A. Use the data file Final Cost Data.xls to estimate the following quadratic total cost function:

(Data is in table)

TC = b₀ + b₁Q + b₂Q²       MC = b_{1 +} b₂ Q

Report your regression results. Interpret the coefficient of determination and F statistic. Test whether each of the independent variables statistically significant at the 95 percent confidence level.

Total COst	Q	Q Squared
11,000.00	0.00	0.00
7,000	100	10,000
13,000	200	40,000
10,000	500	250,000
12,000	900	810,000
19,000	1,000	1,000,000
16,000	1,200	1,440,000
15,000	1,300	1,690,000
16,000	1,400	1,960,000
23,000	1,500	2,250,000
21,000	1,700	2,890,000
25,000	1,900	3,610,000

 

B)  Use your quadratic cost function and the following demand curve.

                        P = 900 - 0.03Q        MR = 900 - .06Q

Calculate marginal cost (MC) and average cost (AC), price (P) and marginal revenue (MR) Graph MC, AC, P, and MR as a function of output (you may use Excel or graph these relationships by hand). Show the price and output that maximizes profit in this graph. Then use algebra to calculate the price and output (view output as a measure of desired run production for the season) that will maximize the firm’s profit. Calculate your profits at this price and output level.

 

C ) Calculate the level of output that minimizes average cost. Show this solution on your graph above. Calculate your profits at this output level.

D) Calculate the price and level of output that maximizes total revenue. Show this solution on your graph above. Calculate your profits at this output level.

E) Assume that the demand and cost data above is for the N. Y. Yankees and Major League Baseball owners impose a lump sum tax of $4 million dollars to help equalize talent across high revenue and low revenue teams. How will the tax affect your profit maximizing output and the price you charge? How will the tax affect your profits? Explain.

F) Now suppose that the league owners impose a “luxury tax” of 50 percent on costs that are above $200,000. Calculate your profit maximizing output and pricing levels, and your profits. Now assume the players’ association has it’s way and the tax is only 25 percent on costs that are above $500,000. Calculate your profit maximizing output and pricing levels, and your profits. (Hint: you may find it useful to find the output level where the luxury tax kicks in and then examine how this tax affects your cost structure at higher output levels). Graph your solutions to the “luxury tax” in your graph above.