Question

Suppose that a price-taker firm has a marginal cost function given by: MC= 20+0.5q. The firm could join a cartel in its industry and agree to a quota of 5 units. The collusion drives the price of the good from $25.45 to $55.00. 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

Solution:-

Producer surplus is the area left of the quantity and above MC curve and below the price

MC = 20 + 0.5*5

= 22.5

Y intercept of the MC curve = 20

PS = 0.5 * (MC - Y intercept of the MC curve ) * Q + (P - MC) * Q

= 0.5 * (22.5 - 20) * 5 + (55 - 22.5) * 5

= 6.25 + 162.50

= 168.75

The producer surplus is $168.75