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Consumer Demand Analysis and Estimation Applied Problems 2. The demand function for Einstein Bagels has been estimated as follows:

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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

QDx

Px

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
14.05

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?