"Adam's Apples" produces apple cider using labor (L) and apples (A) according to the Cobb-Douglas production function Q = F(L, A) = 4L^3/8 A^1/8. The price of apples is pA = 1 and the price of labor is w = 3. Adam's Apples also has a fixed cost for farm buildings, FC = 100.
Required:
1. If Adam's Apples wants to produce 10 barrels of apple cider, Q=10, what is its lowest possible total cost? (Roadmap: (1) Determine the optimal input choice (L*, A*) by tangency condition, MRT SLA (L*, A*) = w/PA and production requirement 10 = F(L*, A*). (2) Variable costs are then found by wl* + PAA*. (3) Total cost is sum of variable and fixed costs.)
2. Determine Adam's Apples' Average Cost function, AC(Q), and marginal cost function, MC(Q).