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: Q R- SQUARE F- RATIO P- VALUE ON F OBSERVATIONS: 20 0.8435 28.75 0.001
VARIABLE ESTIMATE ERROR T- RATIO P- VALUE
INTERCEPT 455120.0 220300.0 1.93 0.0716
P -37260.6 12587 -22.96 0.0093
M 1.49 0.3651 4.08 0.0009
PR -1456.0 460.75 -3.16 0.0060
a. Discuss the statistical significance of the parameter estimates b, c, and d using the p-values. Given the signs of c and d, please comment on the good category of tennis ball and its relationship with tennis rackets.
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 (E), income (EM), and cross- price elasticities (EXR) of demand?
d. What will happen, in percentage terms, to the number of cans of tennis balls demanded if average household income increases by 20 percent?
e. 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?