Consider the following production function: q = (KL)^α, where α > 0. (a) Confirm that the marginal physical product of capital is homogenous of degree zero in the case in which the production function exhibits constant returns to scale. (b) Derive an expression for the cost function of a firm using the production function to produce output of a good. (c) Find the first and second partial derivatives of the cost function with respect to q. Interpret the second partial derivative and relate the sign of the derivative to the returns to scale.
Consider the following production function: q = (KL)^α, where α > 0. (a) Confirm that the marginal physical product of capital is homogenous of degree zero in the case in which the production function exhibits constant returns to scale. (b) Derive an expression for the cost function of a firm using the production function to produce output of a good. (c) Find the first and second partial derivatives of the cost function with respect to q. Interpret the second partial derivative and relate the sign of the derivative to the returns to scale.
Chapter9: Production Functions
Section: Chapter Questions
Problem 9.7P
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Consider the following production function:
q = (KL)^α, where α > 0.
(a) Confirm that the marginal physical product of capital is homogenous of degree zero in the case in which the production function exhibits constant returns to scale.
(b) Derive an expression for the cost function of a firm using the production function to produce output of a good.
(c) Find the first and second partial derivatives of the cost function with respect to q. Interpret the second partial derivative and relate the sign of the derivative to the returns to scale.
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