1. Consider a firm which produces a single output using two inputs according to the following production function: y = min{2K, L}, where y is the firms output, K is machinery (measured in machine-hours)and L is labor supply (measured in person-hours). Let r be the cost of one machine-hour and let w be the wage rate (i.e. the cost of one person-hour).
(a) Suppose that r = 16 and w = 4. Determine the firms cost function c(y).
b) On a diagram that has costs on the vertical axis and output and the horizontal axis, plot the firmscost curve c(y), average cost curve AC(y), and marginal cost curve MC(y).
2. Consider the firm ACME which uses capital, K, and labour, L, to produce widgets according to the following production function: f(K, L) = K^(2/3) *L^(1/3) . Let r and w be the prices of capital and labour respectively. P is the price of widgets. The markets for widgets, capital, and labour are all perfectly competitive.
(b) In the short run, the level of capital is fixed at K = K. Set up the short run profit maximization problem. Calculate the short run optimal level of labour.
(c) In the long run, ACME can vary both K and L. Set up ACME's long run cost minimization problemby using the Lagrange method. What are the cost minimizing levels of K and L in the long run?
(d) Derive ACME's long run cost function.
3. In Freedonia, a single firm is in the domestic steel business. It sells steel at $680 per ton, well above the wold price of $375 per ton. The firm is protected against foreign competition by incredibly high tariffs that ban all imports.The firm has never exported steel. The CEO argues: "The average cost of manufacturing steel, which varies with the rate at which the firm produces steel, is never below $400 per ton. We simply cannot make positive profits selling steel for $375 per ton." Is this argument convincing? Provide a short answer(at most 4 sentences).