Manageral Economics (Economyst Only Please)

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 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
R-Square: 0.8435
F-Ratio: 28.75
P-Value on F: 0.001

Variable

Intercept-Parameter Estimate 425120, Standard Error 220300, T-Ratio 1.93, P-Value 0.0716

P- Parameter Estimate -37260.6, Standard Error 12587, T-Ratio -22.96, P-Value 0.0093

M- Parameter Estimate 1.49, Standard Error 0.3651, T-Ratio 4.08, P-Value 0.0009

PR- Parameter Estimate -1456, Standard Error 460.75, T-Ratio -3.16, P-Value 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 p-values. 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 cross-price 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?

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  1. Thanks for your vote of confidence.

    1) Look at the T-Ratio and especially the P-Value. 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 (P-value < .01). For the intercept, the P-value 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.

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  2. 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?
    The p-value associated with b is consistent with the theory of demand - if the prices rise, the quantity sold will then drop.
    The p-value associated with c is consistent with the theory of demand – when consumers have more (increase in income) they may purchase more tennis balls.
    The p-value 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 cross-price 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 cross-price 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

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