Suppose the short-run production function is [math: q=10L], if the wage rate is £10 perunit of labour, then AVC equals:

Question

BlackTom AI · Accepted Answer

Because q = 10L, one unit of labour produces 10 units of output, so the variable cost per unit of output is constant.

1) Relevant knowledge points and concepts
- Short-run production function q = f(L) relates output q to labour input L; other inputs are fixed.
- Wage rate w is the cost per unit of labour. Total variable cost (TVC) = w · L.
- Average variable cost (AVC) = TVC / q (variable cost per unit of output).

2) Step-by-step reasoning
- Start from q = 10L and solve for L in terms of q:
  L = q / 10.
- Compute TVC using the wage w = £10:
  TVC = w · L = 10 · L.
- Substitute L = q/10 into TVC:
  TVC = 10 · (q / 10).

3) Intermediate calculation steps
- TVC = 10 · (q / 10) = q.
- Now compute AVC = TVC / q = q / q.

4) Why the correct answer is correct
- q / q = 1, so AVC = 1 (i.e., £1 per unit of output). The linear production function implies constant labour required per unit of output, and with a fixed wage this yields a constant AVC independent of q.

5) Why the other options are incorrect
- b. q: This equals TVC (total variable cost), not average variable cost; dividing by q yields 1.
- c. q/10: This equals L (the amount of labour used), not a cost measure.
- d. 10/q: This has wrong algebraic form; it would shrink with q and is not equal to TVC/q given TVC = q.

6) Conclusion
AVC = 1, so the correct choice is a. 1, which matches the provided answer.

Suppose the short-run production function is [math: q=10L], if the wage rate is £10 perunit of labour, then AVC equals:多项选择题

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