Question

For price discrimination to be successful, no arbitrage opportunity can be allowed. 5. Monopoly firm's marginal revenue is less than the price it currently charges. Part III: Short-answer Questions (70 points total) 1. Suppose a monopolist faces a market inverse demand p = 10-Q, and its marginal cost is constant at 4. Assume its fixed cost at zero. (a) Draw on the same graph the monopolist's demand, MR, and MC curves/lines. (10 points) (b) Calculate the profit-maximizing monopoly price, output. (16 points) (c) Calculate consumer surplus and producer surplus under monopoly. (16 points) 2. Assume that the monopolist in question 1 now behaves competitively, meaning that it sets the price at marginal cost. (a) How much would this firm produce and charge in this case? (8 points) (b) Calculate consumer surplus and producer surplus in this case (12 points). (c) Calculate the deadweight loss due to monopoly power (8 points). (Hint: it is the difference of total surplus in 2(b) vs 1(©

Answer 1

1 (a)

Since p = 10 - Q,

Revenue = p × Q=10Q - Q2

Hence, MR = 10 - 2Q.

MC is given fixed at 4.

Demand function is Q = 10 - p.

Plotting all these values in graph attached picture, we get

1 (b)

The monopolist will yield where MR = MC. So,

10 - 2Q = 4

Q = 3.

At this quantity, P = 7.

1 (c)

Consumer Surplus = Area of Triangle ABC = 0.5 × 3 × 3 = 4.5

Producer Surplus = Area of Rectangle ABEF = 3 × 3 = 9

2 (a)

Since the price is now P = MC = 4, this means

Q = 10 – 4 = 6.

2 (b)

The consumer surplus in this case would be = 0.5 × 6 × 6 = 18

The producer surplus will be zero.

2 (c)

Deadweight Loss = Total Surplus in Case B - Total Surplus in Case A

18 - 13.5 = 4.5