The 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...
Question 1 Report
The 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
Answer Details
Marginal revenue \( MR = \dfrac{\Delta TR}{\Delta Q} \) and marginal cost \( MC = \dfrac{\Delta TC}{\Delta Q} \), where \( \Delta Q \) is the increase in output between successive levels.
(a) Working
| Output (kg) | ΔQ | ΔTR | MR ($/kg) | ΔTC | MC ($/kg) |
|---|---|---|---|---|---|
| 0 | - | - | - | - | - |
| 15 | 15 | 30 | \(30\div15=2.00\) | 30 | \(30\div15=2.00\) |
| 35 | 20 | 40 | \(40\div20=2.00\) | 25 | \(25\div20=1.25\) |
| 60 | 25 | 50 | \(50\div25=2.00\) | 20 | \(20\div25=0.80\) |
| 85 | 25 | 50 | \(50\div25=2.00\) | 15 | \(15\div25=0.60\) |
(b) Profit \( = TR - TC \) at each level:
| Output | TR | TC | Profit |
|---|---|---|---|
| 0 | 0 | 15 | -15 |
| 15 | 30 | 45 | -15 |
| 35 | 70 | 70 | 0 |
| 60 | 120 | 90 | 30 |
| 85 | 170 | 105 | 65 |
- (i) Break even at output 35 kg, where \( TR = TC = 70 \) so profit is zero.
- (ii) Highest profit at output 85 kg, where profit \( = 170 - 105 = \$65 \).
- (iii) Equilibrium at output 85 kg. Because MR (\$2) stays above MC at every stage beyond the first, each extra kilogram adds more to revenue than to cost, so the firm keeps expanding to the largest output shown, where profit is maximised.
(c) The firm operates under perfect competition. Marginal revenue is constant at \$2 per kg, which means price is fixed and the firm is a price taker.
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