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Show using math and logic that for constant returns to scale

production functions, MRTS between labor and capital depends only
on the K/L ratio, and not the scale of production.

User GRoutar
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1 Answer

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Final answer:

The Marginal Rate of Technical Substitution (MRTS) between labor and capital depends only on the K/L ratio, and not the scale of production, in constant returns to scale production functions.

Step-by-step explanation:

The Marginal Rate of Technical Substitution (MRTS) between labor and capital measures the rate at which the firm can substitute one input for another while keeping the level of output constant. In the case of constant returns to scale production functions, the MRTS between labor and capital depends only on the capital-labor (K/L) ratio, and not on the scale of production.

For example, let's consider a production function where the amount of output is determined solely by the amount of labor employed. In this case, the MRTS between labor and capital can be calculated as the change in labor units divided by the change in capital units, and it remains constant regardless of the scale of production.

This property holds true for any constant returns to scale production function, where changes in the K/L ratio result in a proportional change in the MRTS between labor and capital. This implies that the MRTS between labor and capital depends solely on the K/L ratio and is independent of the scale of production.

User Eliel
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