MGEA02H3 Chap.6 Short-Run and Long-Run Costs
Short-Run and Long-Run Costs
Short-run cost curves
Total cost splits into fixed and variable cost, and the per-unit curves follow: average fixed cost falls throughout, average variable and average cost are U-shaped, and marginal cost crosses both at their minima.
The minimum of average variable cost is the shut-down price and the minimum of average cost the break-even price.
Traps and the long run
The course repeatedly states a fixed cost that differs from the constant in total cost, so part of the constant is variable.
In the long run all inputs vary and long-run average cost traces the lowest point reachable at each output across all plant sizes, falling with economies of scale, rising with diseconomies, and lowest at minimum efficient scale.
What the answer keys reward
Cost keys subtract the fixed cost stated in the question, form average variable cost, set its derivative to zero and evaluate, and they check the minimum against marginal cost.
They answer change-a-parameter items by naming which curves move and which minima shift, and they treat claims about long-run cost through the envelope and scale effects rather than diminishing returns.
The repeated trap is a constant in total cost larger than the stated fixed cost.
How this topic connects to later chapters
Chapter 7 turns these curves into decisions: marginal cost above the shut-down price is the competitive firm’s supply curve, and the minimum of long-run average cost fixes the long-run price and the number of firms.
Chapter 8 uses a falling average cost to define a natural monopoly and to set the regulated price, so the cost minima found here are inputs to most later questions.
What this chapter covers
- 01
Fixed, variable and total cost
- 02
Average and marginal cost curves
- 03
Shut-down and break-even prices
- 04
Stated fixed cost versus the TC constant
- 05
Long-run average cost as an envelope
- 06
Economies of scale and minimum efficient scale
Worked example · free
Shut-down and break-even prices from one cost equation
- 2Variable cost is 0.5q² + 4q + 32, so AVC = 0.5q + 4 + 32/q.
- 2Minimum AVC at q = 8 is $12, equal to MC = q + 4.
- 2Minimum AC = 0.5q + 4 + 98/q at q = 14 is $18.
Key terms
- Average Variable Cost
- Average variable cost is variable cost divided by output, whose minimum is the shut-down price.
- Marginal Cost
- Marginal cost is the extra cost of one more unit, the derivative of total cost.
- Economies of Scale
- Economies of scale occur when long-run average cost falls as output expands.
- Minimum Efficient Scale
- Minimum efficient scale is the output at which long-run average cost first reaches its minimum.
- Fixed Cost
- Fixed cost is the cost of the fixed input, paid whatever the output in the short run.
- Diseconomies of Scale
- Diseconomies of scale occur when long-run average cost rises with output, often from coordination problems.
Short-Run and Long-Run Costs FAQ
Why does marginal cost cut average cost at its minimum?
When marginal cost is below average cost, each extra unit pulls the average down; when it is above, the average rises. The average is therefore lowest exactly where the two are equal.
What changes when fixed cost rises?
Marginal cost and average variable cost do not change, so neither does the shut-down price. Average cost rises, and its minimum moves up and to the right along the unchanged marginal cost curve.
Is rising long-run average cost caused by diminishing returns?
No. Diminishing returns needs a fixed input and belongs to the short run. Rising long-run average cost reflects diseconomies of scale, such as the difficulty of managing a very large organisation.
How does a wage rise move the cost curves?
A wage rise scales variable cost, average variable cost and marginal cost up in proportion. The output at minimum average variable cost does not change, while the minimum of average cost moves up and slightly to the left because fixed cost is unchanged.
Exam move
Write one total cost equation with a separately stated fixed cost and derive every curve from it. Then change the fixed cost and the wage in turn, and say which curves and minima move. Practise sketching the three average curves and marginal cost from one equation, and label the distance that represents average fixed cost.
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