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Consider again the two ways in which we can view the producer’s profit maximization problem. A: Suppose a homothetic production technology involves two inputs, labor and capital, and that its producer choice set is fully convex. (a) Illustrate the product $3.59
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Consider again the two ways in which we can view the producer’s profit maximization problem. A: Suppose a homothetic production technology involves two inputs, labor and capital, and that its producer choice set is fully convex. (a) Illustrate the product
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  • Economics
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  • University Of Delhi

Consider again the two ways in which we can view the producer’s profit maximization problem. A: Suppose a homothetic production technology involves two inputs, labor and capital, and that its producer choice set is fully convex. (a) Illustrate the production frontier in an isoquant graph with lab...

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  • August 7, 2020
  • 3
  • 2020/2021
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  • economics

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  • University of delhi
  • Economics
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Consider again the two ways in which we can view the producer’s profit maximization
problem.
A: Suppose a homothetic production technology involves two inputs, labor and capital, and
that its producer choice set is fully convex.
(a) Illustrate the production frontier in an isoquant graph with labor on the horizontal axis and
capital on the vertical.

Answer: This is done in panel (a) of Graph 12.4. Since the producer choice set is convex, the
horizontal slices represented by the isoquants must have the usual convex shape. In addition,
the homotheticity property implies that the slopes (or TRS) of the isoquants are the same
along any ray from the origin




b) Does this production process have increasing or decreasing returns to scale? How would
you be able to see this on an isoquant graph like the one you have drawn?

Answer: It has decreasing returns to scale—because the entire producer choice set is convex.
You would only see this in an isoquantmap if the isoquants are accompanied by output
numbers that increase at a decreasing rate along any ray fromthe origin.

(c) For a given wage w and rental rate r , show in your graph where the cost minimizing input
bundles lie. What is true at each such input bundle?

Answer: The input prices give us the slope of the isocost lines — which is (−w/r ). The
isocost drawn in panel (a) is tangent at A — implying that (ℓA,k A) is the cheapest input
bundle that can produce the output level x A. Since the production process is homothetic, it
implies that all isoquants have the same slope along the ray from the origin through A. This

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