Wilpen Co, a price setting firm, produces nearly 80 % of all tennis
balls purchased in the United States. Wilpen estimates the US demand
for its tennis balls by using the following linear specifications:
Q=a + bP + cM + dPR
Where Q is the number 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: S R-SQUARE F-RATIO P-VALUE ON F
a. Discuss the statistical
significance of parameter estimates , b, and d using the
p-values. Are the signs , b, d consisted with the theory
Wilpen plans to charge the wholesale price of 1.65 per can.
The average price of a tennis racket is $110, and the consumers\’
average household income is $24,600
b. What is the estimate number of cans of tennis balls demanded?
c. At the values of P, M, and PRgiven, what are the estimated values of the price (), income (M), and cross-price elasticities (XR) of demand?
d. What will happen, in % terms, to the number of cans of tennis balls demanded if the price of tennis balls decreases 15%?
e. What will happen, in % terms, to the number of cans of tennis balls demanded if the average household increases by 25%?
f. What will happen, in % terms, to
the number of cans of tennis balls demanded if the average price of
tennis rackets increases by 25%?
(a) They’re all significant (p < 0.05) except for the intercept which has a p-value of 0.0716 > 0.05. The signs are consistent with the theory of demand: when the price (P) is increased we expect the demand (Q) to decrease. When the average house income (M) increase we expect the demand (Q) to increase. When the average price of tennis rackets (PR) increase we expect the demand (Q) to decrease. =================================== (b) Q = 425120 – 37260.6 x 1.65 + 1.49 x 24600 1456 x 110 = 240134.01 ====================== (c) Price = $1.65 Income = Q x Price = 241034.01 x 1.65 = $396,221.1165 ================= (d) A decrease of 15% means the new price is 1.65 x 0.85 = $1.4025 (425120 – 37260.6 x 1.4025…
+ 1.49 x 24600 1456 x 110) / 240134.01 = 1.0384 = a rise of 3.84% ================== (e) An increase of 20% means the new average household income equals =24600 x 1.2 = $29520 (425120 – 37260.6 x 1.65 + 1.49 x 29520 1456 x 110) / 240134.01 = 1.0305 = a rise of 3.05% ================== (f) An increase of 25% means the new average price of tennis rackets equals 110 x 1.25 = $137.5 (425120 – 37260.6 x 1.65 + 1.49 x 24600 1456 x 137.5) / 240134.01 = 0.8333 = A decrease of 16.67%