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
(a) (i) The marginal revenue formula is calculated by dividing the change in total revenue by the change in quantity sold. In the case of the question asked, the output (kg) represents the quantity sold.
At output level 15, \(MR = \frac{30 - 0}{15 - 0} = \frac{30}{15} = $2.00\)
At output level 35, \(MR = \frac{70 - 30}{35 - 15} = \frac{40}{20} = $2.00\)
At output level 60, \(MR = \frac{120 - 70}{60 - 35} = \frac{50}{25} = $2.00\)
At output level 85, \(MR = \frac{170 - 120}{85 - 65} = \frac{50}{25} = $2.00\)
(ii) The Marginal Cost Formula is calculated by dividing the change in Total Cost by the change in quantity sold (or output as regards this question).
At output level 15, \(MC = \frac{45 - 15}{15 - 0} = \frac{30}{15} = $2.00\)
At output level 35, \(MC = \frac{70 - 45}{35 - 15} = \frac{25}{20} = $1.25\)
At output level 60, \(MC = \frac{90 - 70}{60 - 35} = \frac{20}{25} = $0.80\)
At output level 85, \(MC = \frac{105 - 90}{85 - 65} = \frac{15}{25} = $0.60\)
(b)(i) The firm's break-even point is at output level 35.
(ii) The firm makes the highest profit at output level 85.
(iii) The firm attains equilibrium at output level 15.
(c) The firm is operating in perfectly competitive market.
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