Theory question 102
Theory of Costs and RevenueSection A (answer one question only from this section)
From the table below, answer the following questions:
Output of beans (kg) | Total Revenue (₦) | Marginal Revenue (₦) | Total Cost (₦) | Marginal Cost (₦)
10 | 150 | — | 250 | —
20 | 200 | 5 | 300 | 5
30 | 350 | 15 | 430 | 13
40 | 450 | F | 500 | 7
50 | 550 | 5 | 550 | M
60 | 600 | 5 | 580 | 3
70 | 630 | X | 700 | 12
(a) Find the value of F, M and X
(b) (i) What would be the profit-maximizing output of this firm? (ii) If this firm were operating under perfect competition, what would be the price of its product?
Show the model answer
(a) MR = change in TR ÷ change in output; MC = change in TC ÷ change in output
F = (450 − 350)/(40 − 30) = 100/10 = ₦10
M = (550 − 500)/(50 − 40) = 50/10 = ₦5
X = (630 − 600)/(70 − 60) = 30/10 = ₦3
(b)(i) Profit is maximised where MR = MC with MC rising. At 50kg MR = MC = ₦5, but output should go on to 60kg because MR (₦5) is still above MC (₦3); beyond 60kg MC (₦12) exceeds MR (₦3). Profit (TR − TC) is highest at 60kg: 600 − 580 = ₦20. (Credit 50kg where MR = MC is shown.)
(ii) Under perfect competition price = MR = MC, so price would be ₦5.
Under perfect competition P = AR = MR.