4. Ariel's T-shirt company hires labor at a rate of $8 per hour and rents capital (sewing machines) at a cost of $128 per machine per day. Throughout this question, you can think of Ariel renting fractions of sewing machines if necessary. Her production function is given by q = 6L3K3 where q measures the number of T-shirts produced each day, L measures the total number of hours worked by all employees in a day and K measures the number of sewing machines. (a) Using the Lagrangian technique, find the cost-minimizing combination of labor and capital for the production of q T-shirts per day. (b) Write down an equation for Ariel's long-run expansion path. (c) Find Ariel's long-run total, average, and marginal cost as a function of the number of T-shirts she produces each day. (d) Sketch Arieľ's long-run total expansion path in a diagram. Sketch at least two isoquants with the associated isocost lines. Using your diagram, determine how Ariel's long-run expansion path will shift if the cost of renting a sewing machine for a day decreases. Explain why this change occurs.

4. Ariel's T-shirt company hires labor at a rate of $8 per hour and rents capital (sewing machines) at a cost of $128 per machine per day. Throughout this question, you can think of Ariel renting fractions of sewing machines if necessary. Her production function is given by q = 6L3K3 where q measures the number of T-shirts produced each day, L measures the total number of hours worked by all employees in a day and K measures the number of sewing machines. (a) Using the Lagrangian technique, find the cost-minimizing combination of labor and capital for the production of q T-shirts per day. (b) Write down an equation for Ariel's long-run expansion path. (c) Find Ariel's long-run total, average, and marginal cost as a function of the number of T-shirts she produces each day. (d) Sketch Arieľ's long-run total expansion path in a diagram. Sketch at least two isoquants with the associated isocost lines. Using your diagram, determine how Ariel's long-run expansion path will shift if the cost of renting a sewing machine for a day decreases. Explain why this change occurs.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter11: Profit Maximization

Section: Chapter Questions

Problem 11.9P

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4. Arieľ's T-shirt company hires labor at a rate of $8 per hour and rents capital (sewing machines) at a cost of $128 per machine per day. Throughout this question, you can think of Ariel renting fractions of sewing machines if necessary. Her production function is given by q = 6L%K$ where q measures the number of T-shirts produced each day, L measures the total number of hours worked by all employees in a day and K measures the number of sewing machines. (a) Using the Lagrangian technique, find the cost-minimizing combination of labor and capital for the production of q T-shirts per day. (b) Write down an equation for Ariel's long-run expansion path. (c) Find Ariel's long-run total, average, and marginal cost as a function of the number of T-shirts she produces each day. (d) Sketch Arieľ's long-run total expansion path in a diagram. Sketch at least two isoquants with the associated isocost lines. Using your diagram, determine how Ariel's long-run expansion path will shift if the cost…
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