Question

”Adam’s Apples” produces apple cider using labor (L) and apples (A) according to the Cobb-Douglas production function Q = F (L, A) = 2(L^1)/(A^3/4). The price of apples is pA = 2 and the price of labor is W = 10. Adam’s Apples also has a fixed cost for farm buildings, FC = 100.
1. If Adam’s Apples wants to produce 100 gallons of apple cider, Q=100, what is its lowest achievable input cost? (Roadmap: (1) Determine the optimal input choice (L∗,A∗) by tangency condition, MRTSLA (L∗,A∗) = W/pA and production requirement 100 = F (L∗,A∗). (2) Variable costs are then found by WL∗ +pA(A∗). (3) Total cost is sum of variable and fixed costs.)
2. Determine Adam’s Apples’ cost function, C(Q). Verify that C (100) gives you same answer as in question 1.
3. Determine Adam’s Apples’ Average Cost function, AC(Q), and marginal cost function, MC(Q).

Answer 1