Question

Suppose that a price-taker firm has a marginal cost function given by: MC= 20+0.2q. The firm could join a cartel in its industry and agree to a quota of 10 units. The collusion drives the price of the good from $24.55 to $50.00.

Suppose that if the firm cheats on the cartel, it has no effect on the price. Calculate the producer surplus of this firm when they cheat on the cartel.

Answer 1

ANSWER:-

Marginal cost of a firm is MC = 20 + 0.2Q. The price of the good in the market is 50 per unit.

Assuming the firm sells Q units of good, the revenue it will earn = Price*quantity = P*Q = 50Q

The firm will optimise its profits by equating his Marginal Revenue = Marginal cost. That is, max profits earned is when MC = MR. We already have MC. To find MR, we will differentiate the revenue with respect to Q.

=> d(Revenue)/dQ = d(50Q)/dQ

=> MR = 50 (using d(aXn)/dX = a*n*Xn-1 where a is a constant)

Therefore MC = MR equals

=> 20 + 0.2Q = 50

Solving this we get:

=> 0.2Q = 50 - 20

=> 0.2Q = 30

=> Q = 30/0.2 or Q = 150

Therefore the firm will produce 150 units of good. We can see this in the following graph:

The yellow region is the producer's surplus. Observe the region is a triangle. Therefore if we caiculate the area of the triangle, we get the producer's surplus.

Area of the triangle = 1/2*base*hieght

Hieght (from the Y axis) = 50 - 20 = 30 units.

Base = 150units

Therfore area = 0.5*30*150 = 2250

Hence the producer's surplus is 2250

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