Manageral Economics (Economyst Only Please)
posted by John Q on .
Wilpen Company, a pricesetting 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 specifications:
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 consumer’s average household income, and Pr is the average price of tennis rackets. The regression results are as follows:
Dependent Variable: Q
Observations: 20
RSquare: 0.8435
FRatio: 28.75
PValue on F: 0.001
Variable
InterceptParameter Estimate 425120, Standard Error 220300, TRatio 1.93, PValue 0.0716
P Parameter Estimate 37260.6, Standard Error 12587, TRatio 22.96, PValue 0.0093
M Parameter Estimate 1.49, Standard Error 0.3651, TRatio 4.08, PValue 0.0009
PR Parameter Estimate 1456, Standard Error 460.75, TRatio 3.16, PValue 0.006
Economics Managerial  Christopher, Wednesday, July 1, 2009 at 9:45pm
Discuss the statistical significance of the parameter estimates a^, b^, c^, and d^ using the pvalues. Are the signs of b^, c^, and d^ consistent with the theory of demand?
What is the estimated number of cans of tennis balls demanded?
At the values of P, M, and Pr given, what are the estimated values of the price (E^), income (E^m), and crossprice elasticity’s (E^xr) of demand?
What will happen, in percentage terms, to the number of cans of tennis balls demanded if the price of tennis balls decreases 15 percent?
What will happen in percentage terms, to the number of cans of tennis balls demanded if average household income increases by 20 percent?
What will happen, in percentage terms, to the number of cans of tennis balls demanded if the average price of tennis rackets increases by 20 percent?

Thanks for your vote of confidence.
1) Look at the TRatio and especially the PValue. You are testing whether the parameter is significantly different from zero. In all parameters except the intercept, the estimate of the parameter is significantly different from zero at the 1% level (Pvalue < .01). For the intercept, the Pvalue is .0716. For the intercept, at the 10% confidence level, you could say the estimate is different from zero.
1b) We would expect a negative relationship between sales and price or sales and price of rackets. (As price goes up, Q goes down) We would expect a positive relationship for income. The estimates are properly that.
2) you did not provide levels for P,M, and Pr. But, this step is otherwise easy. Just plug into your equation. That is Q=425120  37260.6*P + 1.49*M  1456*Pr.
2b) Raise price by a small amount (e.g., 1%) what happens to Q. Elasticity is (%change Q)/(%change P).
Ditto for income and Pr.
3) Repeat steps in 2b cept with the percentages given. 
a. Discuss the statistical significance of the parameter estimates a, b, c, and d, using the pvalues. Are the signs of b, c and d consistent with the theory of demand?
The pvalue associated with b is consistent with the theory of demand  if the prices rise, the quantity sold will then drop.
The pvalue associated with c is consistent with the theory of demand – when consumers have more (increase in income) they may purchase more tennis balls.
The pvalue associated with d is consistent with the theory of demand – if Wilpen increase the price of their tennis rackets then they will sell less of them and consumers will buy less, as well as less tennis balls (no rackets, no balls).
b. What is the estimated number of cans of tennis balls demanded?
Q = a + b*P + c*M + d*Pr
Q = 425120 – 37260.6 P + 1.46 M – 1456 PR
Q = 425120 – 37260.6 * 1.65 + 1.46 * 24600 – 1456 * 110
Q = 239396.01
c. At the values of P, M, and Pr given, what are the estimated values of the price (E), income (Em), and crossprice elasticities (Exr) of demand?
The estimated value for the price elasticities is
E 37260.6(1.65/Q) = 37260.6(1.65/ 239396.01) = 0.257
The estimated values of the income (EM) of demand is
EM = 1.46(24600/Q) = 1.46(24600/239396.01) = 0.150
The estimated values of the crossprice elasticities (EXr) of demand is
EXr = 1456.0(110/Q) = 1456.0(110/ 239396.01) = 0.669
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?
Percentage change in Q = E * percentage change in price = 0.257 * (15%) = 0.04
The number of cans of tennis balls demanded will rise by 4%
e. What will happen, in percentage terms, to the number of cans of tennis balls demanded if average household income increase by 20 percent?
Percentage change in Q = EM * percentage change in income = 0.150 *20% = 0.03
The number of cans of tennis balls demanded will rise by 3%
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?
Percentage change in Q = EXR * percentage change in racket price = 0.669 * 25% = 0.167
The number of cans of tennis balls demanded will drop by 16