Question: This problem works through the task of graphing short-run and long-run cost curves that will look different from those we have graphed in class. Although the cost curves will look different, the logic behind them remains the same. The firm in this question produces output with a fixed proportions production function given by: f (x1, x2) = min {x1, x2} Assume that w1 = 2 and w2 = 4. (This kind of problem was covered in class in Lecture 14 - Cost Minimization.)
(a) Find an expression for the firm's total cost function in the long run.
(b) Use your answer to part (a) to find expressions for the firm's long-run average total costs (LRATC) and long-run marginal costs (LRMC).
(c) Assume that input 2 is fixed in the short run at x2. Find an expression for the firm's short-run cost function, which is a function of y and x2. Divide this by y to also find the firm's short-run average total costs (SRATC).
(d) On the same graph, draw the LRATC curve and SRATC curves for three different levels of x2. (You can choose any values of x2 that you like. Note that each of the SRATC curves will only exist for some values of y.)
(e) Explain the relationship between the LRATC curve and the SRATC curves you have graphed.