The Cobb Douglas Costs Excel App provides a nice link between the Cobb Douglas (CD) production analysis of Chapter 6 (see also Cobb Douglas Production Excel App) and the cost analysis in this chapter. The Cobb Douglas Costs Excel App depicts total and per-unit cost curves based on the CD production function, Q = aLbKc, given prices for labor and capital of w and r, respectively, for a variety of plant sizes. When initially opened, the graphs depict costs given a = 1, b = 0.5, c = 0.5, w = 1, and r = 1.
a. What type of returns to scale exists in this instance?
b. Given equal weighted CD production, and equal factor prices, what does the long-run expansion path look like in terms of capital intensity, k (k is the number of units of capital per unit of labor)? In particular, what is k on the long-run expansion path K = kL.
c. Is Q = 1 produced at minimum cost in this instance by having L = K = 1? What is LAC (1) in this instance?
d. Would LAC change if we considered producing Q = 2 by adjusting plant size accordingly?