Market analysis — 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 (P=MC): First, find the Marginal Cost (MC) by differentiating the Total Cost (TC) function with respect to Q. MC = dTC/dQ = 2 + 0.4Q In perfect competition, a firm maximises profit by producing where Price (P) = Marginal Cost (MC). **P = $8**$ Set P = MC: 8 = 2 + 0.4Q Subtract 2 from both sides: 6 = 0.4Q Solve for Q: Q = 6 / 0.4 = 15 The profit-maximising output is 15 bags of potatoes.

(b) Calculate profit/loss (TR - TC): Total Revenue (TR) = P × Q = $8 \times 15 =$120 **Total Cost (TC) = 25 + 2(15) + 0.2(15)² = 25 + 30 + 0.2(225) = 25 + 30 + 45 = $100**$ **Profit = TR − TC = $120 −$100 = $20**$ The farm makes a supernormal profit of **$20**.$

(c) Find the shutdown price (P = min AVC): The shutdown price is the minimum of the Average Variable Cost (AVC) curve. Variable Cost (VC) = 2Q + 0.2Q² AVC = VC / Q = 2 + 0.2Q Since the AVC function is linear and increasing for Q > 0, its minimum value occurs as Q approaches 0. The minimum AVC is at the lowest possible output (Q=0), where AVC = $2. Therefore, the shutdown price is $2. As long as the market price is above $2, the farm is better off producing than shutting down in the short run, as it can cover its variable costs and contribute to fixed costs.