Question 4. [Costs - Short Run vs Long Run]Following is a firm's production function for soccer balls:q=√k₂l,where k₁ is the fixed amount of k(capital equipment) in the short run, and I is the amount of labor.a)) Calculate the firm's short-run total costs as a function of q, v, w and k₁ (where v = unitcapital price; w= unit labor price)b)(ints) Given q, v, and w, how should the capital stock be chosen to minimize short-run totalcost?c)d)) Using your answer from b) above, calculate the long-run total cost of soccer ballproduction.For v=$1, w=$4, and k₁=100, at what level of q is short-run cost function tangent to thelong-run cost function?

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Following is a firm's production function for soccer balls: a = √k₂l, where k₁ is the fixed amount of k(capital equipment) in the short run, and I is the amount of labor. a) b) c) d) Calculate the firm's short-run total costs as a function of q, v, w and k₁ (where v = unit capital price; w = unit labor price) Given q, v, and w, how should the capital stock be chosen to minimize short-run total cost? 3) Using your answer from b) above, calculate the long-run total cost of soccer ball production. For v=$1, w=$4, and k₁=100, at what level of q is short-run cost function tangent to the long-run cost function?

Following is a firm's production function for soccer balls: a = √k₂l, where k₁ is the fixed amount of k(capital equipment) in the short run, and I is the amount of labor. a) b) c) d) Calculate the firm's short-run total costs as a function of q, v, w and k₁ (where v = unit capital price; w = unit labor price) Given q, v, and w, how should the capital stock be chosen to minimize short-run total cost? 3) Using your answer from b) above, calculate the long-run total cost of soccer ball production. For v=$1, w=$4, and k₁=100, at what level of q is short-run cost function tangent to the long-run cost function?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter10: Cost Functions

Section: Chapter Questions

Problem 10.4P

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