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?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![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 = unit
capital price; w= unit labor price)
b)(ints) Given q, v, and w, how should the capital stock be chosen to minimize short-run total
cost?
c)
d)
) 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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb369eb62-11fd-4878-881a-f7bb242e6acd%2Fb8a746d8-0d74-4cef-92aa-fa8cd28ba2f0%2F9n5e6nq_processed.png&w=3840&q=75)
Transcribed Image Text: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 = unit
capital price; w= unit labor price)
b)(ints) Given q, v, and w, how should the capital stock be chosen to minimize short-run total
cost?
c)
d)
) 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?
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