Consumer Demand Analysis and Estimation Applied Problems

2. The demand function for Einstein Bagels has been estimated as follows:

Qx = -15.87 – 40.73Px + 84.17Py + 0.55Ax

where Qx represents thousands of bagels; Px is the price per bagel; Py is the average price per bagel of other brands of bagels; and Ax represents thousands of dollars spent advertising Einstein Bagels.

a. Calculate the price elasticity of demand for Einstein’s Bagels and explain what it means.

b. Derive an expression for the (inverse) demand curve for Einsteins’s Bagels.

c. If the cost of producing Einstein’s Bagels is constant at $0.10 per bagel, should they reduce price and thereafter, sell more bagels (assume profit maximization is the company’s goal)?

d. Should Einstein Bagels spend more on advertising?

3. The consulting firm that you work for has been hired by the US Government to provide an independent analysis of the demand-side effects of a contemplated increase in the tax on gasoline. They provide you with a data set relating to the period 1962-1987, which they say contains valuable historic lessons relating to the impact of volatile pump prices due to the supply restrictions imposed by the Organization of Petroleum Exporting Countries (OPEC), and the Corporate Average Fuel Economy (CAFE) regulations that required car manufacturers to increase the fuel efficiency of the cars they sold, while at the same time Real Disposable Income (RDI) per capita was rising, the number of passenger cars (NPC) almost doubled, and inflation was pushing up the Consumer Price Index (CPI).

Year |
Q |
P |
NPC |
MPG |
RDI |
CPI |

1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1084 1985 1986 1987 |
43,771 45,246 47,567 50,273 53,312 55,110 58,524 62,448 65,784 69,514 73,463 78,011 74,217 76,457 78,847 80,677 83,233 80,233 73,375 71,718 72,848 73,156 71,180 69,450 71,404 70,984 |
20.36 20.11 19.98 20.70 21.57 22.55 22.93 23.85 24.55 25.20 24.46 26.88 40.41 45.44 47.44 50.70 53.09 74.33 104.73 112.75 102.65 95.36 91.46 89.64 63.63 66.33 |
66,638 69,842 72,969 76,634 80,106 82,367 85,793 89,156 92,095 96,144 100,658 106,119 109,823 111,679 115,170 118,711 121,717 125,750 127,448 129,123 129,500 131,723 133,751 137,308 140,693 142,209 |
14.37 14.26 14.25 14.15 14.10 13.91 13.75 13.70 13.73 13.67 13.29 13.65 13.74 13.93 14.15 14.26 14.49 15.32 15.68 16.36 16.81 17.80 18.28 18.35 19.29 |
6,271 6,378 6,727 7,027 7,280 7,513 7,728 7,891 8,134 8,322 8,562 9,042 8,867 8,944 9,175 9,381 9,735 9,829 9,722 9,769 9,725 9,930 10,419 10,662 10,947 10,976 |
90.6 91.7 92.9 94.5 97.2 100.0 104.2 109.8 116.3 121.3 125.3 133.1 147.7 161.2 170.5 181.5 195.4 217.4 246.8 272.4 289.1 298.4 311.1 322.2 328.4 340.4 |

Where: Qx is the gasoline consumption by passenger cars (in millions of gallons);

Px is the retail (pump) price of gasoline, in cents per gallon;

NPC is the number of registered passenger cars (in thousands);

MPG is the national average of miles travelled per gallon of gasoline;

RDI is Real Disposable Income per capita (in 1982 dollars); and

CPI is the Consumer Price Index (base year 1967).

This data illustrates some very interesting issues that were happening over that tumultuous period of our history. You will note that the pump price of gasoline more than doubled five-fold from the mid-1960s to the mid-1970s, and then doubled again in the early 1980s, due to the OPEC crises. The number of passenger cars climbed relentlessly with the love affair with ‘muscle cars’ despite the increasing pump price of gasoline, and indeed outpacing the increases in real disposable income per capita. The average MPG climbed only slowly as manufacturers increased the fuel efficiency of new cars and consumers slowly traded up to the more efficient cars new cars and retired their older vehicles. The changes in CPI show that the rate of inflation was generally much greater than the rate of increase of pump prices as the increased production and transportation costs due to rising fuel prices pervaded the entire economy, pushing up the prices of food and other household items that drive the CPI.

a. Reconcile the fact that while the quantity demanded of gasoline and pump prices both rise over this period generally, they are inversely related along a demand curve.

b. Conduct a multiple regression analysis to explain the quantity demanded of gasoline in terms of the other data provided. (Transpose this data into an Excel spread-sheet and use the Excel regression tool, if loaded, or alternatively download an ‘add-in’ regression program such as ‘Statpro’ to find the regression statistics).

c. What proportion of the variance in Qx is explained by these other variables? What missing variables might account for the remainder of the variance in the quantity demanded of gasoline?

d. Use the regression equation to predict the quantity demanded of gasoline in 1988 for the values Px = 68.5; NPC = 145,885; MPG = 20.36; RDI = 11,192; and CPI = 354.6.

e. What is the 95% confidence interval for your prediction?