Consider a firm that produces a single output with a single input, labor, using production function F (L) = 100L − 4L², for L ∈ [0, 12.5]. The input price is W = 2. The firm can sell the output at a price of P = 1/16.
1) Determine the firm’s cost function C (Q), that is, the lowest cost of producing Q units of output. State the associated labor choice for a given required output, L(Q). Consider only the range Q ∈ [0, 12.5].
2) What is the firm’s marginal cost curve, MC(Q)?
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