Consider the following production function:
q = (KL)^α, where α > 0.
Answer the following questions:
(a) Under what conditions (i.e. values of α) will the production function exhibit decreasing returns to scale? Under what conditions will it exhibit constant returns to scale? Under what circumstances will it exhibit increasing returns to scale?
(b) 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.
(c) Derive an expression for the cost function of a firm using the production
function to produce output of a good.
(d) 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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