Demand Analysis

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 susing the following linear specification:

Q = a + bP = cM +dPR

Where Q is the number of cans of tennis balls should quarterly, P is the wholesale price Wilpen charges for a can of tennis balls, M is the consumerâ??s average household income, 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

PARAMETER STANDARD
VARIABLE ESTIMATE ERROR T-RATIO P-VALUE

INTERCEPT 425120.0 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 a^, b^, c^, and d^ using the p-values. Are the signs of b^, c^ and d^, 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 consumersâ?? average household income is $26,400.

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 (E^M), and cross-price elasticities (^EXR) 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?