A perfectly competitive rm produces output q with capital K and labor L according to the production function: q = f(K, L) = 4K 1 4L 1 4 The price of labor is w = 4, and the price of capital is r = 4. The rm has xed costs equal to 8. The current market price is 8. (d) Find cost functions T C(q), AT C(q), and MC(q), i.e. as functions of output. At what value of q does the minimum of AT C occur? (e) Find total and marginal revenue as functions of output, i.e. T R(q) and MR(q). (f) Find the pro t maximizing output q ∗ and use that to nd T R(q ∗ ), T C(q ∗ ), π(q ∗ ), L(q ∗ ), and K(q ∗ ).
A perfectly competitive rm produces output q with capital K and labor L according to the production function: q = f(K, L) = 4K 1 4L 1 4 The price of labor is w = 4, and the price of capital is r = 4. The rm has xed costs equal to 8. The current market price is 8. (d) Find cost functions T C(q), AT C(q), and MC(q), i.e. as functions of output. At what value of q does the minimum of AT C occur? (e) Find total and marginal revenue as functions of output, i.e. T R(q) and MR(q). (f) Find the pro t maximizing output q ∗ and use that to nd T R(q ∗ ), T C(q ∗ ), π(q ∗ ), L(q ∗ ), and K(q ∗ ).
Chapter10: Cost Functions
Section: Chapter Questions
Problem 10.3P
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(d) Find cost functions T C(q), AT C(q), and MC(q), i.e. as functions of output. At what value of q does the minimum of AT C occur? (e) Find total and marginal revenue as functions of output, i.e. T R(q) and MR(q). (f) Find the pro t maximizing output q ∗ and use that to nd T R(q ∗ ), T C(q ∗ ), π(q ∗ ), L(q ∗ ), and K(q ∗ ).
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