Question

E. Does the relationship w/MPL = MC hold? Show this explicitly

Alison lives in a small town where she plans to hire workers to help her make candy. Her production function for candy is 0.5 94LKO5 She begins producing with K-4. The cost of capital is S50/unit. The wage depends on the amount of workers she employs. Specifically, w(L)-10 + 2L.

Answer 1

Q = 4LK^0.5 partial differential q/partial differential L = MPL = 4K^0.5 = 4 (4)^1/2 = 8 put k = 4 in q => q = 8L => L = q/8 (Lq) = w (L) L + rk = (10 + (q/8)^2) q/8 + (50 times 4) = (10 + q/4) q/8 + 200 = 10q/8 + q^2/32 + 200 dc(q/dq) = 10/8 + 2q/32 = 20 + q/16. Now checking w/mp = mc is 10 + 2L/8 = 20 + q/16 ? = 20 + 8L/16 10/8 + L/4 notequalto 10/8 + L/2.