A firm's production function is given by y = 10x1/²x1/2 where x₁ indicates the input labor and x2 indicates the input capital. (a) Compute the partial derivatives of the production function. Provide an economic interpretation of each derivative. (b) When an amount of capital available is fixed by x2 = 9, compute the par- tial derivative with respect to ₁ and sketch its graph. Determine whether the derivative is monotone increasing or decreasing, and provide an inter- pretation.

A firm's production function is given by y = 10x1/²x1/2 where x₁ indicates the input labor and x2 indicates the input capital. (a) Compute the partial derivatives of the production function. Provide an economic interpretation of each derivative. (b) When an amount of capital available is fixed by x2 = 9, compute the par- tial derivative with respect to ₁ and sketch its graph. Determine whether the derivative is monotone increasing or decreasing, and provide an inter- pretation.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.11P

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