A fi?rm produces a product with labor and capital. Its production function is described by Q = 2L + 3K: Let w and r be the prices of labor and capital,respectively.
(a) Find the equation for the firm's long-run total cost curves as a function of quantity Q, for input prices, w = 1 and r = 1.
(b) Find the equation for the firm's long-run total cost curves as a function of quantity Q and input prices, w and r (and so as a function of three parameters).
c) Find the solution to the firm's short-run cost-minimization problem when capital is fixed at a quantity of 5 units (i.e., K = 5), and w = 1 and r = 1.
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 the same input prices.