Question

Suppose Market demand is given as Qd = 60 – 2P. Market supply is given as Qs = 2P Also assume ATC = 0.4Q.

a. How many units of the product would the perfectly competitive market supply? What would the equilibrium price be?

b. What are the profit maximizing price and quantity if this market is a monopoly?

c. Calculate the dead-weight loss created if this market started off as perfectly competitive but then became a monopoly.

Answer 1

(c) With reference to figure 1, we observe that the total welfare under perfect competition = area of the triangle AOE = area of the triangle ABE + area of the triangle OBE = consumer surplus (CS) + producer surplus (PS).

Similarly, under monopoly, total welfare = area of the trapezium OAFG = area of triangle ACF (Csonsumer surplus) + area of the trapezium OCFG (producer surplus).

Hence, if the market started off as perfectly competitive but later became a monopoly, then deadweight loss would be equal to welfare under perfect competiton - welfare under monopoly.

That is deadweight loss = area AOE - area OAFG = area EFG = 0.5 * FG * QmQc.

At Qm = 16.67, supply price = Q/2 = 16.67/2 = 8.33.

At Qm = 16.67, demand price = 30 -0.5 (16.67) = 30 - 8.33 = 21.67

Hence, FG = demand price - supply price = 21.67-8.33 = 13.33

  QmQc= 30 - 16.67 = 13.33

Hence, deadweight loss = 0.5 * FG * QmQc = 0.5 * 13.33 * 13.33 = 88.89