10. Exercise 7.10 The Cobb-Douglas production function can be shown to be a special case of a larger class of linear homogeneous production functions having the following mathematical form: Q=y[5K+(1-6)L-P]-/P where y is an efficiency parameter that shows the output resulting from given quantities of inputs; & is a distribution parameter (0 ≤5 ≤ 1) that indicates the division of factor income between capital and labor; p is a substitution parameter that is a measure of substitutability of capital for labor (or vice versa) in the production process; and v is a scale parameter (v > 0) that indicates the type of returns to scale (increasing, constant, or decreasing). Complete the following derivation to show that when v = 1, this function exhibits constant returns to scale. First of all, if v = 1: -P Q = y[§K ³ + (1 -8)L¯P]-1/P = [SKP(-1/P)+(1-8)L−P(-1/p)] Then, increase the capital K and labor L each by a factor of A, or K* = (A)K and L* = (A)L. If the function exhibits constant returns to scale, then Q* = (A)Q. Q* = v[8(x)Kº + (1-6)(A)L¯P]-1/P = = Y[SAK P(-1/P) + (1-8)AL¯P(-1/p)] || || || = = λο

What is the difference between economies of scale, constant returns to scale, and diseconomies of scale?

What are the factor payments for land, labor, and capital?

Do you think that the taxicab industry in large cities would be subject to significant economies of scale? Why or why not?

Automobile manufacturing is an industry subject to significant economies of scale. Suppose there are four domestic auto manufacturers, but the demand for domestic autos is no more than 2.5 times the quantity produced at the bottom of the long-run average cost curve. What do you expect will happen to the domestic auto industry in the long run?

What shapes would you generally expect each of the following cost curves to have: fixed costs, variable costs, marginal costs, average total costs, and average variable costs?

A firm had sales revenue of 1 million last year. It spent 600,000 on labor, 150,000 on capital and 200,000 on materials. What was the firms accounting profit?