EXPENDITURES AND INCOME ELASTICITIES FOR CEREAL PRODUCTS, MARKET SERVICES, AND GRAIN By Kurt R. Anschel A THESIS Submitted to the School for Advanced Graduate Studies of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Economics 1961 ACKNOWLEDGMENTS The author wishes to express his deepest appreciation to Dr. Vernon L. Sorenson for his constant guidance and in- finite patience during the preparation of this thesis. Much is also owed to Dr. James D. Shaffer and Dr. Lester V. Manderscheid for their many helpful suggestions. For helping in the preparation of the data used in this study, the author would like to thank Mrs. Helen P. BishOp, Mrs. Beatrice V. Kelly, Mrs. Constance G. Lane, and Mrs. Dorothy A. Halverson of the Agricultural Economics De- partment's statistical pool and Mrs. Norma E. Ray, and the employees of the I.B.M. Research Center at Michigan State University. Many thanks are due Dr. Lawrence L. Boger and the De- partment of Agricultural Economics for the financial support which made this study possible. 11 EXPENDITURES AND INCOME ELASTICITIES FOR CEREAL PRODUCTS, MARKET SERVICES, AND GRAIN By Kurt R. Anschel A THESIS Submitted to the School for Advanced Graduate Studies of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Economics 1961 f' f If ApprovedQXMA.£-Vj I j ‘- I‘LAA-Z‘A "-4-;- L’AL‘E'L' ABSTRACT This study was undertaken to develop income elastic- ity coefficients for cereal products at retail, for market services embodied in them, and for the grain used as raw materials. It was hypothesized that the income elasticity of demand for cereal products is approximately 0.5, the in- come elasticity of demand for grain is 0.0 and the income elasticity of demand for services in grain products is greater than 1.0. The income and expenditure data were obtained from the Michigan State University Consumer Panel for the years 1955-58. Families of 2 or more persons were selected if they had an increase in income during the second of two con- secutive years, reported expenditures and income each week, and maintained a constant family size during any two con- secutive years. Services are defined as all non-farm additions to the product sold at retail. The quantity of services bought by each family is derived by determining the quantity of raw material included in all cereals purchased and received as gifts and then subtracting the value of grain computed at a constant price from the total expenditures for products at retail. Both time series and cross-sectional analyses of the iv data were made. The income elasticity of cereal products at retail is 0.51 when computed by the time series method. The income elasticity of demand for grain is 0.21. The in- come elasticity of demand for services in grain products is 0.55. The same elasticities coefficients computed by the cross-sectional method are lower. In addition, the income elasticities of seven product groups are derived. The elasticity coefficient for M111 Products (raw grain, flour, etc.) are the lowest of any pro- duct group. Those for bakery products (cakes, doughnuts, pies, etc.) are the highest. Further analysis of the data shows that 88 percent of all retail expenditures are made for services and that bakery products include the highest ratio of services to grain in value terms. The hypothesis that the income elasticity of demand for services is greater than 1.0 was not verified. Because the expenditures for services already are a high preportion of total expenditures, the extent to which the expenditures for services can increase relative to the expenditures for grain is limited. The elasticity coefficient for services cannot diverge widely from the coefficient for expenditures at retail. A mathematical statement and proof of the inter- relationship between elasticity coefficients for the product at retail, for market services and for grain is developed. TABLE OF CONTENTS Chapter I INTRODUCTIONOOOOOOOOOO000......OOOOOOOOOOOOOOOO Purposes 0f StUdyoeooeeoooeee0000000000000eeo The Theoretical Framework.................... PPGVIOUS Studieseeeeeeoeeeeeeeeeeeeeeeeoooeee Time Series Studieseoooooooeoeoe0000000000. CPOSS-Sectional StudieSeeeeeeeeeeeeeeeeeeee II METHODOLOGYOOOOOOIOOOOOOOOOOOOOOOOOOOOOOOOOO... The General Method........................... Sources and Nature of the Data............... Expenditures“.............................. Equivalents................................ Grain Prices............................... Selection of Families........................ Time Periodto0.0000000000000000.0.00.0.0000.0 Selection of Grain Products and Product GroupSOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO Grouping of Families......................... Measurement of Services...................... MethOdOIOgyO0.00.00.000.0000000000000000...00 III THE INCOME ELASTICITIES OF DEMAND FOR CEREAL PRODUCTS AT RETAIL , MARKET SERVICES EMBODIED IN THEM, AND THE GRAINS USED AS RAW MATERIALS Income Elasticities of Demand for Cereal PrOduCtSOOOO00.000000000000000.0.000.000. Income Elasticities of Demand for the Product Groups............................. M111PrOdUCt’SOOOOOOOOOOOOOOOOOOOOOOOOO0.0 Breakfast Cereals........................ MixeSOOOOOOOOOOOOOOO.OOOOOOOOOOOOOOOOO... Macaroni-Spaghetti...0.0.0.0...0.00.00... GraCkerSOOOOOOOOOOOOOOOOOO0.0.0.0....O... Bread and Rolls.......................... Bakery PrOduCtSOOOOOOOOOOOOOOO0.0.0.0.... Income Elasticities of Demand for the Grains. wheatOOOOOOCOOOOOOIOOOOOOOOOOOOOOOOOOOOOOOO CornOOOOOOOOOCOOOOOOOOOOOOIOOOOOOO000...... DurMOOOO0.0000000000000000000.00.0.0...0.. vi Page \o—IqxnkJ #4 TABLE OF CONTENTS - Continued Chapter Page IV THE EXPENDITURE PATTERN FOR CEREAL PRODUCTS AT RETAIL, MARKET SERVICES EMBODIED IN THEM, AND THE GRAINS USED AS RAW MATERIAL........... 43 Introduction.................................. 43 Expenditures for All Cereal Products.......... 43 Cross-Sectional Data........................ 43 Time series DataOOOOOOOCOCOOCOCOOOOOOOOOOOO. 46 Expenditures for Product Groups............... 49 Mill Products............................... 49 Breakfast Cereals........................... 51 MixeSOOOOOOCOOOOOOOOOOOOOOOOOOIIO0.00.0000... 52 Macaroni-Spaghetti.eeeeeeeeeeeeeeeeeeeeeeeee 52 Crackers.................................... 53 Bread and Rolls............................. 54 Bakery Products............................. 54 Expenditures for Grains....................... 55 Wheat. 0 O O C O O O O O O O O O O O O I O O O O O O O O O O O O I O O O O O O O O 56 corn. 0 O O O O O O O O O O O O O O O O 0 O O O O O O O O O O O O O O O O O O O O O 58 mrm. O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O C O O O O O 59 V CONCLUSIONS, LIMITATIONS, AND IMPLICATIONS...... 61 summary or ResultSOOOOOO...OOOOOOOOOOOOOOOOOOO 61 Income Elasticities of Demand for Cereal PraduCt’SOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO. 61 Income Elasticities of Demand for Grains Used as Raw materialsoOOOOO00.00.000.00... 6]- Income Elasticity of Demand for the Product Grou SOOOOOOOOOOOOOOIOOOOOOOOOOOOOOOOOOOOO 62 Cross— ectional Versus Time Series ElasticitieBCOOOO0......O.OCOCOOOOOOOCOOOO 64 The Validity of the Hypotheses................ 65 The Limitations of the Study.................. 68 The sampleOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 68 ConditioninSOOOOO0.0.00000000000000000000000 73 Conclusions and Implications.................. 75 APPENDIX AOCOOOOOOOCOCCOOOOOOOOOOOO.00...00.00.000.000. 77 APPWDIX BOOOOOOOOOCOOOOOOOOOOOOOOOOOOO0.0.000.000.0000 89 APPEIIDIX COOOOOOOOOOOOO00.00.000.00...OOOOOOOOOOOOOOOOO 104 BIBLIOGRAPHY.OOOOOOOOOOOOOOCOO0.00.0000...0.00.00.00.00 108 vii Table I-l II-l 11-2 11-3 11-4 III-l LIST OF TABLES U S D A Household Food Consumgtion Survey of Iéfis: Income Elasticities o emand for Grain Product Expenditures of Non-farm Families Based on Value of Consumption at Home, 1 Week, Spring 1955..................... The Method and Results of Computing the Pounds of Grain in a Pound of Product......... Consumer Price Indexes for Cereal and Grain Products, Food, All Items Excluding Food, and All GOOdS, 1955-5800000eeeeeeeeeeeeeeeeeoe The Purchasing Power of the Dollar, 1955-1958... The Average Expenditure and Range of Expenditure Services in a Dollar's Purchase of Each PrOduCt GroupOOOOOO0.0.0.0...OOOOOOOOOOOOOOOOO Weighted Average Increase of Expenditure of Families Experiencing an Increase in Income... viii Page IO 16 26 26 27 36 CHAPTER I INTRODUCTION Purposes of Study Economists, today, are becoming increasingly concerned with the effects of the inclusion of services in retail pro- ducts on demand. It is generally thought that as income increases, the demand for services increases. This thesis will analyze the effect of increases of income on the ex- penditures for market services embodied in cereal products. In addition, the change in retail expenditures for cereal products at retail and for the grain used as raw material as a result of increases of income will be studied. This study will also give some insight into the future demand situation for cereal products. Recently the retail demand for cereal products has increased. The portion of the family food budget spent on grain products increased more than any other product group during the period 1953-1957.1 The farmer's share of retail expenditures for cereal pro- 1Agricultural Marketing Service, U.S. Department of Agriculture. Farm-Retail Spreads for Food Products. Mis- cellaneous Publication No. 741 (Washington: U.S. Govern- ment Printing Office, 1957) p. 73. ducts decreased more than only one other product group.2 An attempt will be made to determine what can be expected to happen to expenditures for cereal products as consumer in- come continues to increase. The three major hypotheses to be tested are (1) the income elasticity of demand for cereal products at retail is approximately 0.5, (2) the income elasticity of demand for the grain used as raw materials is approximately 0.0, and (3) the high income elasticity for cereal products is due to an income elasticity for market services embodied in them of greater than 1.0. Using data from the Michigan State University Consumer Panel, nine basic income elasticities are derived; the in- come elasticities for all grain product at retail, for all market service embodied within them, and for all grain used as raw materials, the income elasticities for grain, market services, and retail expenditures of seven grain product catagories, and the income elasticities in the three major grains, for the products made from those grains, and the ser- vices added to those grains. In addition to the above major objectives, there is one less important objective. There are two methods for de- termining elasticities, the cross-sectional method and the time series method. very little is known about the differ- ences in these methods. It has been observed that time 2Agricultural Marketing Service, U.S. Department of Agriculture. The Marketing and Transportation Situation. January, 1961. p. 27. series analyses usually results in lower elasticities than cross-sectional studies.3 An explanation is that the time series method describes a short-run adjustment and the cross- sectional method analyzes the long-run adjustment of ex- penditures to income changes. In this thesis, no attempt is made to explain the dif- ference between the two methods, but only to illustrate them. Since the time series method gives results which are better adapted for predictive work in the short-run,most emphasis is placed on its results. Results of this thesis are useful for gaining insight into changes of demand for grain, grain products, and ser- vices included in grain products as a result of income changes. For policy, income elasticities can be used for in- creasing insight into changes of consumption as a result of income subsidies, food stamp plans, and other demand ex- pansion plans. The effects of monetary and fiscal policy can be better understood through the use of income elasticities. The Theoretical Framework This thesis is written within the framework of the received theory of consumer demand. Quantity demanded is 3For example see: Robert J. Bachleda, ”A Comparison of Static and Dynamic Income-Expenditure Relationships for Selected Meat Items." (Unpublished Master's Dissertation, Department of Agricultural Economics, Michigan State University) pp. 75-84. 4 determined by the interaction of (1) the price of the good, (2) prices of all other goods, (3) taste, habit, and custom, (4) the numbers and characteristics of the population, and (5) the purchasing power of the consumer. The purchasing power of the consumer is determined by his money income and the changing value of that income. This thesis is concerned with changes in purchasing power through changes in money income. To measure the effect of changes in income on con- sumption, it is necessary to hold the influence of all the unmeasured independent variables constant. To do this, one must select historical periods in which the variables were known to have been constant, to select periods short enough so that their consequences are negligible, to adjust the data to account for their effects, or to modify the con- clusions so as to allow for their influences. A.measure of the effect of changes in income on demand is income elasticity. Income elasticity may be defined as the ratio of percentage change in the consumer's demand for a commodity to the percentage change in his income that has brought about the change in demand.4 The are measure of elasticity is used in this study since no attempt was made to derive a formulation of the demand schedule for each 4 Tiber Scitovsky. .flglfare and Competition (Chicago: Richard D. Irwin, Inc., 1951) p. 46n. possible income. The are formula is: (E2 ' E1) ”2 + II) (E2 + E1) (Y2 " Y1) where expenditures during the first time period .J'1 u E2 = expenditures during the second time period 21 = income during the first time period Y2 = income during the second time period Elasticities can be measured in percent change of quantity or percent change of expenditure. The latter method is preferable for most studies because it can be used to com- pute the elasticity of several similar products. The three elasticities dealt with in this thesis are highly interrelated. Total expenditures for cereal products by any income group is, by definition, the sum of the ex- penditures for grains and services. An equation expressing the interrelationship between the three elasticities is: (52 + 81) + (32 + 81) where et = income elasticity of total expenditures at retail 98 = income elasticity of services e 2 income elasticity of grain 52 The same expenditures for services during the first time period expenditures for services during the second time period expenditures for grain during the first time period expenditures for grain during the second time period relationship can be expressed in terms of one of the component elasticities: where H u D.) m‘H-f’ r9 .3" It 81 + 82 :: 9 .._._..._._.. - ) eS t + s1 + s2 (9t e8 = (ta + t]) °t _ (82 + 8]) eg (32 + 81) (82 + 81) income elasticity of total expenditures at retail income elasticity of services income elasticity of grain expenditures for services during the first time period expenditures for services during the second time period expenditures for grain during the first time period expenditures for grain during the second time period total expenditures during the first time period total expenditures during the second time period is apparent from the above relationships that the elasticity of either component in the retail product is de- 7 pendent on the change of total retail expenditures and is inversely proportional to the ratio of the expenditure of the component to total expenditures in both time periods. Previous Studies Studies of income elasticities have utilized one of two methods, the time series method or the cross-sectional method. The time series method is usually used to compute the income elasticity of broad product categories using re- gression techniques to study the changesin expenditures over time as income changes. This thesis typifies another use of the time series method by studying the adjustment in expenditure as the income of a selected group of families changes. Time Series Studies The first time series study of the income elasticity of services was made by Bunkers and Cochrane using annual aggregate data from 1913-1954 for the United States. A least-squares method was used to estimate the consumption function for food. Services were estimated by subtracting the adjusted farm product value from the adjusted value of all food expenditures. Cochrane and Bunkers estimated the income elasticity of all food to be between 0.25 and 0.28, and the income elasticity of all food services to be between 0.96 and 1.32.5 5Elmer W. Bunkers and Willard W. Cochrane, ”On the In- This writer knows of only one other attempt to estimate the income elasticity of services. Albert Fourt, using methods similar to those of Bunkers and Cochrane, estimated the income elasticity of all food services to be about 1.2. Fourt used aggregate U.S. data, and multiple regression meth- cds.6 There have been numerous time series estimates of the income elasticity for grains and grain products. We will only mention a few of the more important studies here. Hold and Jureen computed the "quantity" income elas- ticity for flour in Sweden during the years 1921-1939. A ”quantity" income elasticity, is an elasticity expressed in terms of the percentage change in quantity per percent change in income. Wold and Jureen got their data from a consumer panel and used a least-squares method to estimate the re- gression equation. They found a quantity income elasticity of -0.60 for flour.7 Richard Stone estimated income elasticities in his rather complete volume, Measurement of Consumer's Expend- ccme Elasticity of Food Services.” Review of Economics and Statistics. xxxIx (May, 1957) pp. 211-15. 6Louis Albert Fourt. "Empirical Income Elasticities of Demand for Food and Its Component values Produced by Farmers, Manufacturers, and Other Marketing Agencies in the United States, 1929-1956." (Unpublished Ph.d. dissertation, Department of Economics, University of Chicago) p. 41. 7Herman Wold and Lars Jureen. Demand Analysis (New York: John Wiley a Sons, Inc., 1953) p. 291. iture and Behavior in the United Kingdom. He estimated in- come elasticities of bread, cakes and biscuits, miscella- neous cereals, and flour by the time series method. Stone also used least-squares multiple regression methods from data obtained from household budgets. His income elastic- ities were:8’9 Flour -0.15 Bread -0.05 Cakes and biscuits 0.13 Other creals O. 9 Cross-Sectional Studies Cross-sectional studies usually utilize panel or sur- vey data. Studies using panel data usually are limited to relatively few families, utilizing expenditures for a year or more. Surveys usually include large numbers of families for short periods of time and use weekly or monthly data. The cross-sectional method assumes that each income group's consumption level is at equilibrium for all families of that income. With a change in income, the consumption level of the group experiencing the change will be the same as the families already at the higharincdme level. Income elasticity is the percent difference in consumption levels of two income groups per percent difference in income. In 1948 and 1955, the United States Department of Ag- 8Richard Stone. Measurement of Consumer's Expend- iture and Behavior in the United Kingdom. (Cambridge, England: Cambridge at the University Press, 1954) p. 318. 9Results shown rounded off. lO riculture conducted household food consumption surveys. The 1955 survey of 6,060 families was used to compute the income elasticities of all major food products at three dif- ferent income levels for farm and non-farm families. A multi-linear regression method was used to determine the elasticities. Income elasticities computed for grain and cereal products of non-farm families are found in Table I-l. Table I-1 U.S.D.A, Household Food Consumption Survey of 1255: Income Elasticities of Demand for Grain Pro- duct Expenditures of Non-farm Families Based on value of Consumption at Home, 1 Week, Spring 1955. Income Groups Pr°du°t° - 3 99 - 999 so 0 + 1 Flour and other cereal products -.13 -.08 -.04 Flour “e41 -elli’i "e141 Mixes .46 .261} .011 Cereals (breakfast) .04 1 .13 -.021 Other cereals -.24 -.53 .091 Bakery products .32 .061 .021 Baked goods .45 9.02 .15 1Not significantly different from zero at 10 percent level. Source: George E. Rockwell, Jr. Income and Household Size- Their Effects on Food Consum tion. Marketing Research Report No. 32;?) (WasEing‘Eon: U.S. Department of Ag- riculture, Agricultural Marketing Service, 1959) p.8. CHAPTER II METHODOLOGY The General Method Members of the Michigan State Consumer Panel who ex- perienced an increase in income in the second of two con- secutive years during the period 1955-1958 are included in this study. These families are classified by two methods, three income groups and two income groups. Income elastic- ities are computed for each income group of both class- ifications using the cross-sectional and time series methods. Income elasticities for cereal products at retail, for market services embodied in them, and for the grains used as raw materials are computed for each product group at each income level to investigate the relationship between income change and expenditure. The income elasticities are deter- mined by both the time series and cross-sectional methods. Sources and Nature of the Data Expenditures The expenditure data from which the results of this study are obtained was collected by the Michigan State University Consumer Panel. The Panel was drawn from a ran- dom sample of 1,885 Lansing, Michigan, families (here called 12 the master sample). The master sample was stratified accord- ing to family income, family size, homemaker's age, and homemaker's education, and a random sample was drawn from each strata. As members of the panel drapped out, new mem- 'bers were selected from the master sample who best fit the characteristics of the departing family. In addition, newly formed families were added each year to keep the panel rep- presentative over time. From 1951 to 1958 each week approximately 250 families reported food expenditures, meals eaten out, food gifts, food grown at home, family size, and family income. At the end of each year every family was sent a questionnaire to check the annual income against the sum of the income re- ported each week. When the income reported in the annual questionnaire differed from the sum of the income reported each week, a personal interview was arranged to determine the cause of the discrepancy and to determine the correct in- come. The weekly diary was broken down into 14 different product categories such as dairy products, fats and oils, fruits, vegetables, meats, and bakery and cereal products. These larger headings were further broken down into sub-pro- duct groups. Under bakery and cereal products there were 11 subnproduct groups: bread; buns, rolls, and cakes; cookies; doughnuts and pies; mixes; flour and corn meal; crackers; spaghetti, etc.: breakfast cereals; appetizers, etc; and other grain products. Under the sub-product groups were 13 listed the actual products. There were 211 specific bakery and cereal products listed in the diary. The diary did not achieve the form described above un- til 1954. Previously bakery and cereal products were in larger aggregates and as a result the data collected before 1954 was unusable. Data collected in 1954 was also unusable because the coding system was different. Therefore the study is limited to the years 1955-1958. Equivalents In order to estimate the expenditures for market ser- vices it is necessary to know the quantity of grain in each product. An equivalent of the quantity of grain in a pro- duct is expressed in pounds of grain per pound of product. The quantity of purchases and gifts multiplied by the equiv- alent gives the pounds of grain acquired. The grain, valued at its farm price is subtracted from total expenditures, the difference being the value of services. The equivalents are derived from data published by the U.S.D.A. and data made available by the grain products in- dustry in response to a questionnaire sent to a selected group of firms.1 When the data supplied was in terms of fractions of bushels per pound of product, the following. conversion factors were used to reduce bushels to pounds; 1 Production and Marketing Administration, U.S. Depart- ment of Agriculture. Conversion Factors and Weights and Measures for Agricultural Commodities and Their Products. (Hashington, D.C., 1952) pp. 37-43. 14 wheat, 60 pounds per bushel; durum, 60 pounds per bushel; corn, 56 pounds per bushel; oats, 32 pounds per bushel; barley, 48 pounds per bushel; rye, 56 pounds per bushel; buckwheat, 48 pounds per bushel; and rice, 45 pounds per bushel. When the data was received in terms of pounds of flour it was estimated that the following quantities of flour were processed from 100 pounds ofgrain: wheat, 71.53 pounds; durum, 72 pounds; corn, 58.9 pounds; oats, 43.7 pounds; bar- ley, 45.38 pounds; rye, 80 pounds; buckwheat, 60 pounds; rice, 63.7 pounds (from rough rice). The equivalents obtained from the various sources usually differed, and often byka considerable amount. The quantity of grain used for any product differs from firm to firm due to differences in regional tastes and quality. The data used by the U.S.D.A. to compute equivalents comes from a variety of sources including the military, congres- sional investigations, and surveys and the results are in- tended to be averages for the entire industry. The equivalents used in this thesis are computed in a variety of ways. When more than one firm reported_the quantity of grain used to produce a pound of product and the U.S.D.A. also published an equivalent for that product, the U.S.D.A. equivalent is used if it does not differ by more than 10 percent from the average of the industry figures. If the U.S.D.A. figure differs by more than 10 percent, then the average of all data available is used weighing the U.S.D.A. 15 equivalent twice the weight given any industry equivalent. If only one figure was received from the industry, the U.S.D.A. equivalent is used regardless of the difference between it and the industry figure. If no U.S.D.A. figure is available then the average of the industry equivalents is used. In a few cases no sources were available and it was necessary to assign an equivalent based upon the equiv- alents of similar products. Table II-l presents the equiv- alents and the method of computation. Grain Prices The price used for evaluating the grain purchases is derived by averaging the annual prices between 1954 and 1958 as reported in The Grain Situation.2 The prices of grain used are: wheat, 31.94; durum, $2.31; rye, $1.10; rice $4.84; buckwheat, $1.09; corn, $1.25; oats, 3.634; and barley. $.947. Selection of Families Families fitting the following criteria are included in the sample utilized in the study: (1) families of two or more persons who experienced an increase in income in the second of two consecutive years, (2) families who main- tained a constant size during the two year period of income 2It will be noted that 1954 was used to compute the grain price average. That year was included because as originally planned the expenditure data for 1954 was to be included. Because the coding system in 1954 was different from the system used in the following years, 1954 could not be used but the grain prices were not changed accordingly. 16 Table 11-1 The Method and Results of Computing the Pounds of Grain in a Pound of Product Products Equivalent Grain #grain/#product Source I. Mill Products 1. 2. 3. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. cake flour.........wheat graham flour.......wheat white flour........wheat corn meal..........corn corn starch........corn plain rice.........rice prepared rice......rice whole wheat flour..wheat buckwheat flour....buck- wheat barley flour.......bar1ey rye flour..........rye barley.............bar1ey rice...............rice wheat..............wheat soya...............corn oat flour..........oats soya flour.........corn mush...............corn 2.125 1.05 1.398 1.40 1e65 1.00 0.40 1.02 1.67 2.204 1.265 1.00 1.00 1.00 1.40 2.286 1.70 1.932 U.S.D.A.l firms' average U.S.D.A. U.S.D.A. U.S.D.A. U.S.D.A. same proportion as canned spaghetti to white flour U.S.D.A. U.S.D.A. U.S. DOA. firms and (2x) U.S.D.A. avg. unprocessed grain unprocessed grain unprocessed grain same as corn.meal U.S.D.A. U.S.D.A.(corn flour) same as hominy grits 1Production and Marketing Administration, U. 3. Depart- ment of Agriculture. Conversion Factors and Weights and Moe - ures for A ricultural: Commodities and Their Products. wash- IngEon,D. C's I552) PP. 37-E3. 17 Table II-l (can't) The Method and Results of Computing the Pounds of Grain in a Pound of Product Products Equivalent Grain #grain/#product Source II. Cereals 1. 2. 3. 4. 5. wheat cereals......wheat corn cereals.......corn oat cereals........oats rice cereals.......rice miscellaneous......wheat III. Mixes 1. 2. 3. 4. 5. 6. 7. corn oats cakes and muffins..wheat cookies............wheat roll and biscuit ' m1x0000000000000000wheat pie crust mix......wheat p10 nixOOOOOOOOOOOOVheat pancakes and waffles............Wheat rye buck- wheat rice corn breadOOOOOOOOOOOOOOWheat corn muffins and breadOOOOOOOOOOOOOOcorn 1.18 2.240 2.430 1.577 0.393 0.746 O. 810 0.511 0.594 1.153 0.839 0.222 0e630 0.062 0.330 0.1036 0.170 1.074 1.505 U.S.D.A. U.S.D.A. U.S.D.A. U.S.D.A. 1/3 wheat cereal equiv. 1/3 corn cereal equiv. 1/3 oat cereal equiv. firm and (2x) U.S.D.A. avg. firm and (2x) U.S.D.A. avg. firm and (2x) U.S.D.A. avg. firms average U.S.D.A. U.S.D.A. firm and (2x) Us Se DeAe 3V6. firms average 18 Table II-l (con't) The Method and Results of Computing the Pounds of Grain in a Pound of Product Equivalent Products Grain #grain/#product Source 9' fiSkBEBSt SRIIIII..bu ck- 0.862 firm and (2x) wheat U.S.D.A. avg. IV. Spaghetti, Macaroni,etc l. Spaghetti, macaroni (plain)............durum 1e389 UeSeDeAe 2. spaghetti, macaroni (meat).............durum 0.125 U.S.D.A. 3. spaghetti, macaroni (other)............durum 0.556 U.S.D.A. 4. noodles(p1ain).....durum 1.313 U.S.D.A. 5. noodles(other).....durum 0.195 U.S.D.A. 6. minute rice........rice 1.041 U.S.D.A. 7e tapiocaeeeeeeeeeeeerice 00935 U.S.D.A. V. Crackers l. soda crackers......wheat 1.398 U.S.D.A. 2. graham crackers....wheat 0.848 firm and (2x) U.S.D.A. avg. 3. other crackers.....wheat 1.398 U.S.D.A. . cracker meal.......wheat 1.399 U.S.D.A. 5. corn flake crumbs..corn 2.240 U.S.D.A. Products 19 . Table II-l (con't) The Method and Results of Computin the Pounds of Grain in a Pound of Pro uct __ - Equivalent Grain #grain/#pr0duct Source VII. Bread and Rolls 1. 2. 'white bread........wheat special white breads.............wheat 3. mixed breads.......wheat rye 4. wheat breads.......wheat 5. fruit breads.......wheat 6. bunBOOOOOOOOOOOOOOOWheat 7. biscuits...........wheat 8. rolls..............wheat Baked Goods 1. cakes and muffins..wheat 2. cookies............wheat 3. pieBOOOOOOOOOOOOOOOWheat 4. doughnuts..........wheat 5. breakfast rolls....wheat 0.895 0.895 0.657 0.250 0.642 0.600 0.881 0.699 0.881 0.455 0.616 0.224 0.689 0.688 U.S.D.A. similar to white bread U.S.D.A.(rye bread) U.S.D.A.(whole wheat) based on U.S.D.A. U.S.D.A. U.S.D.A. U.S.D.A. (2:) avg. firm and U.S.D.A. firm and (2x) U.S.D.A. avg. U.S.D.A. (21) avg. firm and U.S.D.A. firm average 20 change, (3) families who reported every week during the two year period, and (4) families whose year end reported in- come equaled the sum of the income of each week. Single person families are eliminated because the large number of meals they eat out and their high per capita in- come cause extreme variability in the elasticities. The inclusion of only families maintaining a constant size avoids problems of changing per capita income and changing per capita eXpenditure rates during the year. Families who report most weeks but not every week are not included because 3 gained would have been too small the number of family years to make the necessary adjustments worthwhile. A family is not included in the sample if the income reported at the end of the year and the sum of income reported each week were not equal and the interview arranged to reconcile the difference was unsatisfactory. Time Period The time period problem is one of trying to success- fully eliminate the effects of cycles and seasonal variation of the unmeasured independent variables. The unmeasured independent variables may be classified in six major groups: (1) taste, custom, and habit, (2) the state of the arts, (3) the prices of grain and cereal products, (4) the prices of all other substitute goods, (5) the purchasing power of the dollar, and (6) the numbers and characteristics of the 3A family year is the data resulting from the inclusion of a family for one year. 21 p0pulation. Over a long time period all these variables fluctuate but in shorter periods are more stable. Taste, custom, and habit, numbers and characteristics of the p0pu1ation are usually regarded as fixed during a four year period. It takes much longer for mores, social customs, institutions, and age distribution and papulation of a nation to change significantly. The only exception is a period of tremendous upheaval such as depression or war, but the period 1955-58 was not one of these periods. Technological change in a particular industry does not conform to any periodic movement. An industry's technology may not change for several generations and then may change rapidly. Technological change may be one of two types, the invention of a new process for the production of a commodity already on the market, or the invention of a new product. The invention of a new process will result in a reduction in the cost of production and, if entry into the market is free, the price of the product will fall. This in turn may cause a change in expenditure for the product. The change in aggregate expenditures will depend on the price elastic- ity of the product. If the price elasticity is less than minus one, total expenditures will increase. If it is greatp er than minus one, expenditures will decrease. If an innovation results in a new product on the mar- ket, the product will slowly gain consumer acceptance and ex- penditures for substitute goods may decrease. In some cases the sole area of loss will be to the firms producing a pro- 22 duct used for the same purpose. If the price of the new product is much lower than the price of the products it re- places, expenditures may be drawn from other goods as well, or if the new good replaces an inferior good, expenditures for other goods will increase due to an income effect. The economic effects of innovations which result in the introduction of new products are difficult to determine. New products often require long period of time before re- ceiving full consumer acceptance. During the period of in- creasing acceptance no equilibrium of expenditures for the new product or competing products is established. For the purposes of this study, sales and expenditure figures are used to determine whether any equilibrium has been establishp ed for new products. Until an equilibrium is reached, con- sumption of new products will increase at a rate higher than older products. Innovations can take place at three market levels: within cereal products; among those products which are close substitutes, other foods; and among the not so close sub- stitutes, all other consumer goods. The recent major innovation resulting in the intro- duction of a new cereal product was the invention of pack- aged mixes. The introduction of these products occurred after the Second World War, and by 1955 they had achieved full consumer acceptance.4 4Based on confidential sales figures from an inde- pendent market research.firm. 23 Among the close substitutes, the major innovation is frozen foods. During the period, 1955-1958, there was a very rapid growth of sales of frozen fruits and vegetables.5 The introduction of frozen products makes most fruits and vegetables available the year around. The result is a rap- id increase in the expenditure for fruits and vegetables, and the decrease in the demand for other products including bak- ery and cereal products. The effect is to lower the esti- mates 0f the income elasticity of demand for cereal pro- ducts since the changes in consumption will be diminished as income rises. Innovation in the non-food consumer goods industry con- tinues at a constant rate if all non-food industries are grouped together. It is possible to regard the influence of innovations in these industries as continuing at a constant rate, which means there will be no effects on the results of this study. The only exception may arise out of some unusual situation such as war or depression when for economic or military reasons, the innovations were not available to the public creating a large unsatisfied demand. A variable that may cause some change in the con- sumption of grain products is the prices of grain products relative to the prices of other foods and all other goods. The prices of cereal products decreased from 1955 to 1956 5"1958 Almanac of the Frozen Foods Industry-A Collec- tion of Facts and Statistics." Quick Frozen Foods. xx (March, 1958) pp. 165-196. 24 and thereafter increased. The price of all food increased during the same period. The Consumers Price Index of grain and cereal products decreased 4.3 percent from 1955 to 1956. In 1957 the index rose 4.9 percent and in 1958 rose 2.6 per- cent. During the same period the Consumers Price Index for all food increased 0.8 percent, 3.7 percent, and 4.9 per- cent. Assuming negative price elasticities, in 1956 expend- itures for grain products should have increased relative to expenditures for other food products. In 1957, expenditures should have fallen relative to the expenditures for other food products, and in 1958 they should have risen again. The net effect is probably negligible since the three move- ments tend to cancel each other and the price elasticity of demand for grain products is elastic. Changes of the prices of all other goods have an in- fluence on the expenditures for grain products. The Con- sumer Price Index for all items excluding food shows an.in- crease of 1.8 percent in 1956. 3.4 percent in 1957. and 2.9 percent in 1958. The increases of the prices of all non- food consumer goods are greater than the increases of the prices of cereal products. As a result, expenditures for cereal products, and therefore the elasticities, are in- creased relative to other products. Since the difference be- tween the increase of prices of non-food items and the in- crease in cereal product prices is small, the increase of the elasticities is probably small. Changes in the purchasing power of the dollar and 25 changes in prices had Opposite effects on the income elas- ticities. From 1955 to 1958 the purchasing power of the consumer's dollar fell gradually. The result was that the real income change was not so great as the change in money income of a consumer receiving an increase in income. As a result, the consumer probably did not increase his expend- itures as much as was indicated by the increase in income. Therefore, the three income elasticities are slightly under- estimated. It is very difficult to accurately estimate the degree to which the income elasticities are underestimated as a re- sult of changes in the unmeasured independent variables. In all probability the effects are small. Selection of Grain Products and Product Groups All those products listed in the Consumer Panel Diary under the Cereal and Grain Product category except ap- petizers are included in this study. Products which contain very small quantities of grain such as soups, appetizers, and baby foods are not included because they embody such a small part of total grain consumption. Alcoholic beverages are not included owing to the na- ture of their consumption. Much of the expenditures and con- sumption of alcoholic beverages takes place outside the home, and therefore, would not be included in the Diary. It is also believed that the data for home consumption.might have a strong downward bias. 26 Table II-2 Consumer Price Indexes for Cereal and Grain Products, Food, All Items ExcludingBFood, and All Goods, 1955-5 Index 1955 1956 1957 1958 Prices Cereal and grain products Wholesale.............. 116.2 115.2 116.9 117.9 R0t311eeeeeeeeeeeeeeeee 12909 123e6 13005 13301 roadOOOOOOOOOOOOOOOOO..0. 110.9 111.7 115.4 120.3 All items excluding food. 116.7 118.8 122.8 125.5 All SOOdBOOOOOOOOOOOOO... 114.5 116.2 120.2 123.5 Source: Bureau of the Census, U.S. Department of Commerce. Statistical Abstracts of the United States 1252. (washington: U.S. Government Printing Office, 1959) PP e 330-3380 Table II-3 The Purchasing Power of the Dollar, 1955-1958 Market level 1955 1956 1957 1958 wh01.aaleOOO0.00.00.00.00. 90.3 87.5 85.0 83.9 Retaileeeeeeeeeeeeeeeeeeee 9002 8905 8607 8301 Source: Bureau of the Census, U.S. Department of Commerce. Statistical Abstracts of the United Statesglgfig (washington: U.S. Government Printing Office, 1959) p. 33 . 27 The products are aggregated into seven product groups. The aggregation is made on the basis of product type and quantity of services in the product. The primary criteria is product type although Table II-4 shows that the quantity of services varies with product group. Table II-4 The Average Expenditure and Range of Expenditure Services in a Dollar's Purchase of Each Product Group Average Value of Servins Product Groups Per Dollar Expenditure Range Mill products 3.7443 $.5097-$.9371 Cereals .8510 .7603- .9036 Mixes .8794 .7505- .9821 Macaroni-spaghetti .8983 .7618- .9895 Crackers .8890 .8491— .9421 Bread and rolls .8993 .8408- .9257 Bakery products .9634 .9494- .9808 1Each product in the group weighed equally. The product groups fall into four distinct classes. Mill products contain the greatest heterogeneity of products including some with just over 50 percent services and others with over 90 percent services. The most important products of the group are at the lower end of the scale. Only four products of the 18 products in the group include 80 percent or more services. Cereals, mixes, and macaroni-spaghetti can also be grouped together as being similar in grain-service mix. The 28 individual products in each of these product groups vary from 75 percent to almost 100 percent services. The pro- ducts in each product groups are fairly evenly distributed throughout the range. Crackers and bread and rolls fall in the same class be- cause their range of percent services lies between 85 and 95 percent. The individual products are closely grouped be- tween 88 percent and 92 percent. Bakery products have the highest proportion of services. They vary between 94 percent and 98 percent services with a fairly even distribution in the range. Grouping of Families The families selected are those who reported two or more years and had an increase in income in each succeeding year. For the time series calculations, each family year is classified as either primary or secondary. The primary years are the years before an income increase and the sec- ondary years are the years in which there is an increase in income over the previous year. A family's data for a year may be primary and secondary if the family experienced an increase in income in more than one year and the family fit the other criteria during those years. If the family re- ported three years in succession and during the last two years experienced an increase in income over the previous year, the second year's data would be both in the primary group and the secondary group. 29 All the primary years are placed into one of four per capita income groups, below $1,349, $1,350 to 31,599, 81,600 to 81,999, and above 82,000. Regardless of the size of the increase in income, the secondary years are class- ified according to the income in the primary year. For in- stance, if in 1955, a family had an income of 81,000 and in 1956 an income of $1,450, the 1955 income and expenditures would be placed in the below 81,349 primary year group. The 1956 data would be placed in the below 81,349 secondary group. If in 1957. the same family had an income of 31,650, then the data for 1956 would also be grouped with the 81,350 to 81,599 primary year income group, and the 1957 data would be placed in the 81,350 to 81,599 secondary year income group regardless of the fact that in 1957 the income was above 31.599. The income groups were chosen so as to make it pos- sible to have both two and three income groups with approx- imately equal numbers in each income group. The three in- come group classification is obtained by combining the data of the $1,350 to 81,599 income group with the data of the 81,600 to 81.999 income group. The two income group method results from the combination of the two highest income groups and the combination of the two lowest income groups. Measurement of Services The term ”services" has never been precisely defined in economic terminology and has been used to define a num- 30 her of concepts. The primary use of the term has been to distinguish non-tangible additions to a product such as transportation, installation, personal attention, and repair. The use of services for intangibles is difficult to apply to empirical work. Most intangible additions to a product also involve tangible additions. From an economic standpoint the distinction is unimportant. The economist is interested in the ability of the additions to add value to the product re- gardless of the nature of the addition. In this thesis, all non-farm additions to the grain are called services. It is argued that the consumer can buy the grain directly from the farmer and finish it himself if he so desires. Since the manufacturer is finishing the grain for the consumer, the additions of the manufacturer are services. The concept of services as all non-farm additions to the product is a compromise. Technically all farm additions to the grain after harvesting (e.g. storage) should be in- cluded as services, but this is difficult as there is no convenient measure of some of these services. The value of services is computed by subtracting the value of grain from the total value of the product. The value of grain is determined by first computing the quantity of grain purchased and received by gifts, and then multiply- ing by a constant price of the grain. It would have been possible to use any constant price of grain without affecting the income elasticities for mar- 31 ket services and grain used as a raw material. For instance, if five pounds of a certain product had been bought in the primary years and ten pounds in the secondary years at 3.25 per pound and the products equivalent is 1.5, then the per- centage change in expenditures for grain would be the same whether the grain was worth 8.01 a pound or 8.07 a pound. Primary years Secondary years 5 x 8.25 = 81.25 10 x 3.25 = $2.50 1.5 x 5 = 7.5 lbs. grain 1.5 x.10 = 15 lbs. grain 7.5 lbs. at $.01 = 4.075 15 lbs. at 8.01 = 8.15 All-i=2 .15 7.5 lbs. at 8.07 = 4.525 15 lbs. at 4.07 = $1.05 ‘22:. 1.05 To have a measure of service and grain expenditures which is at least partially realistic, constant prices are used which approximate the prices of grains during 1954-1958. The five year average of annual prices as reported by the U.S. Department of Agriculture are used. If the expend- iture figures of services and grains are to be used and not the elastiCities, it must be understood that they are not exact. Methodology Each family year is grouped into one of four per cap- ita income groups, $0 to $1,349. 31,350 to 81,599. $1,600 to 32 81.999 or $2,000 and above. In order to compute the cross-sectional income elastic- ities, it is necessary to know each income group's average per capita expenditure for each product and the average per capita income. These are computed for the three income group and the two income group classifications aggregating the families from all four years. The expenditures are first computed for each product and these are then summed for product groups, and then the product group totals are summed for total expenditures for given products. The expenditures are divided by the number of persons to determine per capita expenditures. This meth- od makes it possible to compute cross-sectional elasticities for product groups as well as for aggregate expenditure. The formula for cross-sectional income elasticities used is: (E2 " El) (Y2 + 11) (E2 + E1) (Y2 - Y1) where E1 = expenditures of the lower income group — expenditures of the higher income group 21 = income of the lower income group Y2 = income of the higherincome group In order to compute the elasticities by the time series method, the per capita expenditure and income levels are computed for each income group before and after an in- 33 come increase. After grouping the families into income groups according to income in the primary year, the average annual per capita expenditure for each product is computed for each income group for both the primary and secondary years. Also computed is the average per capita income of each income group in the primary and secondary years. The sum of expenditures are computed for each product group and then summed to derive total expenditures for cereal products of each income group during the primary and secondary years. Then the quantity of services is computed by multiplying the quantity of each product by the product's equivalent. This is then multiplied by the average price of the grains, and subtracted from total expenditures to obtain the expenditure for services for each product. From this data elasticities are computed for all product groups, and for total expend- iture. The formula used is: (E2 ' E1) (I2 + $11 (E2 + E1) (Y2 ’ Y1) where E1 = expenditures during the primary years expenditures during the secondary years I‘ll h) N income during the primary years '3: n Y = income during the secondary years Chapter III The Income Elasticities of Demand For Cereal Products At Retail, Market Services Embodied in Them, and the Grains Used as Raw Materials This chapter will present the results of the elastic- ity computations as a means of studying the consumer's cereal expenditure response to an increase in income. The following chapter will be concerned with the data from which the elasticities are derived. Income Elasticities of Demand for Cereal Products The income elasticity for all cereal products at re- tail varies between 0.13 and 0.25 when computed by the cross- sectional method. The income elasticity for market services is slightly higher, ranging from 0.14 to 0.27. As one would expect, the income elasticity computed by the cross-sec- tional method for all grains used as raw materials is lower than the other two elasticities. The elasticities for grains are arrayed between -0.07 to 0.07. The income elasticities computed by the time series method are higher than the elasticities computed by the cross-sectional method. The income elasticities computed by the time series method for all cereal products at retail are between 0.22 and 0.94. The income elasticity of all income groups for cereal products is 0.51. The income elasticity 35 for market services ranges between 0.24 and 1.0, slightly higher than the income elasticity for all grain products at retail. For all groups, the income elasticity for services computed by the time series method is 0.55. Again the in- come elasticity for grains used as raw materials is lower than the other elasticities. The income elasticities for grains are arrayed between 0.10 and 0.40, and the income elasticity of all groups for grain is 0.21. The income group which had an initial income of $1,350 to 81.999 has the highest elasticities when the elasticities are computed by the time series method. In each case this group's income elasticity is the upper limit of the range. On the other hand, the elasticities of the income group with an initial income of 82,000 and more are always the lower limit of the range. ' The high income elasticities of the $1,350 to $1,999 income group are due to the increased expenditures for bak- ery products and bread and roll products. Table III-1 shows that in the first five product groups, the middle in- come group does not have the highest average percentage change of expenditures. The inclusion of the bread and roll product group makes the percentage change of the middle in- come group slightly higher than the other two groups, and after adding the bakery goods category the difference be- comes very large, greater than 4 percent. 36 Table III-1 Weighted Average Increase of Expenditures of Families Experiencinglan Increase in Income Income Product Groups2 I - v 1 - v1 I - VII 80,000 - 81.349 1.0458 1.0280 1.0611 31.350 - 91.999 1.0092 1.0386 1.1045 $2,000 - 0.9951 0.9828 1.0238 1Weighted by expenditures in the 2Product groups are: I II III IV VI VII Mill products Breakfast cereals Mixes Macaroni-spaghetti Crackers Bread and rolls Bakery products Income Elasticities of Demand for the Product Groups Mill Products first year. The income elasticity computed by the cross-sectional method for mill products at retail ranges between 0.10 and 0.19. The income elasticity for services is slightly higher, varying from 0.15 to 0.21. The income elasticity for grains 37 is only slightly lower than the income elasticity for serv- ices, ranging from 0.03 to 0.17. Income elasticity of demand for mill products com- puted by the time series method varies between -1.44 and -0.02. The range of the income elasticity for market serv- ices is even wider and generally lower, being -1.82 to -0.25. The income elasticity of demand for grains used in mill pro- ducts ranges from -1.0 to 0.2. The higher income elastic- ity for grains is due to a shift of expenditures from mill products containing more services to those containing less. The change of expenditures for three products, whole wheat flour, cake flour, and prepared rice products make up 83% of the change of expenditures for mill products of the 32,000 and more income group. The change in expenditure for any of the three products is not more than $6.00 per person. Because these products are consumed by very few families in the income group, it is felt the sample is too small to justify the use of the three income group method when studying the product groups. Therefore, in the follow- ing discussion, the range of income elasticities will only include those elasticities derived using two income groups. Breakfast Cereals The second product group, breakfast cereals, has the following income elasticities of demand when computed cross- sectionally: -O.15 for breakfast cereals at retail, -0.15 for market services embodied in breakfast cereals, and -0.15 38 for grains used as raw materials in breakfast cereals. Com- puted by the time series method, the income elasticities for breakfast cereals are positive. The income elasticities for breakfast cereals are 0.50 and 0.62, for services embodied in than 0.69 and 0.58, and for the grains used as raw mater- ials in breakfast cereals are 0.19 and 0.02. The elastic- ities computed by the cross-sectional method are negative be- cause the higher income groups have fewer children, and, therefore, consume less breakfast cereal per person. Mixes The income elasticity of demand computed by the cross- sectional method for mixes is 0.08, for services is 0.09, and for the grains is 0.01. The income elasticity for mixes computed by the time series method varies from -0.22 to 0.17, for services are -0.20 and 0.16, and for the grains varies between -0.41 and 0.28. Macaroni-Spaghetti The income elasticities of demand for the macaroni- spaghetti product group computed by the cross-sectional meth- od are 0.02 for the total product group at retail, 0.05 for market services in the product group, and-0.13 for grains used as raw materials. The time series method results in an income elasticities for the product group at retail of 0.01 and 0.04. The income elasticities for services are -0.12 and 0.07 and the income elasticities for the grains are 0.70 and "Oelll'e 39 Crackers The fifth product group, crackers, has very different elasticities when computed by the two methods. The cross- sectional method gives results of 0.41 for crackers, 0.42 for the services in crackers, and 0.37 for the grains in crackers. Income elasticities computed by the time series method for crackers are 0.19 and -0.02, for services in crack- ers are 0.20 and 0.01, and for grains in crackers are 0.10 ma. -0e220 Bread and Rolls All per capita income groups spend more for bread and rolls than any other product group. Income elasticity, how- ever, is relatively low. The income elasticities are 0.12 for bread and rolls at retail, 0.14 for services, and -0.02 for the grains. The time series method shows a great deal of consistency between the two income levels. The income elasticity of demand for bread and rolls at retail varies between 0.16 and 0.14, for services embodied in bread and rolls are 0.18 and 0.15, and for the grains used as raw ma- terials in bread and rolls are 0.01 and 0.10. Bakery Products Expenditures for bakery products are almost as high as expenditures for bread and rolls. The income elasticities computed by the cross-sectional method are 0.62 for bakery products at retail, 0.63 for services embodied in bakery products, and 0.61 for grains used as raw materials. Bakery no products is the only product group with elasticities greater than one. The income elasticity for bakery products at re- tail computed by the time series method are 1.62 and 1.01. The income elasticity for services varies between 1.59 and 1.01. The income elasticity for the grains are 2.44 and 1.12. An analysis of the raw data reveals that the elastic- ity for grain is higher than the elasticity for services be- cause of the large increases in expenditures for doughnuts and cookies after an increase in income. Both doughnuts and cookies contain more grain than the other products in the group. Income Elasticities of Demand for the Grains In addition to classifying each product in a product group, each product was classified according to from which grain it was made. As a result, it is possible to compute the income elasticity of demand for each grain, the income elasticity of demand at retail for the products made from each grain, and the income elasticity for the services em- bodied in the products made from each grain. A few products are derived from more than one grain and a portion of their expenditures are added to the various grains from which they were made. Retail expenditures for the product were divided equally among the grains in the product. Only three grains, wheat, corn, and durum, have ex- penditures high enough to justify computation of elastic- ities. Because wheat product expenditures make up about 41 90 percent of all grain product expenditures, the sample is large enough to permit study of the three income group classification. The expenditures per person for durum and corn are very low, and, therefore, the three group class- ification is unreliable for these grains. Wheat The three group cross-sectional classification shows an income elasticity for wheat used as a raw material of approximately 0.0. The income elasticity for all products made from wheat is approximately 0.2, and the income elastic- ity for services added to products made from wheat is about 0.2. The two group cross-sectional classification gives slightly higher results. The income elasticity for wheat is 0.12, for wheat products is 0.30, and for services is 0.32. The income elasticities computed by the time series method are more variable. The range of income elasticities for wheat is 0.15 to 0.39, for wheat products is 0.25 to 1.0, and for services is 0.26 to 1.07. The two group time series method gives results which fall in the above ranges. Corn Cross-sectional analysis results in an income elastic- ity for all corn used as a raw material of -O.20. The in- come elasticity of demand for all products made from corn is -0.23, and the income elasticity of demand for services em- bodied in products made from corn is also -0.23. The income elasticities derived by the time series method are -0.31 and 42 -0.28 for corn, 0.14 and 0.12 for corn products, and 0.21 and 0.18 for services added to corn products. Most of the expenditures for corn and corn products are for breakfast cereals made from corn, and as a result the income elastic- ities for corn are primarily determined by the corn break- fast foods. Durum Although durum is a type of wheat, because it receives a price differential it is dealt with separately in this study. The income elasticity for durum computed by the cross-sectional method is -0.15, for durum products is 0.02, and for services embodied in durum products is 0.05. The income elasticities computed by the time series method for durum vary between 0.56 and -0.l6, for durum products vary between 0.09 and -0.11, and for services are arrayed between 0.01 and -O.lO. Most durum is sold as macaroni and spa- ghetti, and therefore the corresponding elasticities are al- most the same. CHAPTER IV THE EXPENDITURE PATTERN FOR CEREAL PRODUCTS AT RETAIL. MARKET SERVICES EMBODIED IN THEM, AND THE GRAINS USED AS RAW MATERIAL Introduction This chapter presents an analysis of the data which underlies the previously presented income elasticities. The data analyzed includes: (1) expenditures for all grain products, (2) expenditures for the product groups, and (3) expenditures for the three most important grains. Special attention is given to the relationship between expenditures for the product groups and all grain products, and the pro- portion of expenditures for market services in total ex- penditures. Expenditures For All Cereal Products Cross-Sectional Data The $2,000 and higher income group spends 837.62 per person for grain products of which $33.41 is for market services embodied in them. Thus, 88.8 percent of total ex- penditures (retail) is for services. The group with a per capita income between $1,350 and $1,999 spends an average of 834.94 per capita for grain products, 82,68 less than the 44 upper income group. 0f the 834.94,1 88.2 percent is for services. The 30 to 81,349 income group spends $2.79 less per person than the middle income group and $5.57 less than the upper income group. or the $32.15 spent by the lower income group, 86.8 percent or $27.89 is for services. In each case expenditures decrease as income decreases. In addition, the quantity of services purchased decreases both in value and as a percent of expenditures as income decreases. The upper income group spends 7.69 percent more than the middle group and the middle income group spends 8.67 per- cent more than the lower income group. The middle income group spends 10.5 percent more than the lower income group for services and the upper income group spends 8.5 percent more than the middle group for services. The expenditures for services changes more than the expenditures for grain products at retail. The average per capita income of the 32,000 and more income group is $2,941.70. This group contains 140 family years with a total of 346.84 persons. The average family contains 2.48 persons. The middle income group has an average per capita in- come of $1,623.91. One hundred and twenty family years are in this income group containing a total of 404 persons. The average family contains 3.37 persons. 1All income and expenditure figures in this chapter are per capita figures unless otherwise stated. 45 The per capita income of the $2,000 and above group is 81.15 percent higher than the income of the 81,350 and 81,999 group. The average family size of the $1,350 to 31,999 is notably larger than the upper group. The low income group has a per capita income of $1,022.57. A total of 304 persons are represented in 80 family years. The average family contains 3.80 persons. The middle income group has a per capita income 58.8 percent higher than the lower group, and the upper group has an income 187.7 percent higher than the lower group. The average family size of the lower group is almost 0.5 per- sons larger than the middle group and is almost 1.4 persons larger than the upper group. The wide difference in family size is due to the na- ture of the methods used. By grouping the family years according to income per person, the smaller families fall in the higher income groups. One family year in the upper in- come group contains eight persons, one family year contains five persons, 18 family years contain four persons, 21 fam- ily years contain three persons, 96 family years contain two persons, and three family years contain between two and three persons. On the other hand, the lower income group has two fam- ily years containing eight persons, three containing seven persons, eight containing six persons, 11 containing five persons, 23 containing four persons, six containing three persons, and 27 containing two persons. It is apparent that 45 the families with the greater number of persons fall in the lower income groups. Time Series Data The time series data is derived from the expenditures of 521.4 persons falling into 171 primhry and secondary years. The $2,000 and above income group contains 65 pairs of years. There are 150.4 persons represented in these 65 pairs of family years. The average per capita income in the primary years is $2,974.10 and in the secondary years is 33.302.93, an increase of 11.06 percent. The average family size is 2.31 persons. The 81,350 to $1,999 income group represents 196 people in 58 primary and secondary family years. They have an average per capita income of $1,601.13 in the primary years and $1,780.26 in the secondary years. Income increases by an average of 11.19 percent per person in the secondary years. Each family contains 3.38 persons. The lower income group, less than $1,349 per person, has 48 pairs of primary and secondary years. A total of 175 persons are in the group. ‘Average family size is 3.65 per- sons. Average per capita income in the first year is $1,016.80. After an increase in income, average per capita income is $1,255.83, an increase of 23.51 percent per person. The second classification utilizing only two income groups divides the families according to whether income per capita is below or above 81,600. When this method is 47 utilized 242.4 persons in 94 family years are in the group with an income of $1,600 or more. The average family size of the $1,600 and above income group is 2.57 persons. Income per person averages $2,509.75 before an income increase and $2,787.37 after the increase, an increase of 11.06 percent. The low income group, each family having a per capita income of less than $1,600 in the primary years, contains 279 persons in 77 primary and secondary family years. The average family size is 3.62 persons. Per capita income in- creases from $1,188.57 in the primary years to $1,400.75 in the secondary years, an increase of 17.85 percent. In the primary years, the $2,000 and above income group (of the three income groupClassifications) spends $38.45 per person on grain products of which 88.7 percent is for market services. In the secondary years, expenditures in- crease 2.38 percent to 339.37 per person of which 88.8 per- cent or 834.97 is for services. In the secondary years ex- penditures for services increase 2.54 percent. In total, 1.29 percent of income is spent on grain products in the primary years and 1.19 percent in the secondary years. The increased expenditures for grain products are small compared to the 11.06 percent increase in income. Expenditures for services increase slightly more than the expenditures for all cereal products. The 81,350 to 81,999 per capita income group spends 335.73 per person for grain products in the primary years. During the primary years, the proportion of expenditures 48 spent for services is 88.5 percent, slightly less than the corresponding figure of the upper income group. In the secondary years, the middle income group spends 839.46 per person for grain products, even more than the amount spent by the 32,000 and above income group after an income increase. The preportion of cereal product expenditures spent for serv- ices increases to 89.12 percent. The change in retail ex- penditures is 10.44 percent and the change in expenditures for services is 11.24 percent compared to an income increase of 11.19 percent. The middle income group initially spends less than the upper group for grain products. After an income in- crease the amount spent per person is almost the same (8.09 difference) although the income of the middle group does not increase as much in money terms as the income of the upper group. The less than 81,350 income group spends 85.01 less than the middle group for grain products in the primary years. The lower group spends 830.72 per person for grain products of which 86.65 percent is for services. After an increase in income, expenditures for grain products increases 6.11 percent to $32.60 and expenditures for services increase to 87.13 percent of the expenditures for grain products. Al- though the expenditures for grain products increase in money terms, as a percent of income, they decrease from 3.02 per- cent to 2.60 percent. It is significant that in only one case does the per- 49 cent of income spent on services increase (and then only by 0.01 percent). The middle income group spends 1.97 percent of their income on services in the primary years and 1.98 percent after an income increase. Expenditures for the Product Groups The data for expenditures made by three income groups for the product groups is unreliable. For some product groups, the middle income group spends less per capita than either of the other groups. In other cases the middle group spends more, and in still other cases it is just between the higher and lower income groups. When the middle income group is divided into two groups,81,350 to 81.599 and 81,600 to 81,999. the expenditures by one part of the middle in-. come group may be lower than the expenditures of the upper and lower income groups, and at the same time the other part of the middle group's expenditures are higher than all other groups. Because of the small size of the sample used in deriving the data for the middle income group, the ex- penditure pattern of one or two families might have an undue effect on the expenditure pattern of the entire group. Since the data from this group appears to be unreliable, it is necessary to limit the discussion to the two income group classification. Mill Products The expenditures made by the two income groups for mill products in the primary years differ by only 8.20. 50 The high income group (81,600 and more) spends $1.84 for mill products during the primary years and reduces its ex- penditures to 81.71 after an income increase. Retail ex- penditures decrease 7.41 percent. The low income group spends 81.64 before the income increase and after receiving an increase in income,expenditures for mill products decrease to 81.53 per person. In both cases, expenditures for serv- ices embodied in mill products decrease proportionately more than retail expenditures for mill products. The high income group spends 81.01 for services or 54.7 percent of retail expenditures for mill products before an income increase and spends 8.90 or 52.6 percent of retail expenditures for mill products after the income increase. EXpenditures for serv- ices decline 11.10 percent. The low income group's expend- .itures for services decline from 8.90 to 3.79, a decrease of 12.58 percent. The proportion of the grain product budget spent on mill products is low for both income groups. The 81,600 and above income group spends 4.71 percent of its total grain product budget on mill products in the primary years and 4.08 percent in the secondary years. The 81,599 and be- low income group spends 5.29 percent in the primary years and 4.61 percent in the secondary years. Although the difference in expenditures of the two in- come groups for mill products is very small as measured by either portion of income or measured by portion of retail expenditures for grain products, the low income group spends 51 more. Breakfast Cereals The group with a per capita income of 81,600 and above spends $3.36 for breakfast cereals before an income increase and 33.58 afterwards. The low group spends 33.53 before an income increase and 33.83 afterwards. The higher expenditure rate of the low income group is best explained by the larger number of children in the group. The high income group increases expenditures for breakfast cereals 6.74 percent whereas the low income group increases expenditures for breakfast cereals 8.59 percent. The high income group spends 82.88 per capita on services em- bodied in breakfast cereals before an increase in income, and 33.10 after an increase in income. The proportion of retail expenditures spent for services increases from 85.8 percent to 86.4 percent. Expenditures for services increase 7.52 percent. The low income group spends 83.02 for serv- ices before an increase in income and_$3.32 afterwards-an increase of 10.01 percent. The proportion of retail expend- itures spent for services increases from 85.5 percent to 86.6 percent. Expenditures for cereals are the third highest of the seven groups comprising 8.59 percent and 11.35 percent of total expenditures for all grain products of the high and low income groups respectively. 52 Mixes The 81,600 and above income group decreases its re- tail expenditures for mixes from $2.53 to $2.47, a decline of 2.27 percent after an increase of income. The below 81,600 income group increases its expenditures from $2.02 to $2.07, an increase of 2.77 percent. Although the high group decreases its expenditures for mixes, it increases the pro- portion for services 0.2 percent, whereas the low group de- creases the pr0portion for services 0.1 percent. The high group spends 91.31 percent of mix expenditures on services before an income increase and 91.48 percent after an increase in income. The low group spends 90.73 percent of its ex- penditures for mixes on services before the income increase and 90.55 percent afterwards. The mixes comprise 6.46 per- cent of the low income group's grain product budget in the primary years, and 6.48 of the high income group's grain product budget in the primary years. Macaroni-Spaghetti The macaroni-spaghetti product group is the least im- portant of the seven.produ0t groups. The high income group spends $1.26 per person per year before an income increase and 81.26 after an increase. The low group spends 81.20 before an income increase and 81.21 after one. The high group's expenditures for services in the product group de- crease 1.22 percent after an income increase. Services ex- penditures are 85.30 percent of the retail expenditures in 53 the primary years and decrease to 84.19 percent in the sec- ondary years. The expenditures for this product group is 3.22 per- cent of the total grain product expenditures made by the high income group and 3.87 percent of the expenditures made by the low income group. Crackers Persons having a per capita income of $1,600 and more spend 82.35 for crackers before an increase in income. Of the 82.35. 32.03 or 86.34 percent is for services. After an increase in income, the group spends 82.40 for crackers of which $2.07 is for services. Expenditures for services are 86.46 percent of the retail expenditures in the secondary years. Expenditures for the cracker product group increase 1.96 percent. Expenditures for services increase 2.11 per- cent. Persons with a per capita income of less than 81,600 in the primary years spend 81.58 per person on crackers be- fore an income increase, and after the increase the group also spends 81.58. The low income group spends 81.37 for services in both years. The cracker product group is one of the less import- ant product groups. The high income group spends 6.01 per- cent of its total grain product expenditures on crackers and the low group spends 5.08 percent of its total grain product expenditures on crackers. 54 Bread and Rolls The single most important product group is bread and rolls. In the primary years the high income group spends 38.70 percent and the low group spends 42.33 percent of their grain product expenditures on bread and rolls. Bread and rolls is the only product group which over 1 percent of to- tal per capita income is spent. Persons having a per capita income of $1,600 or more in the primary years spend $15.15 on this product group be- fore an increase in income. After the increase, expenditures increase to 815.40 per person, an increase of 1.64 percent. During the same period the expenditures for services rise faster, increasing from 813.25 to 813.49 per person, an in- crease of 1.87 percent. The proportion of retail expend- itures spent for services purchased during the primary years is 87.45 percent and is 87.64 percent in the secondary years. The lower income group spends less per person, but in- creases its expenditure level slightly more. The expend- itures for bread and rolls are $13.17 in the primary years and 813.48 in the secondary years, an increase of 2.37 per- cent. During the primary years 86.50 percent of expend- itures or $11.39 are for services. During the secondary years, $11.67 or 86.60 percent is for services, an increase of expenditures for services of 2.49 percent. Bakery Products The bakery products group is only second in import- 55 ance to bread and rolls. Together the two product groups comprise about 70 percent of all grain product expenditures. In the primary years, the high income group spends 32.31 per- cent of all its grain product expenditures on bakery products. During the same period, the low group spends 25.60 percent of its grain product expenditures on bakery products. The outstanding feature of this product group is the high quantity of services in it. Of the $12.65 spent by the high income group in the primary years, $12.15 or 96.07 per- cent is for services. During the secondary years, the high income group spends 815.00 for bakery products of which ' 314.36 or 95.71 percent is for services. The eXpenditures for bakery products increase 18.58 percent, the most the ex- penditures for any product group increase. The expenditures for services increase 18.15 percent. The low income group spends less per person. In the primary years, the low income group spends $7.96 per person for bakery products of which 95.94 percent is for services. Expenditures increase 18.09 percent in the secondary years to $9.41, of which 95.87 percent is for services. Expenditures for the Grains Expenditures for products made from wheat, corn, and durum make up 95 percent of all cereal product expenditures. Expenditures for wheat products alone account for 90 per- cent of all grain product eXpenditures. The eXpenditures for the products of the other grains are so small the data is unreliable. 56 Wheat When computed cross-sectionally, the $2,000 and above income group spends 90.24 percent or 833.95 of its total retail expenditures for cereal products on wheat products. The 31,350 to 31.999 income group spends 89.00 percent or 331.09 of its total expenditures on wheat products, and the below $1.350 group spends 86.91 percent or 327.94 of its total expenditures on wheat products. The percentage of wheat product expenditures made for services embodied in them is also related to income. The lower income groups spend a smaller percentage of their ex- penditures for wheat products for services. The upper in- come group spends 89.20 percent of its wheat product ex- penditures on services, the middle income group spends 88.58 percent on services, and the lower income group spends 87.24 percent on services. The upper income group spends 9.20 percent more than the middle income group for wheat products. The middle group spends 11.28 percent more than the lower group, and the upper group spends 21.52 percent more than the lower group. The time series calculations for wheat products give similar results. The upper income group spends $34.83 on wheat products in the primary years and 335.77 in the sec- ondary years, an increase of 2.69 percent. or the expend- itures for wheat products in the primary years, 89.09 per- cent is for services embodied in them. After an increase in 57 income, 89.19 percent of the wheat product expenditures is for services. The eXpenditures for services increase 2.80 percent after an increase in income. The upper income group spends 90.59 percent of all its grain expenditures on wheat products in the primary years and 90.86 percent in the sec- ondary years. The income group having a per capita income of $1,350 to 31,999 in the primary years spends 831.96 or 89.45 per- cent of all its cereal product expenditures for wheat pro- ducts. After an income increase the same group spends 335.53 or 90.03 percent of its grain product eXpenditures at retail for wheat products. Expenditures for services account for 88.90 percent of eXpenditures for wheat products in the primary years and 89.60 percent in the secondary years. To- tal wheat product expenditures increase 11.15 percent follows ing an income increase. Service expenditures increase 12.02 percent. The lower income group spends 826.74 for wheat pro- ducts or 87.04 percent of its grain product expenditures for wheat products in the primary years. In the secondary years for wheat products, this group spends 828.54 or 87.53 percent of its grain product expenditures, an increase of expenditures of 6.71 percent. During the same period ex- penditures for services increase 7.24 percent. In the pri- mary and secondary years 87.14 percent and 87.57 percent of retail expenditures for wheat products are for services. 58 Corn Because per capita eXpenditure levels for corn and durum are very small, only the two income group class- ification will be discussed here. The cross-sectional ex- penditure levels for corn are inversely related to income. The $1,600 and above income group spends 8.89 for corn pro- ducts and the below $1,600 income group spends $1.05. The high income group spends 85.65 percent of corn product ex- penditures for services embodied in them and the low income group spends 85.94 percent of the corn product expenditures for services. The decrease in eXpenditure level from the low income group to the high income group is 14.67 percent. The high income group spends 2.35 percent of its expenditures for cereal products on corn products and the low income group spends 3.29 percent. The time series data gives similar results. Although both income groups increase expenditures for corn.products with an increase in income, the low income group increases its expenditures more. The Opposite is true for wheat pro- ducts. The high income group spends 3.87 for corn products in the primary years and 8.89 in the secondary years, an in- I crease of 1.45 percent. The low income group spends 81.01 in the primary years and $1.03 in the secondary years, an increase of 1.94 percent. During the primary years, the high group spends 85.45 percent of its corn product expend- itures for services. This figure increases to 86.11 percent 59 after an income increase. During the primary years, the low income group spends a greater pr0p0rtion of its corn pro- ducts expenditures for services than the high income group. The low income group spends 85.65 percent on services during the primary years and following an income increase spends 86.55 percent of its corn product expenditures on services. Although both income groups spend a very small portion of their grain product expenditures on corn products, the low income group spends a higher portion. The low income group spends 3.25 percent and the high income group spends 2.23 percent of grain product eXpenditures on corn products. Durum The expenditure pattern of durum products is quite dif- ferent from corn products. The high income group spends more for durum products than the low income group and main- tains its expenditure level after an income increase whereas the low income group reduces its level of expenditures after an income increase. The high income group spends $1.20 in the primary years and 31.21 in the secondary years, an in- crease of 0.98 percent. The low income group spends $1.14 in the primary years and reduCes its expenditures to $1.12 after an income increase, a decrease of 1.83 percent. The high income group spends 85.02 percent of durum product ex- penditures for services embodied in them. The low income group spends 83.66 percent of expenditures for services in the primary years. After an increase in income, the high in- come group decreases its pr0portion of retail expenditures 60 spent for services to 84.27 percent and the low income group increases the pr0portion of retail expenditures made for services to 83.78 percent. The low income group spends 3.66 percent of all its grain product expenditures on durum products and the high income group spends 3.06 percent of its grain product expenditures on durum products. CHAPTER V CONCLUSIONS, LIMITATIONS, AND IMPLICATIONS Summary of Results Income Elasticities of Demand for Cereal Products The income elasticity for services is 0.55, only slightly higher than 0.51, the income elastiCity for grain products. The income elasticity for grain is 0.21. These results indicate that as income increases the demand for grain products increases at a rate one-half the percent in- crease in income. Most of the increased expenditures are for services. Income Elasticities of Demand for Grains Used as Raw Materials The income elasticity for wheat is 0.29 for the group having a per oapita income of $1,600 and more. The low in- come group has an income elasticity for wheat of 0.19. The high and low income groups have income elasticities for wheat products of 0.67 and 0.42 respectively. The income elasticities for services embodied in wheat products are 0.71 and 0.45. The increase in expenditures for wheat pro- ' ducts after an increase in income follows the same pattern as the expenditures for all grain products. 62 As income increases the expenditures for corn de- creases. The $1,600 and above group has an income elastic- ity for corn of -0.31. The low income group has an income elasticity for corn at -0.28. The expenditures for corn products and services in corn products increase after an in- come increase. The high and low income groups' income elasticities for corn products are 0.14 and 0.12 respec- tively. The income elasticities for services embodied in corn products are 0.21 and 0.18. The expenditures for durum products and the cereal, durum, increase slightly when the income of the high income group increases. The low income group decreases its ex- penditures for durum products and the cereal, durum, when income increases. The high income group shifts expenditures to products containing more durum and less services after an income increase. The low income group does the same thing, but to a lesser extent. Income Elasticity of Demand for the Product Groups1 Mill products contain the least services of any pro- 1An original purpose of this thesis was to study the effect of fan ly size on expenditure level. Accordingly each of the cross-sectional income groups was divided in two parts according to family size, 2 to 3.9 persons and 4 and more persons. It was found that expenditure for cereal pro- ducts of the groups with 2 to 3.9 ersons spent 340.33 340.74, 839.7 and 840.52 for the 32,000 and more, $1,600 to 31.999, 31.350 to $1,599, and 80 - $1,349 income groups re- spectively. In the same order the groups with 4 and more ' persons spent 329.28, 336.27, 828.80, and $29.55. These results were considered to be inconclusive due to the small sample. 63 duct group. The elasticities for mill products, services em- bodied in them, and grains used as raw materials are all negative. The reduction in expenditures is greatest for those products in the group which contain larger amounts of services. As a result the income elasticity for services is the lowest of the three elasticities. The elasticities for breakfast cereals are the second highest of any product group. Although the elasticities for services in breakfast cereals are relatively high, the income elasticity of grain is approximately zero indicating that there is a shift to breakfast cereals containing more services. Because families with the most children are in the lower income groups, the elasticities computed cross- ssctionally are negative. The high income group decreases expenditures for mixes after an income increase, but the low income group increases expenditures after an income increase. In both cases the expenditures for grains in mixes change the most. The low income group increases its expenditures for grain even more than the expenditures for services, and the high income group decreases its expenditures for grain more than its expenditures for services. Apparently it is in those pro- ducts with a higher pr0portion of grain that demand fluc- tuates most. Demand for macaroni and spaghetti products is almost unaffected by changes in income. The high income group in- creases purchases of products with more services when income 64 increases. The low income families do not increase their expenditures but buy slightly more grain. Expenditures for cracker products increase slightly when the high income group has an increase in income but remains almost stable when the income of the low group in- creases. Both income groups shift to low service products after an income increase. Expenditures for bread and rolls increase only slight- ly after an income increase. The increase of expenditures is almost solely for more services. Expenditures for grain are almost constant. The bakery products group is the only group in which expenditures increase pr0portionate1y more than income. Be- cause after an income increase there is a shift to products with a larger grain content, the elasticity coefficient for services is smaller than for grain. The bread and rolls and bakery products groups account for almost 70 percent of grain product expenditures. Ex- penditures for bread and rolls are about $15.00 per person and expenditures for bakery products are between $7.00 and 812.00. Total grain expenditures vary between $29.00 and $35.00 per person. Cross-Sectional Versus Time Series Elasticities The elasticities computed by the cross-sectional meth- od show no constant relation to those computed by the time series method. The two income group cross-sectional elastic- 65 ities for total retail expenditures, breakfast cereals, bread and roll products, and bakery products are lower than the two income group time series elasticities. The cross- sectional elasticities for the mixes and the macaroni-spa- ghetti groups are between the high and low income groups time series elasticities. Mill products and cracker product groups have cross-sectional elasticities higher than the time series elasticities. It is interesting to note that those groups with the highest expenditures and time series elasticities have cross- sectional elasticities which are lower than the time-series elasticities. However, there is no reason to assume a correlation. These results deviate from what was expected. Cross- sectional elasticities are expected to be higher than time series elasticities. It is possible that when income in- creases, the expenditures for some products increase rapidly and then decrease as a new equilibrium is reached. It is also possible that those products with an increasing demand in the long-run have higher time series elasticities than cross-sectional elasticities. The validity of the Hypotheses The primary objective of this study is to determine the relationship between changing income and the expend- itures for services in grain products. It was hypothesized that the income elasticity for services embodied in cereal products would be found to be above 1.0 and the income 66 elasticity for grain products and for grain embodied in them would be approximately 0.5 and 0.0 respectively. The latter two hypotheses are correct. The income elasticity for grain products is 0.51 and the income elasticity for grain is 0.21. The hypothesis that income elasticity for services would be greater than one appears to be wrong. The elasticity obtained is 0.55. The failure to achieve the predicted results could have occurred in any of three ways, incorrect data or computations, incorrect methodology or an incorrect hypothesis. Spot checks have been made on the data tabulations as computed by the I.B.M. Research Center at Michigan State University. No mechanical mistakes were found. The cal- culations made by the Statistical Pool of the Agricultural Economics Department of Michigan State University were thoroughly checked by the author and the Statistical Pool. In addition checks were built into the calculations so that it was impossible for any recurrent error to have run through the entire calculations. The methodology certainly has some limitations. The sampling techniques had some weaknesses which will be dis- cussed more fully later in this chapter. The general methodology of this thesis is substanti- ated by a completely independent source. The United States Department of Agriculture reported in the Marketing and Transpgrtation Situation that the farmer's share of retail expenditures for grain products during the period 1955 to 67 2 1958 decreased from 16 percent to 14 percent. The results of the thesis are in considerable agreement with the data of the United States Department of Agriculture. Expenditures for grain made up 12 percent of the total expenditures during the years 1955 to 1958. It is reasonable to eXpect the panel to spend slightly less for grain since the average income of the panel member was higher than the United States average income. The third possible cause of the unpredicted results is an incorrect hypothesis. An important tool in our analysis will be the following formula which was first presented in Chapter I: 8 + e = e + 2 61 (e - e ) s t s + s t g 2 l where s8 = the income elasticity of services s8 = the income elasticity of grain ‘t = the income elasticity of total product g1 = expenditures for grain in the primary years g2 = expenditures for grain in the secondary years 31 = expenditures for services in the primary years s2 = expenditures for services in the secondary years 2Agricultural Marketing Service, U.S. Department of Agriculture. The Marketing and Transportation Situation (January, 1957 and January, I959? pp. 4549. 68 Substituting our hypothesis into this formula we find that the expenditures for services and grains must be equal. 51+32 1.0=Os5+———(Os5-O) s1 + s2 s"1“‘12=$1“552 If the income elasticity for services is above one, then the pr0portion of services to grains must be lower. + 2.0 = 0.5 + .SJ—_§2 (0.5 _ 0) 814-82 3(81 + s2) = g1 + g2 In order to have an income elasticity for services of two, only 33 percent of all expenditures could be for services. Therefore, the expenditures for services over the two year period must be no more than 50 percent of the sum of expenditures over the two year period. But there are no grain products with less than 50 percent services. There- fore, it is impossible that the sum of the expenditures for services be less than 50 percent of the total expenditures over the two year period. Thus our hypothesis of an income elasticity for services of greater than 1.0 could not pos- sibly have been valid. This was learned as the study pro- grossed. The Limitations of the Study The Sample The directors of the consumer panel, Doctors Quacken— 69 bush and Shaffer attempted to make the panel representative of the City of Lansing. The method of selection of the pan- el was discussed in Chapter II and need not be repeated here. The representativeness was maintained by making periodic samples of Lansing and adjusting the panel accordingly. Sample censuses were made in 1950, 1954, 1956, and 1958. The final sample census was made in 1958 and compared to a survey of the final panel. The results of the sample census indicated that those families with fewer children and more education had a proportionately larger representation in the panel than actually existed in the Lansing population. The sample census showed that 27 percent of all families had children under ten years of age whereas only 15 percent of the panel had children under ten. Forty-six percent of the panel were families in which the wife was over 40 years of age and with no children in the household, although only 37 percent of the sample census population were in the same category. The sample census showed 44 percent of the housewives of Lansing had 12 or 13 years of education. In the panel, 36 percent of the housewives had 12 or 13 years of education. On the other hand, 20 percent of all Lansing housewives had 14 or more years of education, but 29 percent of the panel housewives had 14 or more years of education. The characteristics used to select and maintain the sample were almost purely demographic, and one can naturally expect some unrepresentativeness due to a self-selection 70 bias. The directors of the panel were quite conscious of this problem and attempted to make some measurement of it after the panel was concluded. The final sample survey in- cluded questions which gave some indications of non-demo- graphic characteristics. The final panel was asked the same questions. The final sample census showed that the panel members tended to be more economical than the average population. Ten percent more of the final consumer panel than the sample survey home canned and gardened. 'Whereas 43 percent of the sample census neither home canned nor gardened, only 36 per- cent of the final panel did neither. A question was asked regarding what determines the size of the family's food bill. Forty-seven percent of the panel indicated that the amount of money available and willingness to spend deter- mined the size of the food bill, and 49 percent said that it was a function of what the family wanted to eat. 0n the other hand, the sample census showed 36 percent thought their food bill was determined economically and 58 percent thought they determined their food bill hedonistically.3 Still another question seemed to draw out the same differences in characteristics. The final panel and sample survey were asked how their food budget was determined. 3Gerald G. Quackenbush and James D. Shaffer. Collect- ing Food Purchase Data by Consumer Panel -— A Methodological Report on the M. S. U. Consumer Panelil951-SE. Technical Bulletin 279 (East Lansing, Michigan State University, 1960) pps 1 -15s 71 There were no significant differences in the number of re- sponses to: (1) our food budget is what is left over after having paid the necessary bills, (2) we have a fixed food budget, and (3) we have no budget, but do have in mind a general maximum amount. It was found that 58 percent of the panel and 50 percent of the sample survey felt they bought what they wanted but were not extravagant. On the other hand only 1 percent of the panel, but 7 percent of the sam- ple survey stated that they bought just what they wanted without concern for the cost of food.4 These latter ques- tions are of course subject to the disadvantage that some of the possible answers are socially unacceptable and there would be some hesitancy in giving them, particularly so for the panel since they had quite a bit of contact with the parties making the survey. On the other hand, the results of the above series of questions are consistent so that it may be concluded that there was some self-selection bias causing the panel to be more economically oriented than the p0pulation-at-large. In addition to the survey discussed above, a survey of a psychological nature was made and compared to a similar survey of the panel members. One portion of the psycho- logical questionnaire attempted to determine differences in the role perception of the housewife. The panel members indicated they awarded more importance than the sample sur- 4Ibid., p. 15. 72 vey respondents to such things as keeping up one's own sp- pearance, cooking, serving a variety of meals, efficient home, sewing, and baking skill. Those checked less often by the panel members were, a companion to her children, raising children, 000perative, working in local civic projects. The panel members more often perceived their role to be in the area of good housekeeping and less often in the affairs of family and community.5 The second part of the questionnaire had to do with self-perception. The results were consistent with the role perception, demographic, and budget determination question- 6 naires. We can conclude that the average homemaker who was willing to participate in the sample was more conscious of food and food expenditures and probably spent less on food than other persons of similar demographic characteristics. The application of these conclusions to the results of the thesis is very difficult. Assuming that the lower and upper income groups had lower expenditure levels in the same proportion to income, then the cross-sectional elasticities would be unaffected. The time series elasticities would be reduced by the same amount in each income group. There would be a tendency for the income elasticity of services to 5Ibid., p. 16. 6Ibid., p. 16. 73 be even further reduced since the person described above would tend to keep eXpenditures for high service products low. Conditioning The greatest problem of a consumer panel Operating over a long time period is that participation in the panel is a learning experience. The maintenance of a weekly food purchase diary enables the housewife to evaluate the effi- ciency of her purchasing activities. If a record is kept at home, weekly comparisons can be made. The directors of the panel recognized this problem and queried the final pan- el members about it. Of the 282 families who responded, 246 or 88 percent felt that participation in the panel had an effect on their knowledge of prices. Of these 246, 148 or 53 percent of the 282 respondents felt that participation had a great effect on their knowledge of food prices. 0f the 282, 178 felt that keeping the diary caused them to be more price con- scious and could give specific examples of how their ex- penditure pattern changed as a result. Seventy-two percent of the panel thought that participation.had at least a little effect on a person's ability to do a better job of food buying. Forty-six percent thought participation had a considerable effect on one's ability to buy food efficiently. Seventy-three percent indicated they changed stores as a re- 74 sult of being a member of the panel.7 Contradicting the above statements was the response to a question regarding the food purchasing pattern. Of those responding. 38 percent indicated no effect on their food purchasing pattern, 39 percent indicated only minor effects on their food purchasing pattern, and only 23 percent in- dicated considerable effects on their food purchasing pat- tern. A few questions were asked to determine what propor- tion of the panel used the diary with the conscious attempt to change their purchasing pattern. Thirty-eight percent indicated they sometimes added up the amount spent in a week. Fifty-eight families or 21 percent indicated they kept a record of food purchases after having sent in the diary. 0f the 58 families, 26 had kept food records before joining the panel. 0f the total number of respondents 42 or 15 percent indicated they had kept records before join- ing the panel and 101 or 36 percent thought they would in the future. Nine families indicated they had kept records before joining, but would not continue to do so and 68 fam- ilies indicated they hadn't before, but would continue to do so after the panel was discontinued.9 71bid., pp. 24-25. 81b1ds’ pps 25‘26s 9Ibid., pp. 26-27. 75 The final question asked was what effect on total food expenditures did participation in the panel have. 0f the 282 respondents, 231 indicated no effect, 49 indicated some effect, and two did not respond to the question. Those who indicated some effect reported an average decrease of ex- penditures of $1.89 or 3.29 per week per family on an en- tire panel basis.10 The question of whether participation in the panel affected expenditures remains unanswered. The responses to the several questions are quite contradictory and one's biases tend to determine the conclusion one draws. Doctors Quackenbush and Shaffer felt that the $.29 figure was a good estimate of the effect of conditioning.‘ This writer disagrees because most of the panel had no measure of their expenditure before joining the panel and the expenditure pattern changes so slowly that the conditioning probably was not observable to the panel member. Conclusions’and Implications The hypothesis that the income elasticity of demand for services in grain products is greater than one is not valid. Eighty-eight percent of grain product eXpenditures are for services and as a result, the eXpenditures for serv- ices can not increase very much relative to grain. The income elasticity of a product is not necessarily 10 Ibid., pp. 27-28. 76 related to the quantity of services in the product. The bread and rolls product group has a high proportion of serv- ices and a low income elasticity. In the future as income increases, the demand for grains can be eXpected to increase only slowly. Demand ex- pansion plans which allow the consumer free choice of his purchases can be expected to have a negligible effect on the demand for grains. The only product group which will have a pr0portionate increase in expenditures as income increases is bakery pro- ducts. The demand for the other product groups with the ex- ception of mill products will increase only slightly in re- sponse to income increases assuming a stable or increasing population. Since the income elasticity of mill products is negative, demand will increase only if p0pulation grows at a rate fast enough to make up for a negative income elasticity or if other factors change. APPENDIX A Table l 78 Income Elasticities of Demand for Grain Products, for Market Services Embodied in Them, and for the Grains Used as Raw Materials Computed by the Cross-Sectional Method Income Groups Elasticities Grain Low Income High Income Products Services Grains 31.350-81.999 $2,000- 0.1283 0.1399 0.0386 80,000-81,349 $1,350-81,999 0.1829 0.2129 -0.0711 80,000-31,349 $2,000- 0.1622 0.1859 -0.0106 30,000-31.599 $1,600- 0.2502 0.2741 0.0752 Table 2 Income Elasticities of Demand for Grain Products, for Market Services Embodied in Them, and for the Grains Used as Raw Materials Computed by the Time Series Method Income Group Grain Products Services Grains $0,000- 0.5093 0.5493 0.2090 $0,000-81,349 0.2819 0.3086 0.1050 1,600- 0.6314 0.6734 . 0.2970 0,000-81.599 0.3792 0.4142 0.1330 79 Table 3 Income Elasticities of Demand for Mill Products, for Market Services Embodied in Them, and for the Grains Used as Raw Materials Computed by the Cross-Sectional Method Income Groups Elasticities Mill Low Income High Income Products Services Grains $1.350-31,999 $2,000- 0.1936 0.2101 0.1743 $0,000-41.349 $1,350-81,999 0.0993 0.1642 0.0250 $0,000-31,349 $2,000- 0.1618 0.2019 0.1156 $0,000-81.599 81,600- 0.1372 0.1447 0.1284 Table 4 Income Elasticities of Demand for Mill Products, for Market Services Embodied in Them, and for the Grains Used as Raw Materials Computed by the Time Series Method Income Group Mill Products Services Grains 1.350—81.999 -1.4376 -l.8174 -0.9964 $0,000-t1,349 -0.0181 -0.2493 0.2372 31,600- -0.7340 -1.1207 -0.2857 80.000-81,599 -0.4557 -0.8191 -0.0427 80 Table 5 Income Elasticities of Demand for Breakfast Cereals, for Market Services Embodied in Them, and for the Grains Used as Raw Materials Computed by the Cross-Sectional Method Income Groups Elasticities Breakfast Low Income High Income Cereals Services Grains 81.350-31.999 $2,000- -0.l648 -0.1698 -0.1350 0,000- 1,349 1,350-319999 'Os0363 -0s0198 -0s1423 0 ,000“ 1 g 349 2 g 000- -0 s 1153 "O s 1100 “'0 s 1471 $0,000-31.599 $1,600- -0.1518 -O.1528 -0.1455 Table 6 Income Elasticities of Demand for Breakfast Cereals, for Market Services Embodied in Them, and for the Grains Used as Raw Materials Computed by the Time Series Method Income Group Breakfast Cereals Services Grains 1.350-31.999 0.7345 0.7946 0.3477 0,000-81,349 0.4974 0.5653 0.0981 $1,600- 0.6219 0.6910 0.1935 80,000-81.599 0.5027 0.5815 0.0167 81 Table 7 Income Elasticities of Demand for Mixes, for .Market Services Embodied in Them, and for the Grains Used as Raw Materials Computed by the Cross-Sectional Method Income Groups Elasticities Low Income High Income Mixes Services Grains $1.350-tl,999 82,000- 0.1693 0.1796 0.0581 30.000- 1.349 $1.350-81.999 0.4015 0.4204 0.2121 0,000- 1,349 $2,000- 0.2881 0.3030 0.1341 $0,000-31.599 $1,600- 0.0811 0.0877 0.0129 Table 8 Income Elasticities of Demand for Mixes, for Market Services Embodied in Them, and for the Grains Used as Raw Materials Computed by the Time Series Method Income Group Mixes Services Grains $2,000- -Os3840 -Os3677 "Os5680 $1.350-tl.999 0.0726 0.0137 0.6516 80,000-81,349 0.2130 0.2452 -0.0920 §I,600- -0.2192 -0.2005 -0.4128 0,000-81,599 0.1668 0.1551 0.2773 82 Table 9 Income Elasticities of Demand for Macaroni—Spaghetti Products Group, for Market Services Embodied in them, and for the Grains Used as Raw Sectional Method Materials Computed by the Cross- Income Groups Elasticities Macaroni- Spaghetti Low Income High Income Products Services Grains 81.350-81,999 $2,000- 0.0020 0.0039 -0.0095 $0.000-81.349 81.350-81.999 -0.1366 -0.0786 -0.4352 30,000-81,349 32,000- -0.6290 -0.0345 -0.2099 $0,000-81,599 $1,600- 0.0242 0.0540 -0.l345 Table 10 Income Elasticities of Demand for Macaroni-Spaghetti Products Group, for Market Services Embodied in Them, and for the Grains Used as Raw Materials Computed by the Time Series Method Income Group Macaroni- Spaghetti Products Services Grains 32,000- 0.4132 0.3441 0.7936 31.350-81.999 -0.0223 -0.0832 0.3284 $0,000-31,349 -0.1099 -0.0958 -0.l799 81,600- 0.0075 -0.ll69 0.6993 83 Table 11 Income Elasticities of Demand for Cracker Product Group, for Market Services Embodied in Them, and for the Grains Used as Raw Materials Computed by the Cross-Sectional Method Income Groups Elasticities Cracker Products Low Income High Income Group Services Grains 31.350-31.999 $2,000- 0.0866 0.0870 0.0838 80.000-81.349 31.350-81.999 0.5613 0.5890 0.3909 80,000-81,349 2,000- 0.3141 0.3273 0.2330 80,000-81.599 81,600- 0.4120 0.4184 0.3720 Table 12 Income Elasticities of Demand for Cracker Products Group, for Market Services Embodied in Them, and for the Grains Used as Raw Materials Computed by the Time Series Method Cracker Income Group Products Group Services Grains 2,000- 0.0524 0.1042 -0.2740 1,350-81.999 0.1034 0.1036 0.1055 $0,000-81.599 -0.0221 0.0080 -0.2153 84 Table 13 Income Elasticities of Demand for Bread and Rolls Product Group, for Market Services Embodied in Them, and for the Grains Used as Raw Materials Computed by the Cross- Sectional Method Income Groups Elasticities (Bread and Rolls Low Income High Income Product Group Services Grains 81.350-§1,999 £2,000- 0.0782 0.0958 -0.0443 $0.000- 1.349 1.350-81.999 -0.0843 -0.0561 -0.2638 80,000-81,349 $2,000- 0.0071 0.0308 -0.1502 $0,000-81.599 81,600- 0.1178 0.1386 -0.0203 Table 14 Income Elasticities of Demand for Bread and Rolls Product Group, for Market Services Embodied in Them, and for the Grains Used as Raw Materials Computed by the Time Series Method Bread and Rolls Income Group Product Group Services Grains 2,000- -0.2579 -0.2331 -0.4402 1.350-31.999 0.5712 0.5812 0.5051 $0,000-81.599 0.1429 0.1498 0.0987 85 Table 15 Income Elasticities of Demand for Bakery Products Group, for Market Services Embodied in Them, and for the Grains Used as Raw Materials Computed by the Cross-Sectional Method Income Groups Elasticities Bakery Products Low Income High Income Group Services Grains $1.350-81.999 82,000- 0.2828 _ 0.2825 0.2892 $0.000-81.349 $1.350-31.999 0.6193 0.6212 0.5719 $0,000-81,599 81,600- 0.6247 0.6256 0.6060 Table 16 Income Elasticities of Demand for Bakery Products Group, for Market Services Embodied in Them, and for the Grains Used as Raw Materials Computed by Series Method the Time Bakery Products Income Group Group Services Grains $2,000- 1.0463 0.9706 2.7892 1,350- 1.999 2.0593 2.0616 2.0065 0,000- 1,349 0.7369 0.7367 0.7408 0,000-81,599 1.0125 1.0081 1.1154 86 Table 17 Cross-Sectional Income Elasticities for Wheat Products, Wheat, and Services Embodied in Wheat Products Income Groups Elasticities Wheat Low Income High Income Products Services Wheat 81.350-81.999 82,000- 0.1524 0.1644 0.0555 80.000-41.349 $1.350-81.999 0.2350 0.2683 -0.0084 $0,000-81,349 $2,000- 0.2007 0.2233 0.0291 $0,000-81.599 $1,600- 0.2964 0.3193 0.1218 Table 18 Elasticities for Wheat Products, Wheat, and Services Embodied in Wheat Products Computed by the Time Series Method Income Group Wheat Products Services Wheat $1.350-81.999 0.9971 1.0703 0.3884 $0.000-$l.349 0.3086 0.3319 0.1474 $1,6oo- 0.6684 0.7134 0.2942 80,000-81.599 0.4176 0.4486 0.1890 87 Table 19 Cross-Sectional Income Elasticities for Corn Products, Corn, and Services Embodied in Corn Products Income Groups Elasticities Corn Low Income High Income Products Services Corn 1.350-§1,999 32,000- -0.2691 -0.2816 -0.1925 0,000- 1,349 1,350-81,999 0.0273 0.0382 -0.0370 $0,000-81,349 $2,000- -0.l476 -0.1502 -0.l321 $0,000-tl,599 31,600- -0.2259 -0.2307 -0.1969 Table 20 Elasticities for Corn Products, Corn, and Services Embodied in Corn Products Com Time Series Metho puted by the Income Group Corn Products Services Corn 19350- 19999 Os2090 Os2531 -0s0679 $1,600- 0.1377 0.2111 -0.3050 88 Table 21 Cross-Sectional Income Elasticities for Durum Products, Durum, and Services Embodied in Durum Products Income Groups Elasticities Durum Low Income High Income Products Services Durum 31.350-31,999 $2,000- -0.0424 -0.0415 -0.0473 0,000. 1,349 19350-319999 “000854 -000217 -004032 0,000“ 1,349 2,000- “000653 -000348 '002172 80.000-$1.599 $1,600- 0.0203 0.0521 -0.1449 Table 22 Elasticities for Durum Products, Durum, and Services Embodied in Durum Products Computed by the Time Series Method Income Group Durum Products Services Durum 2,000- 0.4036 0.3311 0.7887 1.350-81.999 -0.2265 -0.2904 0.1548 80,000-31,349 -0.1149 -0.0946 -0.2125 $0.000-$1.599 -0.1130 -0.1039 -0.1594 LPPHDIX B 90 Table 1 Income and Family Size of Those Families Observed Before and After an Income Change (Time Series)l/ Average Per Capita Income Before Income After Income Income Groups Increase Increase 2,000- 32974.0957 83302.9255 1.600- 1.999 $1742.3077 $1935.2747 0 -$1,350 1016.8000 $1255.8286 (cont') Number Number Average Increase Income Groups of Families of Persons Family Size of Income 82,000- 65 150.4 2.31 11.06% 1,600- 1,999 29 92 3.17 11.08% 1.350- 1.599 29 104 3.59 11.27% $0 -$1.350 48 175 3.65 23.51% ;/ The income of the middle group of the three income group classification and the two group classification may be erived by multiplying income of each group above by the num- ber of persons in the group, adding this product for the appr0priate income groups and dividing by the total number of persons. The same method may be used to derive the ex- penditures for the two and three income group classifications utilizing the eXpenditure data which is included in this Appendix. 91 Table 2 Cereal Product Expenditures and Expenditures for Services Embodied in Cereal Products of Four Income Groups Before and After an Income Change (Time Series) Cereal Product Service Expenditures Expenditures Before After Before Income After Income Income Income Income Group Increase Increase Increase Increase 2,000-. 38.4521 £39.3680 34.1021 34.9694 1,600-$l,999 40.2227 45.6888 35.6476 40.8284 1.350-81.599 331.7565 833.9499. 328.0449 830.1589 80 -81,349 830.7247 832.6025 826.6218 828.4078 (continued) Proportion of Services Change of Expenditures to Retail EXpenditures 7 Bef0re After Cereal Product Service Income Income Income Group EXpenditures Expenditures Increase Increase 82,000- 2.38% 2.54% 88.69% 88.83% $1,600-81.999 13.59% 14.53% 88.63% 89.36% 31.350-81.599 6.91% 7.54% 88.31% 88.83% 80 ~81,349 6.11% 6.71% 86.65% 87.13% (continued) Proportion of Income Spent on Grain Products Before Income After Income Income Group Increase Increase 82.000- 1.29% 1.19% 1,600- 1,999 2.31% 2.36% 19350- 1,599 2.15% 2.06% 0 - 1,349 3.02% 2.60% 92 Table 3 Expenditures for Cereal Product Groups and the Services in Those Groups of Four Income Groups Before and After an Income Change (Time Series) Product Group M111 Products 82, 1, 1 80 Breakfast Cereals 32’ l 88' 82. Mixes 81 819 80 Macaroni- Spaghetti82 81. 81 80 Crackers E, 81 80 Income Groups 000- 600- -$1, 99 350— 1. 99 -81.349 000- ,600-81.999 350-31.599 ' 0349 000- ,600-81.999 350-‘19599 ' 1,349 .000- 5350-819599 ~8l.349 .000- 600-81. 999 .350-81, 599 -81.349 Product Group Before Income Increase 82. 0208 1.5604 1.6609 81. 6349 33.5043 3.1362 33.8871 3.3175 82.8197 82.0646 82.3004 81.8483 81.2091 81.3416 81.1226 81.2523 1.9983 2.9090 81.7862 81.4598 Expenditures After Income 81.8862 1.4210 1.3538 81.6287 83.6294 83.5228 34.0843 3.6838 82.7085 82.0923 82.3078 81.9330 81.2626 81.2598 81.1895 81.2237 2.0093 3.0105 81.7444 81.4757 Service Expenditures Before Income Increase Increase 81.1238 8 .826% .9368 8 .8766 3.0017 3.3578 2.8143 82.5878 81.8643 82.1059 81.6656 81.0270 81.1514 80.9556 81.0423 2.5158 81.5643 81.2469 After Income Increase .9875 .7528 .7087 .8318 ##5## 83.1456 83.0280 33.5687 3.1701 82.4900 81.8950 82.0841 81.7538 81.0647 81.0580 81.0209 81.0215 31. .7415 2 5965 81. 5347 81.2674 (continued) 93 Table 3 (continued) Expenditures for Cereal Products Groups and the Services in Those Groups of Four Income Groups Before and After an Income Change (Time Series) Proportion of Services Change of Expenditures in Product fter an Income Group Increase Expenditures Product Before After Product Income Group Service Income Income Group Groups Expenditures Expenditures(Increase) Mill Products 2, 000- -6. 66% -12.13% 55. 61% 52.35% 1, ’600- 1,999 -8. 93% - 8.87% 52. 94% 52.98% 1 350-1.599 -18. 49% -24.33% 56. 39% 52.35% -80 -81, 349 -0.38% - 5.11% 53.62% 51.07% Breakfast Cereals 82,000- 3.57% 4.79% 85 55% 86. 67% 81, 600-81, 999 12. 33% 12. 538; 32. 9g; 35. 9g; 1, 350- 1. 599 2 3 7. 3 80 -1.34 9 11. 501% 12.64% 84. 83% 86.06% Mixes 82,000- -3.94% -3.78% 91.78% 91.93% £1,600-fil.999 1.34% 1.65% 90.30% 90.57% 1.350- 1.599 0.32% -1.o4% 91.54% 90.31% 80 -81,349 4.58% 5.30% 90.12% 90.73% Macaroni- Spaghetti 82,000- 4.42% 3.67% 84.94% 84.33% 81,600-81.999 -6.10% -8.11% 85. 82% 83.98% 81.350-81.599 5.96% 6.83% 85.12% 85.83% 80 -81,349 -2.28% -2.00% 83. 23% 83.48% Crackers 2, 000- ~ 0. 5% 1.10% 86 20% 86.67% 1, ’600-81, 999 3. 9% 3.21% 86. 48% 86.25% 31 .350- -g1, .599 -2.34% -1.89% 87. 58% 87.98% 0 - 1,349 1.09% 1.64% 85.42% 85.88% (continued) 94 Table 3 (continued) Expenditures for Cereal Product Groups and the Services in Those Groups of Four Income Groups Before and After an Income Change (Time Series) Proportion of Total Retail Expenditure Spent on Product Product Group Expenditures as a Percent Group_ of Income Before After Before After Product Income Income Income Income Income Group Groups Increase Increase Increase Increase Mill Products 82,000- 5.26% 4.79% .07% .06% 81,600-81.999 3.88% 3.11% .09% .07% 81.350-81.599 5.23% 3.99% .11% .08% 80 -81.349 5.32% 5.00% .16% .13% Breakfast 1% % % % Cereals 2 000- 9.1 9.22 .12 .11 1:600-31.999 7.80% 7.71% .18% .18% 1.350- 1,599 12.24% 12.03% .26% .25% 0 -$1,349 10.80% 11.30% .33% .29% Mixes 2,000- 7.33% 6.88 .09 .08 19600’$19999 5.13% 4.58% 012% .11 $0 -319349 6.02% 5.93% 018% 016% Macaroni- 3 14% 3 1% 4% 4% Spaghetti 2,000- e 02 .0 00 §I,600- 1,999 3.34% 2.76% .08% .07% 1’350‘ 19599 3.54% 3.50% .08% 007% 80 -81.349 4.08% 3.75% .12% .10% Crackers 2 000- 5.20% 5.10% .07% .06% 81:600-81,999 7.23% 6.59% .17% .16% £10350'319599 5.62% 5.14% 012% 011% 0 - 1.349 4.75% 4.53% .14% .12% (continued) 95 Table 3 (continued) Expenditures for Cereal Product Groups and the Services in Those Groups of Four Income Groups Before and After an Income Change (Time Series) Product Group Service Expenditures Expenditures Before Affer Before Affer Product Income Income Income Income Income Groups Groups Increase Increase Increase Increase Bread and Rolls 82. 000- 815.0589 814.6575 813.2446 812.9250 1, 600- 1.999 15.2893 16.5661 13.2496 14.3931 1:350-1,599 11.8220 12.2745 10.3115 10.6997 80 -8l.349 813.9687 814.1973 812.0318 812.2524 Bakery Productsfi2, ,000- 311.8411 13.2144 11.3945 12.6152 1 600- 81. 999 13 9215 17.8163 13.3442 17.1050 31. 350- -§1:34 .599 87 9. .11% 310. 956 g 8.8135 810.5422 602 6.9443 8.1108 (continued) . Proportion of Change of Expenditures Services in After an Income Product Group Increase Expenditures Bef3re A553? Product Income Product Group Service Income Income Groups Groups Expenditures Ehcpenditures Increase Increase Bread and Rolls 82, 000- -2.67% -2.41% 87.95% 88.18% 81. 600-81, 999 8.35% 8.63% 86.66% 86.88% 81:350-8L 599 3.83% 3.76% 87.22% 87.17% 80 -81, 349 1.64% 1.83% 86.13% 86.30% Bakery Products 82,000- 11.60% 10. 71% 96.23% 95. 47% 1 600- 1 999 27. 98% 8 .8 96.01% 31:350- 1:599 19.81% @2818 98. 03% 95.88% 80 -$1,349 16.80% 16.80% 95.87% 95.87% (continued) 96 Table 3 (continued) .Expenditures for Cereal Product Groups and the Services in Those Groups of Four Income Groups Before and After an Income Change (Time Series) Pr0portion of Total Product Group Retail EXpenditure Expenditures Spent on Product as a Percent Group of Income Before After Before After Product Income Income Income Income Income Groups Groups Increase Increase Increase Increase Bread and Rolls 82,000- 39.16% 37.23% .51% .44% 1.600- 1.999 38.01% 36.26% .88% .86% 1.350- 1.599 37.23% 36.15% .80 .75% 0 - 1.349 45.46% 43.55% 1.37% 1.13% Bakery Products 82,200- 30.79; 33.57% 140% 140% 1 00- 1,999 34.61 38.99% .80% .92% 11350- 1,599 28.90% 32.39% .62% .67% 97 Table 4 Before and After an Income Increase for Four Income Groups (Time Series) Expenditures for Products Made from Wheat, Durum, and Corn and the Cereals in Those Products EXpenditures for Product Made From the Cereal Grains Expenditures Before After Before After Income Income Income Income Income Groups Increase Increase Increase Increase Wheat 2, 000- 834.8527 855.7595 35.7983 83.8668 1, 600-81, 999 36.3712 841.5278 4.0115 84.2177 1:350- $1. 599 28.0606 850.2171 5.1559 $3.254} $0 -$l:349 325.7424 828.5369 83.4385 33.5468 Durum 82,000- 8 1.1576 8 1.2076 8 .1775 8 .1928 81.600-81.999 8 1.2637 8 1.2150 8 .1830 8 .1867 81,350-81,599 8 1.0921 8 1. 0830 8 .1572 8 .1591 80 -81.349 8 1.1675 8 1.1396 8 .2035 8 .1946 Corn 2,000- .8476 8 .7979 8 .1288 8 .1149 1,600- 1.999 .9145 3 1.0260 3 .1244 3 .1361 1.350- 1.599 1.1182 1. 0628 .1527 .1405 80 -81.349 8 .9454 8 1.0095 8 .1402 8 .1373 (continued) 98 Table 4 (continued) Expenditures for Products Made from Wheat, Durum, and Corn and the Cereals in Those Products Before and After an Income Increase for Four Income Groups (Time Series) Pr0portion of Cereal Expenditures in Change of Expenditures Expenditures for Products Before After Income Income Income Groups Retail Cereal Increase Increase Wheat 32,000. 2.69% 1.80% 10.90% 10.81% .1,600-81,999 14.18% 5.14% 11.03% 10.12% 81,350-81,599 7.69% 3.14% 11.18% 10.70% 80 -81,349 6.71% 3.15% 12.86% 12.43% Durum “2,000- 4.32% 8.62% 15.35% 15.97% §1,600-%1,999 -3.85% 2.02% 14.48% 15.37% 1.350- 1.599 -0.83% 1.21% 14.39% 14.69% 80 -8l,349 -2.39% -4.37% 17.43% 17.08% Corn 2,000- -5.86% '10'49% 15.20% 14.40% 1,600-81.999 12.19% 9. 1% 13.60% 13.27% 81,350-81.599 -4.95% -7.99% 13.66% 13.22% 80 -81,349 6.78% -2.07% 14.83% 13.60% (continued) 99 Table 4 (continued) Expenditures for Products Made from Wheat, Durum, and Corn and the Cereals in Those Products Before and After an Income Increase for Four Income Groups (Time Series) Retail Expenditures for Products Made From the Grains as a Percent of Percent of Income Total Cereal Prodnm EXpended for the Expenditures Grains' Products Before After Before After Income Income Income Income Income Groups Increase Increase Increase Increase Wheat 82,000- 90.59% 90.86% 1.17% 1.08% 81,600-81,999 90.42% 90.89% 2.09% 2.15% 81.350-81.599 88.36% 89.00% 1.90% 1.84% 80 -81.349 87.04% 87.53% 2.63% 2.27% Durum 2,200-3 3.01; 3.22; .04; .02; l 00" 1 999 301 20 0 007 .0 81:350-811599 3.44% 3.19% .07% .07% 80 -81,349 3.80% 3.50% .11% .09% Corn 82,000- 2.20% 2.03% .03% .02% 81,600-8l,999 2.27% 2.25% .05% .05% 81.350-81.599 3.52% 3.13% .08% .06% 8O ~81.349 3.08% 3.10% .09% .08% 100 Table 5 Income and Family Size of Four Income Groups (Cross Sectional) Number Number Of . of Average Income Group Income Families "Persons Family Size 82,000- 82941.6999 140 346.84 2.4774 81.600-81.999 81765.8000 64 200 3.1250 81.350-81.599 81470.3883 56 204 3.6429 30 -$1,349 $1022.5558 ' 80 304 3.8000 Table 6 Expenditures for Cereal Products and Services in Cereal Products of Four Income Groups (Cross Sectional) Retail Proportion Expenditures of Services as a Income Retail Service in Retail Percent of Groups Expenditures Expenditures Expenditures Income g2, ,000- 837. 6245 833. 4083 88.19% 128% 1 600-81, 999 838. .5541 834 1139 2.18% 81.350-81,599 831. 390 27.5807 87.86% 2.13% 80 -8l,349 832.1488 27.8909 86.76% 3.14% 101 Table 7 Expenditures for Cereal Product Groups and the Services in Those Groups of Four Income Groups (Cross Sectional) Expenditures Proportion in in the Services in Product Product Service Product Group Group, Income Groups Group_ Expenditures Expenditures Mill Product 2, 000- 1.8 2 1.010 4. 8% S g1, 600 1.999 g1.629§ §0.8708 52 .7% 1:350-1,599 1.6626 0.9202 55.35% 80 -81.349 81.5830 8 .8309 52.49% Breakfast Cereals 82,000- 83.3561 82.8863 86. 00% 81,600-81.999 83.5148 83.0166 85.83% 81.350-81.599 83.8647 83.3476 86. 62% 80 -81.349 83.7529 83.2112 85.57% Mixes 82,000- 82.3957 82.1989 91.79% 1,600- 1.999 1.8597 1.6865 90.69% 1.350- 1.599 2.4790 2.2719 91.65% 80 -81.349 81.8091 81.6364 90.45% Macaroni- Spaghetti 82,000- 81.2096 81.0278 84.97% 81,600-81,999 81.2955 81.1046 85.26% 81.350-81.599 81.1225 80.9479 84. 45% 80 -81,349 81.2856 81.0628 82. 67% Crackers 2, 000- 2.0315 1. 582 86. 55 1, ’600- -§1,999 ,2.2007 81. 982 862 5% 81 350- 1.599 81.6695 81.4502 86. 86% $0 -$1.349 81.4952 81.2773 85. 43% Bread and Rolls 2, 000- 314. .4094 12.6623 87.88% 31, ,600-81. 999 15.2008 13. .2250 32. .00% 1 350- 1, 5 9 12.3733 10. 7 07 30 :319329 314M§12 2899 85.25% Bakery Products 82,000- 812.3700 811.8638 95.91% 81,600-81,999 812.8339 812.3122 95.93% 81.350-81.599 8 8.2187 8 7.8821 95.90% 80 -81.349 8 7.9121 8 7.5824 95.83% (continued) 102 Table 7 (continued) Expenditures for Cereal Product Groups and the 'Services in Those Groups of Four Income Groups (Cross Sectional) -Product Group Expenditures as a Percent of Product Product Total Retail Group Expenditures Group Income Groups Expenditures Percent of Income Mill Products $2,000- 4,92% 0,06% 81,600-81.999 4.28% 0.09% 81.350- 1.599 5.30% 0.11% 80 - 1,349 4.92% 0.15% Breakfast Cereals $2,000- 8.92% 0.11% ‘1.600- 1.999 9.12% 0.20% 1.350- 1.599 12.31% 0.26% 80 —81,349 11.67% 0.37% Mixes 82,000- 6.37% 0.08% 81,600-81.999 4.82% 0.11% 81.350-81.599 7.90% 0.17% #0 -81.349 5.63% 0.18% Macaroni- Spaghetti 82,000- 3.21% 0.04% 81,600-81.999 3.36% 0.07% 81.350-81.599 3.58% 0.08% 80 -81.349 4.00% 0.13% Crackers 2,000- 5.40% 0.07% 31.600-81.999 5.71% 0.12% 81.350-81.599 5.32% 0.10% 80 -81.349 4.65% 0.15% . Bread and Rolls 82.000- 38.30% 0.49% 1:600"19999 39.43% 0.86% ‘1.350- 1.599 39.42% 0.84% 80 - ~81,349 44.51% 1.40% B k grgggcts 2,000- 32.88% 0.42% '1.600- 1.999 33.29% 0.73% 1.350- 1.599 26.18% 0.56% 0 - 1,349 24.61% 0.77% 103 Table 8 Expenditures of Four Income Groups for the Products Made From Wheat Durum, and Corn and the Cereals in Those Products (Cross Sectional) Proportion EXpenditures of Cereal in for Products Expenditures Income Made From Cereal for Products Groups the Grain EXpenditures From the Grain Wheat 82,000-. 833.9536 83.6671 10.80% £1,600- 1,999 334.7033 3.8688 11.15% 1.350- 1.599 27.5534 3.2404 11.76% 80 -81,349 827.9410 83.5652 11.91% Durum '2,000- 3 1.1226 8 .1 32 15.43% 11.600-81.999 1.2310 80.1 52 15.04%. 81.350. 1.599 3 1.0715 80.1709 15.95% 80 - 1.349 1.1959 80.2139 17.89% Corn 82,000- 8 0.8724 $0.1266 14.51% “l,600-8l,999 8 0.9298 0.1309 14.08% 80 - 1.349 1.0067 0.1439 14.29% (continued) Ex enditures for Pro ucts Made from Expenditures the Grain as a for Products Made Income Percent of Total from the Grain as a Groups Retail Expenditures Percent of Income Wheat 82,000- 90.24% 1.15% £1.6OO-gl.999 90.01% 1.97% 1.350- 1,599 87.78% 1.87% 80 -81.349 86.91% 2.73% Durum 2,000- 2.98% 0.04% 1,600-81.999 3.19% 0.07% 81.350-81.599 3.41% 0.07% 80 -81.349 3.72% 0.12% Corn 82,000- 2.32% 0.03% 81.600-81.999 2.41% 0.05% 1.350-gl.599 3.53% 0.08% o - 1,349 3.13% 0.10% APPENDIX C 105 Derivation of Formula Showing Interrelationship of the Income Elasticities of Retail Expenditures and its Two Components Given various eXpenditures t1, t2, SI, 82, 81’ 52 and incomes y1 and y2 where t1 = expenditures at retail during the first time period t = eXpenditures at retail during the second time 2 period S1 = expenditures for services during the first time period 82 = expenditures for services during the second time period 51 : expenditures for grain during the first time period 52 = expenditures for grain during the second time period income during the first time period y2 : income during the second time period then the elasticities can be written as 8:212:11 t t + t y - y (1) 2 l 2 1 E8 = §2_:_El .{2_1_31 (2) S2 + S1 y2 ' y1 8 ' 61 y + y 2 E8=———-i——l<3> 62 + 81 y2 ‘ y1 where Et = the income elasticity of retail expenditures the income elasticity of service eXpenditures the income elasticity of grain expenditures 106 by definition t1 : 81 + 81 (4) t2 : 52 + 52 (5) Combining (4) and (5) with (1) is defined as _ ($2 - 51) (1'2 + yl) + (82 - 61) (3'2 + 71) Et 4. _ (82 + 81) (Y2 - Y1) + (82 81) (12 - yl) Further simplification yields E = (82 - 51) (Y2 + yl)+ (82 - 81) (ye + yl) t (82 + 51) (ye - Y1) (32 + 51) (72 - yl) .Et (62 + 511 (S2 + SI) Since (S2 - SI) (Y2 + yl) = E (S+S)(y-y) 8 it can be combined with 1.2 to give Et = E + (82 -§l) (172 + yl) 'Et (52 + 51) + Multiplying (1.4) by the identity §2___§1 82 + 61 the following form is obtained (82 - 61) (1'2 + yl) (62 + 81) Et : ES + (82 + 61) (y2 - yl) (52 + SI) _ E (82 + 61) (S2 + 31) Since £§2_:_§ll (y2+ yll = E8 (62 + 61) (3'2 - yl) substituting (1.6) into (1.5) + + Et = E8 + E (52 51) - E8 (52 51) 5 (82 + SfT 782 + 81) (1.1) (1.2) (1.3) (1.4) (1.5) (1.6) (1.7) 107 : 55 (S2 + 81) + Eg,(52 + 81) (1.8) t t1 + t2 E In terms of Es, (1.8) can be written _ (51+ 521 EB - Et + (31 + 82) (Et - E6) (1.9) The use of (4) and (5) allows (1.9) to be written as either of the following equations (t + t ) t t E8 = S2 31) Et - (1 - _2_:__l_) Es (1.10) ( 2 + 1 S2 + S1 t t E = (2 + 1) Et - (52 + 51) E (1.11) 8 (52 + 51) (82 + S ) 1 BIBLIOGRAPHY Agricultural Marketing Service. 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