Discuss statistical significance of parameter estimates


Question 1. Antitrust authorities at the Federal Trade Commission are reviewing your company’s recent merger with a rival firm.  The FTC is concerned that the merger of two rival firms in the same market will increase market power.  A hearing is scheduled for your company to present arguments that your firm has not increased its market power through this merger.  Can you do this?  How?  What evidence might you bring to the hearing?

Question 2. The MorTex Company assembles garments entirely by hand even though a textile machine exists which can assemble garments faster than a human can. Workers cost $50 per day, and each additional laborer can produce 200 more units per day (i.e, marginal product is constant and equal to 200). Installation of the first textile machine on the assembly line will increase output by 1,800 units daily. Currently the firm assembles 5,400 units per day.

a) The financial analysis department at MorTex estimates that the price of a textile machine is $600 per day. Can management reduce the cost of assembling 5,400 units per day by purchasing a textile machine and using less labor? Why or why not?

b) The Textile Workers of America is planning to strike for higher wages. Management predicts that, if the strike is successful, the cost of labor will increase to $100 per day. If the strike is successful, how would this affect the decision in question above to purchase the textile machine? Explain.

Question 3: 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 tennis balls by using the following linear specification:

        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 consumers’ average household income, and PR is the average price of tennis rackets.  The regression results are as follows:

Dependant Variable: Q    R-Square    F-Ratio    P-Value on F
Observations:         20      0.8435        28.75        0.001

Variable     Parameter Estimate    Standard 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 consumers’ average household income is $24,000.

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 (EM), 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?

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Macroeconomics: Discuss statistical significance of parameter estimates
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