Question

Difficulty: HardLong-Run Costs and Production

A solar panel manufacturing company increases all of its production inputs—factory space, machinery, and labor—by 25%25\%. Consequently, its total output of solar panels increases by 15%15\%. At the same time, the chief financial officer argues that the firm cannot lower its unit costs further because fixed capital overhead costs cannot be varied in the long run. Which of the following correctly identifies the firm's returns to scale and evaluates the officer's cost argument?

  1. The firm is experiencing decreasing returns to scale, and the officer is incorrect because all inputs and costs are variable in the long run.Answer
  2. B
    The firm is experiencing increasing returns to scale, and the officer is correct because fixed overhead costs remain constant across all time horizons.
  3. C
    The firm is experiencing decreasing returns to scale, but the officer is correct because plant capacity constitutes a fixed cost in both short-run and long-run analysis.
  4. D
    The firm is experiencing constant returns to scale, and the officer is incorrect because fixed costs diminish to zero automatically as output expands.

Answer

The firm is experiencing decreasing returns to scale, and the officer is incorrect because all inputs and costs are variable in the long run.
The correct answer identifies that the firm operates under decreasing returns to scale because output expands by 15%15\%, which is less than the 25%25\% proportional increase in all inputs. It also correctly refutes the officer's argument by applying the fundamental economic principle that all inputs—and therefore all costs—are variable in the long run.

Step-by-Step Solution

1
Calculate the ratio of output change relative to input change to determine returns to scale.
Proportional change in inputs = +25%+25\%. Proportional change in output = +15%+15\%. Since %ΔOutput<%ΔInputs\% \Delta \text{Output} < \% \Delta \text{Inputs} (15%<25%15\% < 25\%), the firm experiences decreasing returns to scale.
Returns to scale measure how output responds when all inputs are scaled simultaneously by a given proportion.
2
Evaluate the financial officer's statement regarding fixed costs in the long run.
The officer's assertion that capital overhead costs cannot be varied in the long run is economically incorrect.
By definition, the long run is a time horizon long enough for a firm to vary all factors of production. Consequently, there are no fixed costs in the long run; all costs are variable.

Key Concept

Long-Run Production and Returns to Scale
Rate this question