Different market structures — 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 profit-maximising output (Q): A perfectly competitive firm maximises profit where Price (P) = Marginal Cost (MC). The firm is a price taker, so P = MR = $40.$ First, find the Marginal Cost (MC) by differentiating the Total Cost (TC) function with respect to Q: MC = dTC/dQ = d(150 + 10Q + 0.5Q²)/dQ MC = 10 + Q Set P = MC: $40 = 10 + Q$ Q = 40 - 10 Q = 30 units

(b) Calculate short-run profit: Profit = Total Revenue (TR) - Total Cost (TC) TR = P × Q = $40 \times 30 =$1200 TC = 150 + 10(30) + 0.5(30)² = 150 + 300 + 0.5(900) = 150 + 300 + 450 = $900$ Profit = $1200 -$900 = **$300**$ Since profit is positive, the firm is earning supernormal profit.

(c) Long-run adjustment: In the short run, the firm is making $300 of supernormal profit. In perfect competition, there are no barriers to entry. This profit acts as a signal, attracting new firms to enter the industry. As new firms enter, the industry supply increases, shifting the market supply curve to the right. This causes the market price to fall. Entry will continue, and the price will keep falling, until all supernormal profits are competed away and firms are only earning normal profit (where P = minimum AC). The market will then be in long-run equilibrium.