Consider a profit maximizing firm.
A: Explain whether the following statements are true or false:
(a) For price-taking, profit maximizing producers, the “constraint” is determined by the technological environment in which the producer finds herself while the “tastes” are formed by the economic environment in which the producer operates.
(b) Every profit maximizing producer is automatically cost-minimizing.
(c) Every cost-minimizing producer is automatically profit maximizing.
(d) Price taking behavior makes sense only when marginal product diminishes at least at some point.
B: Consider the production function x = f (ℓ) = αln (ℓ+1).
(a) Does this production function have increasing or decreasing marginal product of labor.
(b) Set up the profit maximization problem and solve for the labor input demand and output supply functions.
(c) Recalling that ln x = y implies ey = x (where e ≈ 2.7183 is the base of the natural log), invert the production function and derive from this the cost function c (w, x).
(d) Determine the marginal and average cost functions.
(e) Derive from this the output supply and labor demand functions. Compare them to what you derived directly from the profit maximization problem in part (b).
(f) In your mathematical derivations, what is required for a producer to be cost minimizing? What, in addition, is required for her to be profit maximizing?