Theory question 102
Market StructuresThe cost and output schedule of a firm is shown in the table below.
Output (kg) | 0 | 15 | 35 | 60 | 85
Variable cost ($) | 0 | 30 | 55 | 75 | 90
Total cost ($) | 15 | 45 | 70 | 90 | 105
Total revenue ($) | 0 | 30 | 70 | 120 | 170
(a) Using the data in the table, at each level of output, calculate the firm's: (i) marginal revenue; (ii) marginal cost.
(b) At what output level did the firm: (i) break even; (ii) make the highest profit; (iii) attain equilibrium?
(c) Identify the market structure in which the firm operates.
Show the model answer
(a)(i) MR = ΔTR/ΔQ: 0→15 kg: 30/15 = $2; 15→35: 40/20 = $2; 35→60: 50/25 = $2; 60→85: 50/25 = $2
(ii) MC = ΔTC/ΔQ: 0→15: 30/15 = $2; 15→35: 25/20 = $1.25; 35→60: 20/25 = $0.80; 60→85: 15/25 = $0.60
(b)(i) Break-even at 35 kg (TR = TC = $70).
(ii) Highest profit at 85 kg: 170 − 105 = $65 (profits: −15, −15, 0, 30, 65).
(iii) MC = MR ($2) at 15 kg; but MC is falling there, so the profit-maximising equilibrium in the table is 85 kg, the output with the highest profit (MR > MC beyond 15 kg).
(c) Perfect competition: MR (= price = $2 per kg) is constant at every output.
Divide each change in TR or TC by the change in output, since output rises in uneven steps.