7.30. Consider the production function in LearningBy-Doing Exercise 7.6: For this production function, the marginal products of labor, capital, and materials are and Suppose that the input prices of labor, capital, and materials are w ! 1, r !

1, and m ! 1, respectively.

a) Given that the firm wants to produce Q units of output, what is the solution to the firm’s long-run costminimization problem?

b) Given that the firm wants to produce Q units of output, what is the solution to the firm’s short-run costminimization problem when K ! 4? Will the firm want?