Suppose that the firm uses three inputs to produce its output: capital K, labor L, and materials

Question:

Suppose that the firm uses three inputs to produce its output: capital K, labor L, and materials M. The firm's production function is given by Q = K1/3L1/3M1/3. For this production function, the marginal products of capital, labor, and materials are MPK = 1/3K−2/3L1/3M1/3, MPL = 1/3K1/3L−2/3M1/3, and MPM = 1/3K1/3L1/3M−2/3. The prices of capital, labor, and materials are r = 1, w = 1, and m = 1, respectively.