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Cost Functions: A firm operates with a production function, y = 4√lk and input prices Pe = 6 and Pk = 7. In the short run, capital is a fixed input, k = 36. (a) Find the firm's cost function, c(y), the minimum cost to produce a given amount of output. (b) In the long run, both labor and capital are variable inputs. Suppose that py = 20; what will the firm do in the long run? What if the price is py = 0.50?¹

Cost Functions: A firm operates with a production function, y = 4√lk and input prices Pe = 6 and Pk = 7. In the short run, capital is a fixed input, k = 36. (a) Find the firm's cost function, c(y), the minimum cost to produce a given amount of output. (b) In the long run, both labor and capital are variable inputs. Suppose that py = 20; what will the firm do in the long run? What if the price is py = 0.50?¹

Microeconomic Theory
Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter10: Cost Functions
Section: Chapter Questions
Problem 10.3P
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2. Cost Functions: A firm operates with a production function, y = 4√lk and input prices Pe = 6 and Pk = 7. In the short run, capital is a fixed input, k = 36. (a) Find the firm's cost function, c(y), the minimum cost to produce a given amount of output. (b) In the long run, both labor and capital are variable inputs. Suppose that what will the firm do in the long run? What if the price is py: = 0.50?¹ = Py 20;
Transcribed Image Text:2. Cost Functions: A firm operates with a production function, y = 4√lk and input prices Pe = 6 and Pk = 7. In the short run, capital is a fixed input, k = 36. (a) Find the firm's cost function, c(y), the minimum cost to produce a given amount of output. (b) In the long run, both labor and capital are variable inputs. Suppose that what will the firm do in the long run? What if the price is py: = 0.50?¹ = Py 20;
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