4. Suppose that the demand for bentonite is given by Q = 40-0.5P, where Q is in

Question

4. Suppose that the demand for bentonite is given by Q = 40-0.5P, where Q is in tons of bentonite per day and P is the price per ton. Bentonite is produced by a monopolist at a constant marginal and average total cost of $10 per ton a. Derive the inverse demand and marginal revenue curves faced by the monopolist. b. Equate marginal cost and marginal revenue to determine the profit-maximizing level of output. c. Find the profit-maximizing price by plugging the ideal quantity back into the demand curve d. How would your answer change if marginal cost were instead given by MC = 20 + Q

Explanation / Answer

Q = 40 - 0.5P

a. P = 40 /0.5 - Q/0.5

P = 80 -2Q

TR = P*Q = 80Q -2Q2

MR = dTR/dQ = 80 -4Q

b. MR = MC

80 -4Q = 10

4Q = 80 - 10

Q = 17.5

c. P = 80 -2x17.5

P = 45

d. New equilibirum, 80 -4Q = 20 + Q

5Q = 60

Q = 12

P = 80 - 2x12

P = 56

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