Question

Suppose there is a monopolist in the market for a specific video game facing a demand curve: P = 34 - 0.5Q. The monopolist marginal cost curve is MC = 2, its total variable costs are TVC = 2Q and it faces a total fixed costs equal TFC = $294.
Note: Keep as much precision as possible during your calculations. Your final answer should be accurate to at least two decimal places.

a) Graph the demand curve and marginal cost curve, then derive and graph the marginal revenue curve.

b) Calculate the equilibrium monopoly quantity and price.
c) What is the profit for the monopoly?
d) What is the consumer surplus?

Answer 1

a)

b) Monopoly profit is max when MR = MC

Thus, 34 – Q = 2

Q = 32

Price $= 34 – 0.5 \times 32 = 34 -16 = 18$

c) Profit $= (18 \times 32) – 294 – (2 \times 32) = 576 – 294 – 64 = 218$

d) Consumer surplus $= \frac{1}{2} \times 16 \times 32 = 256$