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 From Regression results: Q = 425120.0 - 37260.6 +1.49 - 1456.0 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 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 â, b, ?, and d using the p-values. Are the signs of b, ? and d consistent with the theory of demand?
b. What is the estimated number of cans of tennis balls demanded?
c. At the values of P, Mp and PR given, what are the estimated values of the price (Ê), income (ÊM), and cross-price elasticities (ÊXR) 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 the average household income increases by 20 percent?