Question: A monopolists inverse demand function is p = 100 2Q, so its marginal revenue is MR = 100 4Q. Its cost function is C =

A monopolist€™s inverse demand function is

p = 100 ˆ’ 2 Q,

so its marginal revenue is

M R = 100 ˆ’ 4 Q .

Its cost function is

C = 25 + 4 Q + 2 Q^{2}

and its marginal cost is therefore

M C = 4 + 4 Q .

a. Create a spreadsheet with column headings Q, p, MR, MC, R, C, profit, and CS (consumer surplus). Enter the values 1 to 25 in one-unit increments in the quantity column and enter the appropriate formulas in all the other cells. Determine the profit maximizing output and price for an unregulated monopoly. What is the monopoly€™s profit and the consumer surplus at this output and price?

b. Now use your spreadsheet to determine the price, quantity, profit, and consumer surplus if the regulator imposes a price cap (ceiling) of 70.

c. Which of the two pricing structures yields the highest total surplus? If the regulator wants to use price cap regulation and wants to maximize total surplus, what price cap should the regulator choose?

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Demand function P 100 2C MR 100 4Q Total Cost C 2Q 2 4Q 25 Marginal Cost MC 4Q 4 a Q P MR MC TR C Profit CS 1 98 96 8 98 31 67 1 2 96 92 12 192 41 151 4 3 94 88 16 282 55 227 9 4 92 84 20 368 73 295 1... View full answer

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