Suppose that Marie produces milk q using her own labor l and cattle k using the production function q = f(k, l) = k2/3ℓ1/3 Although Marie does not need to pay anyone to use either input, the opportunity costs of
Suppose that Marie produces milk q using her own labor l and cattle k using the production
q = f(k, l) = k2/3ℓ1/3
Although Marie does not need to pay anyone to use either input, the opportunity costs of labor and cattle are w = 1 and v = 16, respectively, and P is the price of milk.
a) Set up Marie’s short run profit maximization problem and find her short run supply curve q(P).
b) Now consider Marie’s problem in the long run, where her stock of cattle may vary. Set up her long run cost minimization problem and find her labor ℓc(q) and capital kc(q) demands and cost function C(q).
c) Set up Marie’s long run profit maximization problem and find her long run supply curve q(P).
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