Linking product and cost curves; short-run and long-run costs

Marginal product and marginal cost

If each worker costs a wage W, then:

• MC = W / MP: when MP is rising, MC is falling; when MP is at its maximum, MC is at its minimum; when diminishing returns set in, MC rises.
• AVC = W / AP: AVC is at its minimum where AP is at its maximum.

So the U shapes of the short-run cost curves come directly from rising then diminishing marginal productivity.

Long-run average cost

In the long run the firm can choose any scale of plant. Each scale has its own U-shaped short-run average cost (SRAC) curve. The long-run average cost (LRAC) curve shows the lowest average cost of producing each output when all factors can vary.

Diagram in words: draw several overlapping SRAC curves, each lower and further to the right while economies of scale apply, then higher once diseconomies set in. The LRAC is the 'envelope' that touches each SRAC from below.

Why the LRAC is U-shaped

The shape of the LRAC is not caused by diminishing returns (no factor is fixed in the long run). It falls because of economies of scale and rises because of diseconomies of scale. Do not confuse the two explanations: it is a common exam error.

Worked example

The wage is $60 per worker. The 4th worker has a marginal product of 15 units; average product at 4 workers is 12 units. Find MC and AVC.

1. MC = W / MP = 60 / 15 = $4.
2. AVC = W / AP = 60 / 12 = $5.

Answer: MC = $4, AVC = $5.

Check yourself

1. The wage is $90 per day. An extra worker adds 30 units per day. Find the marginal cost per unit.
   Show answer

   $3. MC = W / MP = 90 / 30 = $3.

2. The wage is $90 per day and average product is 18 units per worker. Find AVC.
   Show answer

   $5. AVC = W / AP = 90 / 18 = $5.

3. When marginal product is at its maximum, marginal cost is
   • at its maximum
   • at its minimum
   • equal to average fixed cost
   • zero
   Show answer

   at its minimum. MC = W / MP, so the largest MP gives the smallest MC.

4. The long-run average cost curve is U-shaped because of
   • the law of diminishing returns
   • falling average fixed cost
   • economies and then diseconomies of scale
   • changes in the price of the product
   Show answer

   economies and then diseconomies of scale. In the long run no factor is fixed, so diminishing returns do not apply.

5. Which statement about the LRAC curve is correct?
   • It touches each short-run average cost curve from below
   • It always lies higher than every SRAC curve
   • It is drawn for one fixed plant size
   • It is always horizontal
   Show answer

   It touches each short-run average cost curve from below. LRAC shows the lowest cost for each output when the firm picks the best plant size.

6. Diminishing returns explain the rising part of which curve?
   • Long-run average cost
   • Average revenue
   • Short-run marginal cost
   • Average fixed cost
   Show answer

   Short-run marginal cost. As MP falls with a fixed factor, MC rises in the short run.

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Sources

• Pearson Edexcel International Advanced Subsidiary/Advanced Level in Economics specification (XEC11/YEC11), Unit 3 Business behaviour and Appendices 6 and 7

Last updated 8 November 2026. Spotted a mistake? Tell us.