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Chapter 7 - Demand and Data

Chapter 7 - Demand and Data - Chapter 7 Demand theory and...

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Chapter 7 Demand theory and Data In the present chapter, I hope to explain how one can go about applying consumer theory in understanding observed consumer decisions. Consider a case in which we observe the amounts of a particular good, demand for a good at different points in time, the price of the good, and the consumer’s level of income. As a concrete example, consider the data in table 7.1, which describes per capita chicken consumption in the united states over the years 1960 to 1982: 165
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166 CHAPTER 7. DEMAND THEORY AND DATA Per capita Real Real Real Real Real Chicken Disposable Retail Retail Retail Composite Year Cons., lbs. per cap. Inc. Price, Chicken Price, Pork Price, Beef Price 1960 27.8 397.5 42.2 50.7 78.3 65.8 1961 29.9 413.3 38.1 52 79.2 66.9 1962 29.8 439.2 40.3 54 79.2 67.8 1963 30.8 459.7 39.5 55.3 79.2 69.6 1964 31.2 492.9 37.3 54.7 77.4 68.7 1965 33.3 528.6 38.1 63.7 80.2 73.6 1966 35.6 560.3 39.3 69.8 80.4 76.3 1967 36.4 624.6 37.8 65.9 83.9 77.2 1968 36.7 666.4 38.4 64.5 85.5 78.1 1969 38.4 717.8 40.1 70 93.7 84.7 1970 40.4 768.2 38.6 73.2 106.1 93.3 1971 40.3 843.3 39.8 67.8 104.8 89.7 1972 41.8 911.6 39.7 79.1 114 100.7 1973 40.4 931.1 52.1 95.4 124.1 113.5 1974 40.7 1021.5 48.9 94.2 127.6 115.3 1975 40.1 1165.9 58.3 123.5 142.9 136.7 1976 42.7 1349.6 57.9 129.9 143.6 139.2 1977 44.1 1449.4 56.5 117.6 139.2 132 1978 46.7 1575.5 63.7 130.9 165.5 132.1 1979 50.6 1759.1 61.6 129.8 203.3 154.4 1980 50.1 1994.2 58.9 128 219.6 174.9 1981 51.7 2258.1 66.4 141 221.6 180.8 1982 52.9 2478.7 70.4 168.2 232.6 189.4 Summary Statistics Var. Obs. Mean Std. Dev. Min Max Chicken 23 39.67 7.37 27.8 52.9 Income 23 1035.07 617.85 397.5 2478.7 Price 23 48.00 11.11 37.3 70.4 Pork P 23 90.40 35.22 50.7 168.2 Beef P 23 123.43 51.50 77.4 232.6 Comp P 23 107.86 39.81 65.8 189.4 Table 7.1: Data comes from table 7.23 in Gujarati (1995). All prices are measured in cents per pound. The composite price in the last column is a weighted average of beef and pork prices, where the weights are determined by relative consumption of beef and pork.
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167 The data in table 7.1 describes yearly quantity of chicken purchased, per capita, in pounds, and also includes some information on (real) prices of chicken, and on the prices of two related goods. Thus, we should be able to come up with a decent description of the per capita demand for chicken by putting this data to use. A fundamental tool of statistics and data analysis is the Linear Regression . This is the technique by which one fits a line through a set of points to characterize the relationship between a dependent variable, y (in our case, chicken consumption) and a set of explanatory variables x i (in our case, prices and income). Given a data set consisting of prices, incomes, and quantities demanded, the most natural thing in the world for this statistician to do would be to estimate a linear regression characterizing the relationship. If x c is quantity demanded, p c is the price of x c , p p and p b are the prices of related products, and I is income, demand for x might be described as: x c = α + βp c + δI + γ p p p + γ b p b (7.1) Just to be clear, in our case, x c is chicken consumption, p c is the real price of chicken in cents, I is disposable income, and p p and p b are the prices of pork and beef, respectively. Estimation of (7.1) is straightforward, but given your knowledge of microeconomic theory, you might be thinking something along the following lines: “If I knew the utility function underlying this demand function, I could find out what the indirect utility function was. I then could figure out the expenditure function. With expenditure and indirect utility, I could conduct a thorough welfare analysis of consumer demand.”
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