Market structure — practice questions

(a) TR = P × Q = (50 − Q)Q = 50Q − Q² MR = dTR/dQ = 50 − 2Q

(For linear demand P = a − bQ, MR = a − 2bQ.)

(b) MC = dTC/dQ = 10 Profit max: MC = MR → 10 = 50 − 2Q → Q = 20 P = 50 − 20 = £30

Profit = TR − TC = (30 × 20) − (100 + 200) = 600 − 300 = £300

(c) Perfect competition: P = MC → 50 − Q = 10 → Q = 40, P = £10

Monopoly produces half the competitive output at three times the price.

DWL: welfare loss from underproduction — consumers pay more and buy less. Monopolist gains producer surplus but total welfare falls.

(a) Find the profit-maximising output: In perfect competition, a firm is a price taker, so its Marginal Revenue (MR) is equal to the market price. MR = $40.$ The profit-maximising condition is MR = MC. First, find the Marginal Cost (MC) by differentiating the Total Cost (TC) function: TC = 100 + 10Q + Q² MC = dTC/dQ = 10 + 2Q

Set MR = MC: 40 = 10 + 2Q 30 = 2Q Q = 15 bushels

(b) Calculate the economic profit: Profit = Total Revenue (TR) - Total Cost (TC) TR = Price × Quantity = $40 \times 15 =$600 TC = 100 + 10(15) + (15)² = 100 + 150 + 225 = $475$ Profit = $600 -$475 = **$125**$ The farmer earns a supernormal profit of $125.$

(c) Long-run adjustment: The existence of supernormal profit ($125) will signal new firms to enter the wheat market. This is possible because there are no barriers to entry in perfect competition. As new firms enter, the total market supply of wheat increases. This increase in supply will cause the market price to fall. The price will continue to fall until all firms in the market are only making normal profit (i.e., where Price = minimum Average Total Cost). The farmer's individual profit will be competed away.