A production function in which the inputs are perfectly substitutable would have isoquants that are

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BlackTom AI · Accepted Answer

Question: A production function in which the inputs are perfectly substitutable would have isoquants that are

- In a case where inputs are perfect substitutes, the production function can be written as a linear combination of the inputs, such as f(K,L) = aK + bL. The isoquant for a given output level q is the set of (K,L) satisfying aK + bL = q, which is a straight line in the K-L input space. This reflects a constant, linear rate of technical substitution between inputs.

- Because the isoquant is a straight line, you can replace some amount of one input with the other at a constant rate without changing output, hence the linear shape. The slope is determined by the relative productivity weights (a and b), specifically the trade-off where ΔK/ΔL = -b/a along the isoquant.

- If the question intends to contrast with other shapes, note that:
  • If inputs are imperfect substitutes, isoquants would still be convex curves but not perfectly linear, reflecting a diminishing marginal rate of substitution.
  • If inputs were gross complements, isoquants would be L-shaped, indicating a fixed proportion of inputs is required.

- The key misconception to avoid is thinking isoquants with perfect substitutes would be curved or convex; the defining feature is the straight-line, linear isoquant due to the constant trade-off rate between perfectly substitutable inputs.

- Since the provided answer option is "linear," this aligns with the standard result that perfect substitutes yield linear isoquants in the input space.

A production function in which the inputs are perfectly substitutable would have isoquants that are Single choice

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