1. Bridget has a limited income and consumes only wine and cheese; her current con- sumption choice is four bottles of wine and 10 pounds of cheese. The price of wine is $10 per bottle, and the price of cheese is $4 per pound. The last bottle of wine added 50 units to Bridget’s utility, while the last pound of cheese added 40 units.
a. Is Bridget making the utility-maximizing choice?Whyorwhynot?
b. Ifnot,what should she do instead?Why?
2. In an article abou the financial problems ofUSAToday,Newsweekreported that the pa per was losing about $20 million a year. A Wall Street analyst said that the paper should raise its price from 50 cents to 75 cents, which he estimated would bring in an addi- tional $65 million a year. The paper’s publisher rejected the idea, saying that circulation could drop sharply after a price increase, citing The Wall Street Journal’s experience after it increased its price to 75 cents. What implicit assumptions are the publisher and the analyst making about price elasticity?
3. Wilpen Company, a price-setting firm, produces nearly 80 percent of all tennis balls purchased in the United States. Wilpen estimates the U.S. demand for its tennis balls by using the following linear specification:
Q ?? a ?? bP ?? cM ?? dPR
where Q is the number of cans of tennis balls sold quarterly, P is the wholesale price Wilpen charges for a can of tennis balls, M is the consumers’ average household in- come, and PR is the average price of tennis rackets. The regression results are as follows:
DEPENDENT VARIABLE: QT OBSERVATIONS: 32
PARAMETER VARIABLE ESTIMATE
INTERCEPT 51.234 T 3.127 D1 ??11.716 D2 ??1.424 D3 ??17.367
R-SQUARE 0.9817
STANDARD ERROR
7.16 0.524 2.717 0.636 2.112
F-RATIO 361.133
T-RATIO
7.15 5.97 ??4.31 ??2.24 ??8.22
P-VALUE ON F 0.0001
P-VALUE
0.0001 0.0001 0.0002 0.0985 0.0001
DEPENDENT VARIABLE: Q OBSERVATIONS: 20
PARAMETER VARIABLE ESTIMATE
INTERCEPT 425120.0 P ??37260.6 M 1.49 PR ??1456.0
R-SQUARE 0.8435
STANDARD ERROR
220300.0 12587 0.3651 460.75
F-RATIO 28.75
T-RATIO 1.93
??22.96 4.08 ??3.16
P-VALUE ON F 0.001
P-VALUE
0.0716 0.0093 0.0009 0.0060
a. Discuss the statistical significance of the parameter estimates aˆ, bˆ, cˆ, and dˆ using the p-values. Are the signs of bˆ, cˆ and dˆ consistent with the theory of demand?
Wilpen plans to charge a wholesale price of $1.65 per can. The average price of a tennis racket is $110, and consumers’ average household income is $24,600.
b. What is the estimated number of cans of tennis balls demanded?
c. At the values of P, M, and PR given, what are the estimated values of the price (Eˆ ), income (Eˆ M), and cross-price elasticities (Eˆ XR) of demand?
d. What will happen, in percentage terms, to the number of cans of tennis balls demanded if the price of tennis balls decreases 15 percent?
e. What will happen, in percentage terms, to the number of cans of tennis balls demanded if average household income increases by 20 percent?
f. What will happen, in percentage terms, to the number of cans of tennis balls demanded if the average price of tennis rackets increases 25 percent?