Problem
A firm produces a product with labor and capital. Its production function is described by Q = min(L, K). Let w and r be the prices of labor and capital, respectively. a) Find the equation for the firm's long-run total cost curve as a function of quantity Q and input prices, w and r.
b) Find the solution to the firm's short-run costminimization problem when capital is fixed at a quantity of 5 units (i.e., Derive the equation for the firm's short-run total cost curve as a function of quantity Q. Graph this curve together with the long-run total cost curve for w = 1 and r = 1.
c) How do the graphs of the long-run and short-run total cost curves change when w = 1 and r = 2?
d) How do the graphs of the long-run and short-run total cost curves change when w = 2 and r = 1?
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.