Question

Suppose a perfectly competitive industry can produce Roman candles at a constant marginal cost of $10 per unit. Once the industry is monopolized, marginal costs increase to $12 per unit because $2 per unit must be paid to politicians to ensure that only this firm receives a Roman candle license. Suppose the market demand for Roman candles is described by the following equations:
P = 20 ? (1 /50) Q ? MR = 20 ? (1/ 25) Q
[i.] Calculate the perfectly competitive output and price.
[ii.] Calculate the monopoly output and price.
[iii.] Calculate the change in consumer surplus from the monopolization of Roman candle production.
[iv.] Calculate the government’s revenue that resulted from the monopolization of Roman candle production.
[v.] Calculate the deadweight loss that resulted from the monopolization of Roman candle production.

Answer 1

Given P = 20- 1/50Q and MR = 20-1/25Q,

(i) Equilibrium in perfect competiton is atrained at a point where P = MC.

Thus, 20-1/50Q = 10 or Q = 500 and P = 10.

(ii) Monopoly equilubrium is attained at a point where MR = MC.

Thus, 20-1/25Q = 12

which gives Q = 400 and P = 12.

(iii) comsumer surplus under perfect compwtition = 1/2(20-10)(1000-500) = 2500.

Consumer surplus under monopoly = 1/2(20-12)(400) = 1600.

(iv) Governments revenue = 2(400) = 800.

(v) Deadweightloss from monopoly = 1/2(500-400)(12-10) = 100.