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A firm produces a product with labor and capi- inputs. The production function is described by LK. The marginal products associated with this uction function are MP, = K and MP = L. Let 1 and r = 1 be the prices of labor and capital, ectively. nd the equation for the firm's long-run total cost as a function of quantity Q. olve the firm's short-run cost-minimization problem capital is fixed at a quantity of 5 units (i.e., K = 5). ve the equation for the firm's short-run total cost as a function of quantity Q and graph it together the long-run total cost curve. ow do the graphs of the long-run and short-run cost curves change when w = 1 and r = 4? ow do the graphs of the long-run and short-run cost curves change when w = 4 and r = 1?

A firm produces a product with labor and capi- inputs. The production function is described by LK. The marginal products associated with this uction function are MP, = K and MP = L. Let 1 and r = 1 be the prices of labor and capital, ectively. nd the equation for the firm's long-run total cost as a function of quantity Q. olve the firm's short-run cost-minimization problem capital is fixed at a quantity of 5 units (i.e., K = 5). ve the equation for the firm's short-run total cost as a function of quantity Q and graph it together the long-run total cost curve. ow do the graphs of the long-run and short-run cost curves change when w = 1 and r = 4? ow do the graphs of the long-run and short-run cost curves change when w = 4 and r = 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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8.11. A firm produces a product with labor and capi- tal as inputs. The production function is described by Q = LK. The marginal products associated with this production function are MP, = K and MP = L. Let w = 1 and r = 1 be the prices of labor and capital, respectively. a) Find the equation for the firm's long-run total cost curve as a function of quantity Q. b) Solve the firm's short-run cost-minimization problem when capital is fixed at a quantity of 5 units (i.e., K = 5). Derive the equation for the firm's short-run total cost curve as a function of quantity Q and graph it together with the long-run total cost curve. c) How do the graphs of the long-run and short-run total cost curves change when w = 1 and r = 4? d) How do the graphs of the long-run and short-run total cost curves change when w = 4 and r = 1?
Transcribed Image Text:8.11. A firm produces a product with labor and capi- tal as inputs. The production function is described by Q = LK. The marginal products associated with this production function are MP, = K and MP = L. Let w = 1 and r = 1 be the prices of labor and capital, respectively. a) Find the equation for the firm's long-run total cost curve as a function of quantity Q. b) Solve the firm's short-run cost-minimization problem when capital is fixed at a quantity of 5 units (i.e., K = 5). Derive the equation for the firm's short-run total cost curve as a function of quantity Q and graph it together with the long-run total cost curve. c) How do the graphs of the long-run and short-run total cost curves change when w = 1 and r = 4? d) How do the graphs of the long-run and short-run total cost curves change when w = 4 and r = 1?
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