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Question: (Requires calculus) The demand facing a monopolist is
Q = 50 - 2P
and total cost is
TC = Q + 4Q2
Find the monopolist's optimal price, quantity, and profit. Graph the solution.
a. If this were instead a perfectly competitive market with a supply curve the same as the monopolist's marginal cost, what would output and price be? Graph the solution.
b. What would be the total profit made by competitors? Why would there be no deadweight loss?
c. The price of the monopolist's only input doubles, which doubles total cost to
TC = 2Q + 8Q2
What happens to output, price, and profit? Graph the new solution and compare it with the old one. Why is the rise in input costs not passed on in full to customers as a higher price?
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