Firms, costs and revenue
Key terms
Define each term.
Multiple choice
Circle the correct answer.
A car manufacturer takes over a firm that makes car tyres. What type of merger is this?
A firm's total cost is $500 when it produces nothing. Which statement is correct?
A firm increases output from 100 to 120 units by hiring more workers, and its output per worker falls. What has happened?
Worked problems
Show your working.
Finding the profit-maximising output from a cost table. A firm faces total costs of $100 at zero output, then $160, $200, $230, $270, $330 and $420 for outputs of 1 to 6 units. It can sell any quantity at $80 per unit. Identify its fixed cost, calculate profit at each output, and state the profit-maximising level.
Calculating average and marginal product and finding diminishing returns. A firm with one machine employs 1 to 6 workers. Total product is 10 units with 1 worker, 24 with 2, 42 with 3, 56 with 4, 65 with 5 and 70 with 6. Calculate the average and marginal product of labour, and state where diminishing marginal returns begin.
Confirming the profit-maximising output with marginal analysis. Using the same cost schedule as before, with TC of $100, $160, $200, $230, $270, $330 and $420 for outputs 0 to 6 and a price of $80, calculate marginal cost at each output and use the MC = MR rule to find the profit-maximising level. Then explain why the rule and the total-profit method agree.
Chains of reasoning
The steps are in the wrong order. Write the letters in the order that makes a linked chain.
How minimum efficient scale determines market structure
- A It cannot match the larger firm's price and remain profitable, so it either grows, exits or occupies a niche the large firm does not serve.
- B The industry therefore settles into oligopoly or monopoly, not because of any anti-competitive conduct but because the cost structure permits nothing else.
- C An industry requires large indivisible capital equipment, so fixed costs are high relative to variable costs.
- D Minimum efficient scale is consequently large, perhaps a substantial fraction of total market demand.
- E Average fixed cost therefore falls steeply as output rises, and long-run average cost continues falling over a wide range of output.
- F The number of firms able to survive at efficient scale is limited by the size of the market divided by minimum efficient scale.
- G A small firm operating below that scale has higher average costs than a large rival.
Diagrams
Draw a diagram with output on the horizontal axis and cost on the vertical axis. Draw a horizontal total fixed cost line, an upward-sloping total variable cost curve starting at the origin, and the total cost curve above them. Then, on a second diagram, draw average fixed cost falling continuously and average total cost as a U shape.
Draw an average total cost (ATC) curve with output on the horizontal axis and average cost on the vertical axis, shaped like a U. Label the falling section 'economies of scale', the lowest point 'lowest average cost', and the rising section 'diseconomies of scale'.
Draw a set of short-run average cost curves for three different plant sizes, then draw the long-run average cost curve as the envelope beneath them. Mark minimum efficient scale. On a second diagram, draw an LRAC that falls continuously across the entire range of market demand and mark where market demand sits.
Extended answer
Plan your answer: list the points you would make in each paragraph.
Assess whether firms always seek to maximise profits. (13 marks)
Answers
Merger: The joining together of two or more firms to form a single firm, whether by agreement or by one firm taking over another.
Productivity: Output per unit of input in a given period, most commonly measured as output per worker or output per worker-hour.
Economies of scale: The fall in average (unit) costs of production that a firm experiences as it increases the scale of its output.
B. The tyre maker supplies the car manufacturer, so it is at an earlier stage of the same production chain. Joining with a supplier is backward vertical integration, which secures the supply of an input and removes the supplier's profit margin from the car maker's costs.
B. At zero output no variable costs are incurred, so all cost at that point is fixed. The loss is $500 only at zero output; producing and selling reduces it if price exceeds average variable cost. Average cost cannot be calculated at zero output, since dividing by zero is undefined.
B. Total output rose from 100 to 120, so production increased. Output per worker fell, so productivity decreased. The firm is producing more but less efficiently, which typically raises average cost and is the everyday appearance of diminishing returns.
Step 1. Identify fixed cost. Total cost at zero output is $100. Nothing is being produced, so no variable cost is being incurred, and the whole $100 is fixed cost.
Step 2. Calculate total revenue at each output. At $80 per unit: 1 unit $80, 2 units $160, 3 units $240, 4 units $320, 5 units $400, 6 units $480.
Step 3. Calculate profit as TR minus TC at each output. 1 unit: 80 - 160 = -$80. 2: 160 - 200 = -$40. 3: 240 - 230 = $10. 4: 320 - 270 = $50. 5: 400 - 330 = $70. 6: 480 - 420 = $60.
Step 4. State the profit-maximising output. Profit is highest at 5 units, where it is $70. Producing a sixth unit adds $80 to revenue but $90 to cost, so profit falls to $60. The firm should produce 5.
Step 5. Check with average cost. At 5 units, AC = 330 / 5 = $66. Price is $80, so profit per unit is $14 and total profit is 5 x $14 = $70, confirming the earlier figure. Two routes to the same answer is a useful check in an exam.
Notice the firm makes a loss at low output because fixed costs are spread over too few units. A loss at some output levels does not mean a firm should shut down, which is a distinction developed at A Level.
Step 1. Calculate marginal product. Worker 1: 10. Worker 2: 24 - 10 = 14. Worker 3: 42 - 24 = 18. Worker 4: 56 - 42 = 14. Worker 5: 65 - 56 = 9. Worker 6: 70 - 65 = 5.
Step 2. Calculate average product. 1 worker: 10 ÷ 1 = 10. 2: 24 ÷ 2 = 12. 3: 42 ÷ 3 = 14. 4: 56 ÷ 4 = 14. 5: 65 ÷ 5 = 13. 6: 70 ÷ 6 = 11.7.
Step 3. Identify where diminishing marginal returns begin. Marginal product rises to 18 with the third worker and then falls, to 14 with the fourth. Diminishing marginal returns begin after the third worker.
Step 4. Check the link between marginal and average product. While MP is above AP, AP rises (workers 2 and 3). The fourth worker's MP of 14 equals AP of 14, so AP is at its maximum. After that MP is below AP and AP falls.
Total product is still rising at the sixth worker. Diminishing returns means each extra worker adds less, not that output falls.
Step 1. Calculate marginal cost for each unit. Unit 1: 160 - 100 = $60. Unit 2: 200 - 160 = $40. Unit 3: 230 - 200 = $30. Unit 4: 270 - 230 = $40. Unit 5: 330 - 270 = $60. Unit 6: 420 - 330 = $90.
Step 2. Identify marginal revenue. The firm sells any quantity at $80, so it is a price taker. MR is constant at $80 for every unit.
Step 3. Apply the rule. Produce every unit for which MC is below MR. Units 1 to 5 have MC of 60, 40, 30, 40 and 60, all below $80. Unit 6 has MC of $90, above $80, so it should not be produced. Output is 5.
Step 4. Note the diminishing returns. MC falls to $30 at the third unit and then rises to $90 at the sixth. The fall reflects increasing returns as specialisation becomes possible; the rise from the fourth unit onwards is diminishing marginal returns to the variable factor.
Step 5. Explain why the two methods agree. Total profit rises whenever an extra unit adds more revenue than cost and falls when it adds less. The output at which that switches over is exactly where MC crosses MR, so finding the peak of total profit and applying the marginal rule must give the same answer. The marginal method is preferred because it works directly from the diagram.
The MC = MR rule holds in every market structure. What changes between structures is the shape of the MR curve, not the rule, and saying so explicitly is worth a mark in structure comparison questions.
C, E, D, G, A, F, B
- An industry requires large indivisible capital equipment, so fixed costs are high relative to variable costs.
- Average fixed cost therefore falls steeply as output rises, and long-run average cost continues falling over a wide range of output.
- Minimum efficient scale is consequently large, perhaps a substantial fraction of total market demand.
- A small firm operating below that scale has higher average costs than a large rival.
- It cannot match the larger firm's price and remain profitable, so it either grows, exits or occupies a niche the large firm does not serve.
- The number of firms able to survive at efficient scale is limited by the size of the market divided by minimum efficient scale.
- The industry therefore settles into oligopoly or monopoly, not because of any anti-competitive conduct but because the cost structure permits nothing else.
This chain answers questions asking why some industries are concentrated and others are not, and it is a better answer than any list of barriers to entry, because it explains where the barrier comes from.
The key insight is why average fixed cost falls continuously without ever reaching zero: a constant amount is being divided by a rising output. This is 'spreading the overheads', and it is the reason average total cost falls at low output even when variable costs per unit are rising.
Label the axes with average cost, not total cost. The whole point of economies of scale is what happens to cost per unit, and a diagram of total cost cannot show it.
The second diagram is natural monopoly and is worth drawing separately, because it is the case where competition is not merely absent but inefficient: splitting output between two firms would raise average cost. That is the analytical basis for regulating rather than breaking up utilities, and it recurs in the market structures and government intervention topics.
Define and frame: Define profit maximisation as producing where MC equals MR with MC rising, and distinguish normal from supernormal profit. Identify the word carrying the question, which is 'always', and state that the answer depends on who controls the firm, over what time horizon, and in what market conditions.
Analysis: the case for: Profit maximisation is the assumption the whole model rests on and it is not arbitrary. Owners want returns; supernormal profit funds investment and provides a buffer; competitive pressure means a firm not maximising is vulnerable to takeover or to being undercut. Show the MC equals MR condition on a diagram and note that it predicts firm behaviour well in competitive markets over long periods.
Analysis: the alternatives: Take the alternatives seriously rather than listing them. The divorce of ownership from control means managers, whose pay and status depend on firm size, may pursue revenue or growth maximisation instead. Satisficing follows from that. Survival dominates in a downturn or for a start-up. Predatory or penetration pricing sacrifices present profit for market share, which is profit maximisation over a longer horizon rather than an alternative to it. Social and environmental objectives may be genuine or may be long-run profit maximisation through reputation.
Evaluation: Weigh rather than list. The time horizon dissolves several apparent exceptions: growth and market share strategies are consistent with maximising long-run profit. Market structure matters, since a firm in perfect competition that fails to maximise makes losses and exits, while a monopolist has slack to pursue other aims. Firm type matters, as cooperatives and state-owned firms have different constituencies. And information matters: firms may intend to maximise and fail, because they do not know their own marginal cost and revenue curves with any precision.
Judgement: Conclude that profit maximisation is a good approximation rather than a universal description: strongest for owner-managed firms, for competitive markets and over long horizons; weakest where ownership and control are separated, where market power provides slack, and in the short run. Add that the model's usefulness does not depend on being literally true, since it predicts behaviour well enough to be the right starting point. A conclusion that merely lists exceptions without saying when they bind will not reach the top level.