8.13. A firm produces a product with labor and capital.

Its production function is described by Q ! L " K. The marginal products associated with this production function are MPL ! 1 and MPK ! 1. Let w ! 1 and r ! 1 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 when the prices of labor and capital are w ! 1 and r ! 1.

b) Find the solution to the firm’s short-run costminimization problem when capital is fixed at a quantity of 5 units (i.e., and w ! 1 and r ! 1. Derive the equation for the firm’s short-run total cost curve as a function of quantity Q and graph it together with the long-run total cost curve.