Theory question 102
Theory of Costs and RevenueTable 1 below represents the output levels of a firm producing hand sanitizer. Use the information to answer the questions that follow.
Output (units) | 0 | 10 | 18 | 28 | 36 | 45
If the cost function of the firm is given as C = 30 + 4q, where C is the total cost and q is the units produced, calculate the:
(a) total cost in dollars of producing: (i) 18 units; (ii) 36 units.
(b) Average cost in dollars of producing: (i) 28 units; (ii) 45 units.
(c) What is the marginal cost in dollars of producing 28 units?
(d) Determine the profit made from producing 45 units when the market price is fixed at $5.00 per unit.
(e) Determine the fixed cost of the firm. Explain your answer.
Show the model answer
(a)(i) 30 + 4(18) = $102; (ii) 30 + 4(36) = $174
(b)(i) TC = 30 + 4(28) = 142; AC = 142 ÷ 28 ≈ $5.07; (ii) TC = 30 + 4(45) = 210; AC = 210 ÷ 45 ≈ $4.67
(c) MC = (TC28 − TC18) ÷ (28 − 18) = (142 − 102) ÷ 10 = $4 (each extra unit adds $4)
(d) TR = 5 × 45 = $225; TC = $210; profit = $15
(e) $30: at q = 0, C = 30 + 4(0) = 30, the cost that must be paid even with no output.
Substitute each output into C = 30 + 4q.