Expenditure minimization: set-up. Use the Lagrange multiplier method to set up 3 equations in 3 unknowns, the first order conditions derived from the Lagrangian, where your objective is to minimize expenditures M, given the functions wL + rK = M(L,K) and q = k^0.5L^0.5 + L, where: w = 12, r = 3, q = 36. (Think about, but no need to write down, the reasons that this system of equations is so much harder to solve than the system in Example 10.1 of N&S.)

L :

FOCs:

Give the formulas for the marginal product of labor MP_L , the average product of labor AP_L, and the marginal product of capital MP_K for the production function q = L + K^0.35L^0.65. See example 9.1 or the lecture notes for the definitions.

MP_L =

AP_L =

MP_K =