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.
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'.
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.
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.