The market for pizza is a monopoly and demand is given by: Qd = 48 4P. Initially

Question

The market for pizza is a monopoly and demand is given by: Qd = 48 4P. Initially, the monopolist’s marginal cost is MC = 6. Suppose the monopolist reduced her marginal cost to $4 through some non-drastic innovation.

a. What is the monopolist’s profit prior to the innovation?

b. What is the monopolist’s profit after the innovation?

c. What is the additional profit after the innovation?

d. Compared to the results in Question 1, does the monopolist have more or less incentive to innovate than a seller from a competitive market? Why? (show your calculations)

Explanation / Answer

Demand is given by: Qd = 48 4P and so inverse demand is 4P = 48 - Q or P = 48/4 - Q/4. This implies that inverse demand is P = 12 - 0.25Q. This gives a marginal revenue of MR = 12 - 0.5Q. . Suppose the monopolist reduced her marginal cost to $4 through some non-drastic innovation.

a. Initially, the monopolist’s marginal cost is MC = 6. Then the monopolist produces at MR = MC or 12 - 0.5Q = 6 or Q = 6/0.5 = 12 units and a price of P = 12 - 0.25*12 = $9. Then the monopolist’s profit prior to the innovation is (9 - 6)*12 = $36.

b. Now the monopolist’s marginal cost is MC = 4. Then the monopolist produces at MR = MC or 12 - 0.5Q = 4 or Q = 8/0.5 = 16 units and a price of P = 12 - 0.25*16 = $8. Then the monopolist’s profit after the innovation is (8 - 4)*16 = $64.

c. The additional profit after the innovation is $64 - $36 = $28

d. The answer depends on question 1 but yes, a monopolist has more incentive to innovate than a seller from a competitive market because its profits are not increased much while monopolist profits are much higher (it can charge a different price)

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