply increase by either raising yield per unit of land, or decreasing the cost of production per unit of land. The effect of these changes would be to increase the rent-earning capability of land, graphically shifting the rent line for a crop upward and parallel to its old line (this would look identical to an increase in demand). In reality, the amount of shift of the rent line would depend upon the relative elasticities of demand for all crops. Since farm products do historically have low elasticities (Dunn, 1954), there could be some expansion of zones when supply was increased, but not necessarily very much. Generally, the effect on production when there is a change in conditions of supply is different for different crops. An innovation that required many inputs, for example, would Port ISLAND 1 ISLAND 2 ISLAND 3 Figure 18. Spatial Changes in Production Resulting from a Yield Increasing Innovation 69 tend to favor intensively produced, inner zone crops over those in the relatively extensively used outer zones. This type of innovation could potentially contract production zones (Dunn, 1954). For the archipelago model, the extent to‘which.a.yieldeincreasing innovation alters the produbtion surface is dependent upon the discontiguous distance between islands and area of production.on them, as well as the degrees of demand elasticities for the crops involved. The situation is similar to that for increased.demand; an increase in rent-earning capability (from greater yields per unit of land) will enable a crop to extend its outer margin further from the Port or Pier. IEventually, an inner zone crop may displace lower rent crops completely off the island, if demand increases correspondingly; Crops less able to take advantage of a.yield-increasing innovation therefore, would have the best chance of maintaining their status on larger islands. (If the innovation favors an outer zone crop, the reverse sequence of spatial adjustments would take placeJ This unequal.ability to take advantage of an innovation is shown in Figure 18, where crops -a, 4b and —c have increasingly smaller yield improvements (corresponding rent increases are labelled a}, E” and c' in the figure). In Figure 18, crop—a now dominates on the Port-island, while areas planted in crops -b and—c have been considerably reduced. On Island -2, a small, nearby island, crop—c is outbid completely. This case demonstrates that because of areal limitations, a change in technology that improves yield has even more pronounced.results in the Isolated Archipelago than on the uniform plain. ZHowever, if Island—2 were larger, crop—c could regain its outer position.(as shown.by the dashed line). On Island-3, distance decay from high transport costs 70 has eliminated the potential for production of crop—a. Crops -b and —c, however, assume their normal zonal positions. Here they may utilize more of the land on Island-3 because the yield-increasing innovation has increased rent for all crops. This improvement, by reducing the supply of crop -c (on the islands as they are shown in Figure 18) would set the stage for innovations in land and sea transport, so that the land available beyond currently profitable margins, such as the wilderness area on Islandr3, could go into production. 'When a yield increase raises the supply of a crop but the demand for it does not change (100% inelastic), the initial result is an oversupply; A sequence of spatial change in production then occurs. At first the rent for each unit of land will increase because of the new ability to raise production. IHowever, because no increase in quantity is desired at the Port, the price will then fall for the crop; this will reduce the rent on each land unit until a new equilibrium is reached. Spatially, the result will be a shrinking of each zone because the area of land required to produce the amount demanded has decreased. In the Isolated Archipelago model, there is no real difference from what occurs on.the uniform plain. As the rent from the crop first rises because of the yield increase, then falls due to oversupply, the extent of the zone of production on the outer islands will expand then contract in tune with spatial conditions on the Port- island. This is because neither type of transport cost is directly affected by the change. However, the yield increasing innovation could, in turn, produce 71 — Pie-innovation Production Zone Area Now Producing Twice the Old Yield Figure 19. Spatial Changes in Production Resulting from a Yield Increasing Innovation Occurring Under Conditions of Constant Demand 72 a transport innovation. This could reduce costs for shipping the crop by either land, sea, or both. If land transport costs were reduced by the same rate on all islands, the effect would allow land in the interiors of all islands to compete with the land nearer to the Port and Piers. Zones would expand proportionately on all islands, then recontract due to further price reductions at the Port. If only water transport costs were reduced, the zones on all outer islands would expand, but they would shrink on the Port-island because the rent of land there had not changed while it had increased on outer islands. If both types of transport had cost-reducing innovations, the change in zones would be determined by the relative reduction for each. This is depicted in Figure 19 for a one product example. Further Modifications In the second part of the partial equilibrium analysis, several of the assumptions utilized thus far will be relaxed. The categories of assumptions dealt with will be the following: transport, number of markets, non-perfect supply factors and non-uniform soil fertility. Modification 9: Transport Assumptions The modification of transport was partly considered in terms of innovations in the previous section and in Chapter Two. A further modification involves relaxing the assumption that the land and sea networks are undifferentiated. In general, the effect of this relaxation in the uniform plain has been to expand zones of production in those areas capable of taking advantage of the innovation (Beckmann, 1968; Found, 1971 ; Peet, 1969; Dunn, 1954; Hall, 1966; Horvath, 1968; Griffin, 1973; Singh and Singh, 1978), while inhibiting 73 expansion elsewhere (Griffin, 1973; Horvath, 1968; Couper, 1967). On land, the innovation could be the result of inclusion of cheaper water transport, as in Thunen's modifications, or the improvement of either the transport surface or the type of vehicle utilized. Water Transport Innovations and Discontiguity For the Isolated Archipelago the most influential transport improvements would be in sea shipping. These might include increased fuel efficiency, speed of transport or cargo capacity. Each of these innovations would bring differential advantages for different crops. Graphically, this overall change in transport rates has been shown by a lessening of the negative slope of the rent lines (Dunn, 1954). The market place value does not change, but as rates are reduced, the costs for shipping any crop to the Port will decrease. The result will be to expand the potential distance to the margin of production. A water transport improvement, such as the utilization of a more fuel efficient ship, will bring a decline in rates that will benefit all crops. These benefits will accrue differentially over space. Production of inner zone crops will again tend to dominate on islands near the Port, and their new ability to produce rent on land further away will push the lower rent crops toward the back side of outer islands. Perishable products will only be grown on islands some distance away when there is improvement in the speed of transportation. Reducing a three-day journey to two days, for example, may change the production surface of an island completely, as farmers switch to crops 74 with a higher market value. Bulky inner zone products would be able to take advantage of both these innovations. Decreased fuel costs would be especially beneficial in extending the production to outer islands. To the extent that an improvement in transport time would be achieved by a smaller, faster ship plying the waters, bulky products may benefit less. If a boat of identical size, but with a more powerful engine were brought into service, then bulky and perishable crops might benefit equally. --- Old Marginal Rent Line for Sea Transport —— New Line, after Introduction of Innovation L___J Amount of Expansion of Rent- producing Distance Crop a Crop c Figure 20. Increases in Potential Range of Crop Production Resulting from a Sea Transport Innovation Outer zone crops would benefit more by a decrease in fuel costs or increased cargo capacity than by an improvement in speed. They have less steep marginal rent slopes than inner zone products, which reflects a smaller rate of decline in their transport costs. This 75 means that proportionately equal reductions in unit costs for shipping 'will translate into a larger extention of the zone of production for outer zone products. Figure 20 shows this relationship between water tnansport inprovements and distance for crops of inner and outer zones (crops —a and —c, respectively). In each case transport rates are assumed to fall by one-third. It can be seen that the increase in distance of potential production has increased much more for crop -c. Crop-a 'would.now have a production advantage on inner islands; crop-c on those that are more distant. water Transport Innovations and Area, Pattern and Innovation Considerations of area.and.pattern will modify the effects of a transport innovation in accordance with the local conditions. For example, in the graphs and diagrams drawn.so far, the limitation of production on the surface of large islands has often occurred because of the increasing costs of land transport from the farm to the Pier. A second cause could be insufficient sea cargo capacity. Increasing the amount that could be transferred.from Pier to Port would of course produce the greatest spatial production change on larger islands, as land could profitably be exploited further into the interior. On smaller islands the result would be an increase in intensity. In the perfect competition model, an innovation may cause change or result from it. Peet (1969, 1970/71) showed.that both had occurred in the case of transport. 'Where conditions of rising demand existed at the northern European market, there was also the demand for improvement of transport in the hinterland, the American frontier. ID1 '76 ISLAND 4 I “ ‘ O I I I ISLAND 3 I ISLAND 2 : I l l l l I l I I I ,,’ I ”’ ’ ISLAND 5 I ’I””’ ISLAND 1 Figure 21. Zonal Effects Resulting from Two Island Patterns: Clustered and Isolated 7’7 the nineteenth century, this demand-supply disequilibrium resulted in considerably lowered sea transport rates and also the development of the American railroad network. According to Peet (1969, 1970/71) the need for agricultural products created conditions that produced the transport innovations. These then enabled greater expansion of the zones of production in America. In an archipelago, variations in pattern may also either cause one of the above innovations in transport, or the innovation may introduce spatial changes on the islands. For example, several small islands clustered together may be able to attain a sufficient areal extent to have the same effect on transport rates as a large island. That is, the area under production may make increased cargo capacity economical, which would reduce rates and permit crops from inner zones to be grown. In this case there may be multiple sea transport costs - a short haul cost for transport on a smaller ship between islands in the cluster; then a long haul cost to transport the crop on the larger ship traveling to the Port. This example of a clustered pattern is shown in Figure 21. It is contrasted with Island-5, which is forced to grow only crop-c because its isolation does not permit the necessary scale economies to occur. A linear pattern of islands may also benefit from an increased cargo capacity. In this case, the potential for making a series of stops on outer islands may provide the necessary demand for increase in shipping capacity. When a large boat (or competition between shipping companies) becomes available, rates could fall. A hypothetical example is given in Figure 22. 78 0 Piers \\ \\ Trade Route $535 % Production Zones ”PO" 1 Figure 22. Zonal Effects Resulting from a Linear Pattern of Islands Couper (1968) looked at trade in three South Pacific archipelagos: Fiji, Tonga, and the Gilbert and Ellice Islands (now Kiribati). This work can be reinterpreted as an analysis of how pattern affects transport cost and trade. In Fiji.(Figure 23), the two main islands of Viti Levu and Vanua Levu form two points of a triangle. The third point does not exist per se, but is composed of the hundreds of small atolls that together compose the Lau Group. The capital city, Suva, has attained primate city status, which made it equivalent to the Town in the Isolated State. Couper argued that the fragmented pattern of the Lau Group kept transport costs high and prevented the development of much of the trading potential between this group and Suva. This fragmentation represents the opposite case from the hypothetical example of 79 \ \\ Vanua Levu J é OUTER 0.0 ZONE copn\A\ a 0 OJ \9\\\ 4° .\ a b \ :o" \ ’°o \ . . \\Cb MIDDLE \ ° Suva ZONE COPRA \ ' o yaqona Q \ INNER zone COPRA ° \\ fresh produce\ \ 0‘ o yaqona \\ 4’13 \ \L ° Figure 23. Zonal Patterns of Crop Production in Fiji (adapted from Couper, 1969) clustering, where trade was permitted to develop to a greater extent than would have been the case if the four islands were more separated. Couper found that three rings of production existed in Fiji; the crops produced in each were (from inner to outer): (1) vegetables, yaqona (a narcotic powder made from tree roots) and copra; (2) yaqona and copra; and (3) copra. The Lau Group was only able to engage in the copra trade. He proposed that for a broader range of crops to be produced there would have to be a 'rationalization' of location of new sea ports in the Lau Group. This would establish a link between designated centrally located ports within the Lau islands, and with Suva. Islanders could then transport their vegetables and yaqona to a 80 larger, more efficient cheaper boat, offering economies of scale in shipping and thus enabling them to take advantage of demand.in the capital. The 'fragmented! pattern.vnmihi thus become 'clusteredJ In Tonga, Couper again found trading was affected by island pattern. Tonga essentially consists of three distinct archipelagos that are arranged linearly in the Pacific Ocean (Figure 24). These are: (1) Tongatapu Group in the south, where the capital — Nuku' alofa, is located; (2) three smaller atoll groups clustered together in the middle; and (3) the Vava'u group in the north. In the Tongatapu and vayaiu Groups vegetables, bananas and copra are brought to market. In the central atolls only banana and copra trade ‘was possible. As in Fiji, this was again due to inaccessibility. Islands not falling within these three groups could only trade in copra. .A major difference between Tonga and.Fiji was that no Tongan city was large enough to play the equivalent role of Suva, and the pattern consisted of three clusters of islands separated by a sufficiently great distance to preclude inter-cluster trading. Finally, in the Gilbert and Ellice Islands (Figure 25), smallness of island.size and.extreme distances (sometimes over 800 miles) prevented ring development around the main city, Tarawa. Copra trade, however, did.extend.to the furthest islands, making this an example of a single crop production surface. Non-linear Rates A final way that water transport change may affect production is through a nonrlinear rate structure. Dunn (1954) has noted that transport rates most commonly are zonal. This type of rate tends to 81 runes bananas ve - etables bananas Tongatapu Figure 24. Crop Zonation in Tonga (from Couper, 1969) 82 ”. ‘ nfiIes _ __ ____-2000 ‘2' tons 888 iii-Funafuti Figure 25. The Copra Export Zone in the Gilbert and Ellice Islands (from Couper, 1969) 83 decline by smaller amounts over longer distances, thus giving the advantage to outer zone crops. Zoning may also occur because of clustering or linearity'(iea, pattern). Islands that are sufficiently close to each other to achieve economies of scale in transport may benefit from lowered rates, while smaller or more isolated islands may have higher rates than their linear distance from the Port would indicate. Effects of a Land Transport Modification in.an Archipelago On an island, a land transport improvement will mimic the effects on production discussed in the conventional Thunen model. However, there will be an additional modification because of the areal limitations characteristic of islands. Improvements that benefit.all crops equally in terms of lowered rates or that help higher rent crops more (such as providing greater accessibility) will tend to push the lower rent crops further into the interior, or off the island entirely. On the other hand, the improvements (such as greater cargo capacity) that provide most benefits to lower rent crops will reduce the outer margins of production for the higher rent crops. Thus, the only difference between the archipelago case and the uniform plain is that because of limited area for production, the lower rent crops may be pushed back sufficiently to cause a shortage. Multiplelflarkets The result of the introduction of a second town in the uniform plain is that rings of the higher rent crops form around the new Town, more-or-less in areal proportion to its size. Production of outer zone crops is less modified - the land use at a location may not 84 ISLAND 3 ISLAND 1 ISLAND 2 ISLAND 4 Figure 26. Zonation in a Multiple Market Archipelago - Four Possibilities 85 change although the destination of the products could be the new Town. In the archipelago, this modification is more complicated due to factors of discontiguity and area. Figure 26 shows an archipelago consisting of four islands where the rent and transport costs for Islands -2 and -3 are assumed to be equal because both islands are the same distance from the Ports To show the multiple market situation, let the Piers become Ports. .Assuming an initial population of zero, let these new Ports grow so that the population-area ratio of each is proportional to the population—area ratio of the Port-island. Comparisons of the effect of this population.growth will now be made separately for Islands -2, -3 and -4. (Assume three distinct two- island archipelagosJ On Island-2, it is assumed that the demand for land from Port-1 has already exhausted the entire supply, and there exists some positive rent for crop-c at the furthest point. Obviously, if a second Port were to develop, intensity of production would.immediately begin to increase on both islands. Cheater demand and intensity would simultaneously raise the rent lines for all crops (Katzman, 1974). After all spatial adjustments had occurred, the final boundaries for crop zones would be determined by the production functions and the ratio between land and sea transport costs for each crop. Intensity on Island-2 would be less than on Island-1 because the price for crops at Port-2 would always be lower than at Port-1. Port-2 will remain smaller because of its smaller hinterland, therefore excess demand will originate from Port-1 and there will continue to be the need to pay sea transport costs to send the produce to Island-1 (Visser, 1982). 86 Assume now that Port development began to occur on Island-3, a large island located the same distance from Port-1 as was Island-2. In this two-island case just the opposite production situation would result. On Island-3 assume there is excess area for crop production. 'When only Port-1 exerted demands, some production occured on Island-3. Then, as the Pier begins to develop into a smaller Port, the demand made by the new residents will increase overall demand for the archipelago. This will raise the price, and by extention the land rent, at both ports. 'What is likely to happen? On Island-3, with a land surplus, it can be assumed that expansion will occur into the hinterland, because of the assumption of perfectly elastic supply factors. On Island-1, where no additional land exists, intensity will have to be increased to raise yields to meet the new level of demand. This will occur because the benefits of lower sea transport rates that had been accruing to Port-1 would now be negated by the price rises caused by the new local consumption. That is, cost at Port—3 plus sea transport cost would help raise the price at Port-1. The new equilibrium rent level would be where the changes in.intensity on Island-1 created rent equal to what was obtained on Island-3 after the new demand and sea costs were accounted.for. IExports from Island-3 to Port-1 would not decline in quantity; they would simply cost more because of the new demand exerted at Port-3. As the new Port grows in size, sufficient land will still exist to satisfy all demand. Because of its availability, land at the margin will continue to be brought into production, while land in the inner zones will be used more intensively; JMore precisely, the distances inland where the same level of intensity exists on the 87 islands will be different because of the different values of transport costs. When it is further assumed that the population of each island could rise to a level in proportion to surrounding area of supply, then Port-3 will eventually become larger than Port-1. ‘As this occurred, sea trade would fall to zero (or flow in.both directions), then reverse direction as the demand price for crops at Port-2 became greatest. A third relationship is represented by the arrangement between Islands -1 and -4 in Figure 26. Here, ocean distance is initially assumed to be sufficiently great so that no crop can profitably be grown.on.Island—4 for export to Islande1. Then local demand is assumed to exist as population increase has turned Pier-4 into a new Port. 'Will trade occur between the two islands? The initial answer is no, because the combined production costs on Island-4 and sea transport costs to Island-1 are sufficient to reduce to zero rent for all produce grown.for export at the new Port. Fbr distances further inland on Island-4, land transport costs also must be added; this results in a negative rent value. Since demand exists at Port-4.(Figure 27b), production will occur, but only for local consumption. Trade will not begin to occur until Port—4 attains the same population as Port~1 because of excessive transport costs. Farmers located at either market (ie., at zero distance) will then be indifferent as to whether they produce crop—a for consumption by Port-1 or by Port-4.(Figure 27a). Farmers located at any distance inland must always produce for the port on their own island, because the combined transport costs required for 88 A. a b C Port 1' Port 4 B. ‘\ \»a \ \ ‘ \ ‘ \ ~ ‘ b — ~ \ ‘ ‘ . -— ~ ~ . V ‘ ‘ - \ ‘ c— — — ~ - - — vAvAVA'AvAvAVA'AVAV:AVAVXVAVA'AVAVA'A'AVAVAVA'sz‘vAvAvfirAvAv‘vAv; ' 1‘ Port 1 Port 4 Figure 27. Hypothetical Sets of Transport Costs from Port-4 to Port-1 export would reduce rent to a negative value. In this scenario, then, discontiguity has prevented a combining of the levels of the demand for the two Ports and thus inhibits trade. This is the opposite result from what occurred as Ports -2 and -3 developed. Noneperfect Elasticities ngSEpply Factors Throughout this thesis it has been assumed that supply of all factors except land have been 100% elastic. ‘Whenever or wherever an input was needed, it was considered instantly available. As the literature on the Thunen model has developed, this assumption has been 89 changed. Supply has been broken down.into factors of capital, labor or land. Each of these, in turn, has been given an elasticity coefficient to determine how much the factor will increase per unit change in demand. This removal of the assumption of an infinite supply of any of the factors, and the corresponding assumption of constant returns to scale (unitary elasticities), would represent a step towards realism in the Isolated Archipelago model. For example, labor could be assumed to be available in one location but not another, necessitating further transport costs for its import to the farm. This is even more likely to be the case for capital inputs; these could be assumed to exist at the Port or Ports, and would require additional transport costs for shipment to outer islands and/or farms located in the interior. The optimal rate of intensity for production of a cropiat a location on an island would be found by calculating the substitution ratios for land, labor and capital, and the set of transport costs required for importing supply factors and exporting the crops. Finding this optimal intensity lies beyond the scope of this thesis. It is obvious, however, that relaxing an assumption such as infinite availability of supply factors would lower the theoretically optimal level of intensity, while relaxing an assumption of constant returns to scale could either increase or decrease intensity at any location. Breaking up the uniform plain into an archipelago will complicate this problem even further by requiring calculations for a bimodal transport system. 9O Uniform.Fertility 'When the assumption of uniform fertility is abandoned, land will become less, equally or more fertile. On islands, such features as lagoons or mountains commonly reduce the area of productive land to coastal strips or even less. The result in an Isolated Archipelago would reflect even more the limitations discussed already with.respect to area. ‘When mountains are high or steep the rent surface on that land is reduced to zero. If some production is possible there perhaps may be some rent earned on the land, provided land transport to the Pier or Port is available. Lack of production area has the effects of either limiting the size of the demand-population or increasing the intensity of production. In the general case it is impossible to say which will occur. If land is more fertile, however, distance may be overcome by increased yields. Summany The above analysis has shown that a change in either demand or supply that increases the rent per unit of land will tend to bring more land into production, at least initially. This expansion reveals the importance of the limited area available for cultivation in an archipelago setting. The crop for which the increase in rent is occurring may outbid all other crops for land on an island if demand rises. If demand does not rise, the zone of production will shrink if the change in rent has originated because of a supply-increasing innovation. 'When rent increases for only one crop in a multi-crop system this could cause several shifts in the spatial equilibrium of crop production. This may be called "spatial cobwebbing," if the 91 production zones change from island to island. The water distance between islands may be sufficient to require a water transport innovation to bring the outer island into the economy if it is too far away from the Port to benefit from an increased rent value. Finally, on archipelagos, the proper perspective is perhaps to view both demand and supply as originating from 'point' locations. In this way, the Isolated Archipelago represents the opposite condition from case studies that have analyzed the model from the 'macro' perspective. In the section dealing with the alteration of the assumptions of the undifferentiated transport network it was noted that for a general improvement in transport, such as increased fuel efficiency, zones ‘would expand in a manner similar to the uniform plain. Considerations of area.and discontiguity, however, showed that there would more than likely be differential expansion. Inner zone products, especially bulky crops, would gain further advantage on inner islands, while outer zone crops would be able to dominate more on islands further away; An increase in speed of transport would help perishable products gain a rent advantage on islands previously beyond the spatial margins of profitability; Increases in cargo capacity would help outer zone crops most. This innovation would also permit islands located in clustered or linear patterns to take advantage of economies of scale. Interpretation of Couper's study showed that discontiguity and pattern played major roles in defining the economy; In Fiji, fragmentation of islands had prevented the development of a regional port, which in turn had prevented production of inner zone crops even though demand existed. In Tonga, three distinct clusters of islands had established within-group zones, but only copra was grown 92 throughout the nation. In the Gilbert and Ellice Islands a linear arrangement permitted copra trade, though smallness of’area may have prevented an urban center from creating demand. Finally, a non-linear (zonal) system of transport rates gave an advantage to outer zone crops, as the cost per unit distance declined. 'When the assumption.of'a single market was relaxed, it was seen that if lack of area was a consideration, intensity of production would increase. If excess area existed, expansion of the hinterland of the second market could occur. If enough land existed and the population of the second Port became greater than that of Port-1, trading patterns could reverse. Finally, if discontiguity was so great that two islands had no trade potential, population at a growing second port would have to increase until the size Port-1 was attained before trade would develop. Generally, noneperfect inputs of supply or a nonpuniform plain could be said to inhibit the formation of concentric zones. ‘Whenever the supply of any input, landllabor or capital, is not perfect, the cost for it rises, the optimal intensity may decline, and the land rent will be decreased. Chapter Four Towards Testing the Isolated Archipelago Model The intent of the previous two chapters has been to examine how the familiar Thunen model might be altered when the uniform plain was modified into an archipelago. Specifically, the effects of discontiguity, finite area, island pattern and shape were focused upon. Because these features have many forms in existing archipelagos, the analysis was made as idealized as possible. The intent of this final chapter will be to explore how the zonal forms that emerged from the preceding analysis might be found in existing archipelagos. This will involve formulating a set of sub—hypotheses regarding the effects on zonation of discontiguity, limited area, pattern and shape. Then, potential methods of testing the hypotheses will be discussed. An initial comparison will be made between the findings of this thesis and the conditions of zonal development in South Pacific archipelagos discussed by Brookfield (1969). Finally, some suggestions for further research will be made. Testing the Archipelago Model The intention to do a case study first requires selection of a study area. For archipelagos, this region may or may not be readily apparent. Many archipelagos are distinctly set apart in the ocean and the political boundaries of the state correspond exactly with the physical areas of the islands. However, many island nations are composed of several groups of archipelagos. This makes research at other than the national scale possible. Thus, a choice must be made regarding the scale of the study. 93 94 Once the archipelago boundaries have been chosen, the task becomes one of comparing the assumptions of the model with.existing conditions. As noted in the Introduction, these assumptions could be placed into five categories: spatial, physical, transport, economic and behavioral. This comparison will indicate the appropriateness of the study site for testing and also what data and testing procedures are best suited for the analysis. The hypothesis of the Thunen model — that agricultural zonation occurs as distance from the market increases, may be refined a prigri when particular assumptions are not met in the study area. For archipelagos, it is especially important to consider the spatial assumptions. Several questions must be answered, such as: 'What are the local conditions of discontiguity, pattern, island area and shape? Is there one dominant Port, or do several competing ports of similar size exist? Does it appear that more than one of the spatial features could be exerting a combined influence on location of production? When these questions are answered in fine detail, it will be possible to construct hypotheses regarding the expected zonation in the study area. In terms of this thesis it was shown that zonation in models of archipelagos is affected by the four spatial properties. It is logical to hypothesize that this will also be the case for existing archipelagos. Therefore, the overall hypothesis for location of agricultural production in archipelagos is that zonation will be affected by the properties of discontiguity, limited area, pattern and shape, as well as by distance. Because of the uniqueness of archipelagos, going further in constructing definite subhypotheses is 95 inappropriate until a case study area has been chosen. However, a general set of subhypotheses may be offered, based on the idealized results obtained in Chapters Two and Three. (1) Discontiguity between islands will tend to cause discrete drops in the rent surface. (2) Islands with greater areal extent will tend to show zonal patterns, while smaller islands will tend to be more specialized. (3) A clustered pattern will tend to show zonation that transcends each.island by itself. .As islands become more randomly dispersed, zonation tendencies will diminish. (4) Shape will have a unique effect on zonation only when an island is very narrow; These four sub-hypotheses may serve as guidelines for developing more location-specific hypotheses for the case study area. In order to test for the effects of the spatial features on zonation, knowledge of the state of the economy, transport system, human motives and physical conditions in the archipelago must also be known. In the original Thunen model, a relatively uncomplicated agricultural economy created zonation of distinct crop types and intensities of production. This distinctiveness is often blurred today because the agricultural economy has developed. Nevertheless, when studying a location, a choice between which of the 'theories' to concentrate on is generally made by the researcher; ‘When crop type is picked as most appropriate, distinct zones of production are searched for. This calls for use of air photos or data on location of production of different crops. Crop type studies are generally confined to less developed agricultural regions, where relatively 96 simple conditions prevail (Chisholm, 1962; Couper, 1966; Horvath, 1969; Mitchell, 1971; Griffin, 1973; Oyeleye, 1973). If intensity of production is chosen, an economic analysis is conducted. Rent, the monetary surplus accruing from production on a unit of land, is the important variable. This is often a very difficult variable for which to gather sufficient data, as data values for the remaining parameters of the rent equation must also be found (Muller, 1973). Therefore, surrogates for rent have been utilized, such as net income per unit area (Muller, 1973, Kellerman, 1977), or linear programming maximization routines used with agricultural production data (Jones, 1976). If a surrogate measure is used, this data gathering process may be circumvented. In this type of analysis, finding discrete zones of production is less important than finding that the overall value of land declines with increasing distance. Knowledge of the transport system, especially over water, is crucial for the study of archipelagos. Having good data on the locations where ships obtain the production will enable the researcher to map the break-of-bulk points for the archipelago. Knowledge of the destination of the products permits the demand component to be mapped. These two features together will establish the location of the agricultural production system. When this is known, the influence of the spatial features present in the archipelago may be examined more carefully. The relationship between demand and supply has both a spatial and a temporal component. Combined, these will define the amount of discontiguity existing between two locations. When this is known for the set of relevant 97 locations in the archipelago being considered, hypotheses about the expected effects of discontiguity may be formulated. This knowledge of the demand and supply interrelationship also permits the influence of pattern to be examined for the study area. As noted, the pattern in an archipelago may consist of anything from several isolated islands having contact with a Port, but not with each other; to clustered islands where the effects of the intervening sea surface could be reduced. Knowing the routes and availability (temporal accessibility) of transport services will again permit hypotheses to be constructed around the effects of the pattern on production in the archipelago. Third, the location of the break-of-bulk points permits conjecture about the effects of area on production. Specifically, the subhypotheses that larger area promotes zonation may be developed. A larger area will.necessitate a larger perimeter. This will tend to increase the number of breakpof—bulk points, located along the coast of the island. Zones would then tend to radiate inward from these break—of-bulk locations. 'When level of demand and physical conditions permit, these zones will overlap» The tendency will thus be for more outer zone products to be produced in the interior of the island. This same phenomenon will occur with regard to island shape. Zones will emanate from the break—of-bulk location or a secondary port into the interior, unless the island is so linear that this is impossible. The physical assumptions of the model, uniform soil fertility and level topography, must be known in order to exclude areas either too 98 poor in soil quality or too rugged from the potential land areas where zonation is possible. These variables have the same function in both the archipelago and uniform plain contexts. Finally, a reasonable level of rationality should be demonstrated for the archipelago under study; This variable also plays the same role as in the uniform plain context. 'When the background data on the assumptions of the model have been collected and interpreted to provide the set of hypotheses relevant to the study area, a testing of the predictive ability of the model becomes possible. ‘As originally conceived, the major objective of this thesis was to test archipelagos in the South Pacific. Brookfield.(1969) has done research in this area. His work will now be examined for the purpose of providing an initial comparison between those archipelagos and the Isolated Archipelago model. Brookfieldfls Analysis of Agricultural Zones in the South.Pacific In addition to the work by Couper (1966) that has already been examined, Brookfield.(1969) has analyzed the existing conditions in several South Pacific archipelagos1 from a Thunenian perspective. This analysis showed.that in some instances obvious zonal patterns had occurred, though they were very incompletely developed over the island-scapes. These zones had emerged to provide the Port markets with agricultural goods. The characteristics of each zone is summarized below. The inner ring grew specialty crops for the European and Chinese residents of the Ports. These crops were "risky fresh vegetables" (p. 146) that were perishable but sold for a good profit. Generally, the shape of this ring was "distorted" and varied in size depending on 99 the corresponding size of the market. The inner boundary could go well into the city, where urban residents grew gardens to supplement their income. The outer edge often extended into the middle zone. Goods were sold at various outlets; the market place itself, in stores, or by hawkers. The relationship between the grower and land had several common variations. The land supply was often limited to a farmer, and might be rented. Sometimes the farming was done only as a part-time, income-supplementing activity. The farmers were often European, Asian or non-local villagers. They also were usually men. The middle zone was labeled the "main supplying ring." Its width was also dependent upon market size. A consideration for this ring was cost of transport. Local villagers, mostly women, were the main sellers, however hawkers occasionally bought the produce from them to re—sell to the Port residents. One of the assumptions of the Thunen model - the farmer as income maximizer, had to be altered considerably here. The cash economy might not yet have become a significant motivator, resulting in much less intensive production by the villagers. Additionally, a choice between cash crops or food crops for the market had to be made. If the latter were chosen, these were likely to be native staples, as opposed to fresh vegetables. These staples were still fairly high in value compared to their bulk and did not perish easily. If not sold at the market, they could be consumed at home or brought back another time for a second try. Selling these crops often provided an excuse for going to town. The outer limit of this ring was where the road from town ended, where the shore or virgin forest began, or where transport facilities were no longer 100 accessible or were too costly. An interesting phenomenon occurred because of these high transport costs. In these economies, land transport rates, often for a taxi, were based upon zones of varying distances, not the weight of the produce. Thus, people at the outer limit of the zone could be forced to 'intensify' to overcome transport costs by taking larger amounts to the market than did sellers from less distant locations. This ring ended when this marketing strategy failed to overcome costs of distance. The outer ring was characterized by the existence of specialists. Brookfield (1969) referred to these people as colporteurs, who bought from the farmer at a price as little as possible above production costs. These buyers took full responsibility for transport to the market and subsequent resale of the produce. This was a very commercial arrangement and occurred most commonly on archipelagos where the economy was more fully developed. Brookfield (1969) noted that because of lack of commercial development, only one or two of the above zones might exist in an archipelago economy. He also noted that the reason behind the appearance of zones was because each had a "specialist participant" who was an economic maximizer. These specialists were: the market gardener, the owners of transport who carried the produce from the villages, and the colporteur who bought and transported the produce. The remainder of the population was not motivated by maximization considerations, they were "satisficers" or "risk minimizers," as the case might be. Because of this, Brookfield (1969) felt that uncertainty models were better adapted to the South Pacific than were static, demand-supply models. 101 Comparison.ofIBrookfieldfls‘Work'with the Isolated.Archipelago The comparison of Brookfield's (1969) rings with the conclusions reached for the analysis done in this thesis will provide some indication of the utility of the model to predict conditions of production in an archipelago. It was first seen that changing the location of the central Town to a Port tended to isolate the interior of the island. This was validated by Brookfield%s(1969) work. For the Ports he considered, specialty and staple zones developed into the interior of the Port- island. These two crop zones did tend to remain either somewhat near the Port, or along whatever road network existed. Distant locations on this island often had transport costs that were prohibitively expensive, and were unable to enter the economy. A second prediction derived from a Port location was that outer islands would be brought into the economy at the expense of the interior of the Port-island. This was because of cheaper sea transport costs. ‘Yet a second expectation was that less land on the outer islands would theoretically be capable of producing rent because of discontiguity; 180th of these expectations were shown.to be valid by Brookfield's (1969) work. Some outer islands, for example those that were very near to the Port (ie., clustered), had begun to sell vegetables and staples at the market. 'Yet the reality that demand levels were not sufficiently high at the Port, and that supply of sea transport was not 100% elastic kept the market economies from expanding. If anything, the discontiguity factor played a stronger role here than was emphasized in the analysis. Separation by water produced an isolation component that was only partially overcome by 102 the sea transport. Perishable specialty crops would be particularly affected. This was predicted but not stressed in the static analysis (see Figure 9). Outer islands that were fairly distant from the Port had virtually no role in the market economy. This was even more true of interior locations on these islands. It was only through a specialist occupation, the col rteur, that outer islands became involved in the economy at all. Thus, the concept of isolation, discussed as a type of pattern, proved to be very pervasive in the South Pacific, where agricultural produce grown for the market was concerned. Regarding the conditions for ring formation that were exclusive to an archipelago, the condition that marginal rent lines must cross over land, not water, was found to be realistic. Vegetable production had a very steep marginal rent slope for sea transport, due to perishability. Zonation on outer islands was rare because distance between them and the Port—island reduced the rent value of vegetables to zero over the water. With regard to shape, the diagrams (Figures 13 and 14) showing how break-of-bulk points alter zonation on islands of diverse shapes would seem to be the accurate conception of the existing conditions. Finally, with regard to the problem of increased demand and lack of area, Brookfield (1969) noted that when space for gardens had become a problem in Fila island, a small island outside of Port Vila, Vanuatu, the women who had sold produce in the Vila market began to sell cooked food instead. This unusual type of ‘intensification' came about because overpopulation had produced a shortage of available garden area. Yet because there was an unmet demand for cooked food, 103 and its production gave the existing garden land a higher rent value, this option was chosen. It is thus an example of how demand and land scarcity combine to force a change in production. In spite of these supportive findings, Brookfield's (1969) research showed that the assumptions of the model often were not met. Thunen assumed a "fully commercial but pre-industrial economy" (Horvath, 1969), populated by economically rational people. The villagers engaging in subsistence farming generally were not yet sufficiently motivated by a desire for cash to grow the crops that would maximize their incomes. This was especially true for outer islands. Also, any production on outer islands for consumption at the Port tended to require a colporteur. These specialists would collect whatever was profitable from villages located along the coast. Interiors were not yet developed for the market economy. In this case then, the model is in advance of the existing conditions of the region. Only when demand reaches much higher levels will multiple- crop rings theoretically begin to occur in island interiors. Suggestions for Further Research Brookfield's (1969) research has shown that, where the assumptions of the model can be met, the expected zonal patterns did emerge. The hypothetical influence of discontiguity, finite area, pattern and island shape could not be tested fully in the archipelagos he considered because the model is in advance of the existing economic conditions. Therefore, it would seem appropriate to find a more developed archipelago to test. Two come to mind very quickly. Both 104 JapanandNewZealand2 have highly developed economies, which have spread spatially throughout their respective archipelagos. Both have large cities creating demand, as well as extensive agricultural hinterlands and highly developed transport networks. In both cases the populations could be considered as reasonably maximizing in their economic behavior. It is in archipelago nations at this level of development, then, that the extentions of the Thunen model discussed in this thesis would seem to be most appropriate. Endnotes 1. The Pacific market places analyzed by Brookfield included: Popondetta, Northern Papua; Kerema, Gulf District, Papua; Honiara, Solomon Islands; Apia, western Samoa; and Port Vila, New Hebrides (now vanuatu). 2. Mbran.(1979) did a Thunen study in New Zealand, but limited his work to the immediate vicinity of Auckland. BIBLIOGRAPHY: VON THUNEN LITERATURE Abler, Roland, J. S. Adams and P. Gould. 1971 . Spatial Organization: the Geographer's View pf thg World. Englewood Cliffs, New Jersey: Prentice Hall, Inc. Alonso, William. 1964. Location and Land-Use: Toward a General Theory 93 Land Rent. Cambridge, MA: Harvard University Press. Bannister, Geoffrey. 1977. "Land Use Theory and Factor Intensities." Geographical Analysis, 9, 4, 319-31. Beckmann, Martin. 1968. Location Theory. New York: Random House. ----. 1972. "Von Thunen Revisited: A Neoclassical Land Use Model." Swedish Journal _o_f Economics, 74, 1, 1-7. Belding, Richard. 1981. 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