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3. Suppose a production function is given by F(K, L) KL2; the price of capital is $10 and the price of labor $15. What combination of labor and capital minimizes %3D the cost of producing any given output?

3. Suppose a production function is given by F(K, L) KL2; the price of capital is $10 and the price of labor $15. What combination of labor and capital minimizes %3D the cost of producing any given output?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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increasing, constant, or decreasing returns to scale? 100KL. If the price of capital is $120 per day and the and L the number of person-hours of labor. In addition Now consider the dual problem of maximizing price of labor $30 per day, what is the minimum cost of this problem for the Cobb-Douglas production fu ginning of this section, we assu C < 2Co- Even though wages doubled, th cheaper capital, thereby keeping the increase in tota than doubled. This is the expected result. If a firm su duced with the expenditure of C, dollars. We lea labor, it would substitute away from labor and em choices. To get you started, note that the Lagran 1. qf the following production functions, which exhibit 2. The production function for a product is given by q : number of computerized stitching-machine hours, bns 9ohun show that equations (A7.24) and (A7.25) descrit = AK“L- ulwL + rK Co). MF (L,L) >con stont 1, PFlukiML). returi (uk u)> MF (K,) n うincreasi Flu.Liu Eしうdecs Flv. EXERCISES a. F(K, L) = K²L b. F(K, L) = 10K + 5L c. F(K, L) = (KL)5 to capital and labc in the production areesingstelefodea. By minimizing %3D Vorl wore tion, derive the as a function rates on mac %3D total cost fune price of labor $30 per day, what is the minimum cost of producing 1000 units of output? 3. Suppose a production function is given by F(K, L) KL?; the price of capital is $10 and the price of labor $15. What combination of labor and capital minimizes the cost of producing any given output? 4. Suppose the process of producing lightweight parkas by Polly's Parkas is described by the function and the cons b. This process per hour. T the process what are to technology ing returns c. Polly's Pa week. At workers q = 10K*(L – 40)² and how machine and ave where q is the number of parkas produced, K the
Transcribed Image Text:increasing, constant, or decreasing returns to scale? 100KL. If the price of capital is $120 per day and the and L the number of person-hours of labor. In addition Now consider the dual problem of maximizing price of labor $30 per day, what is the minimum cost of this problem for the Cobb-Douglas production fu ginning of this section, we assu C < 2Co- Even though wages doubled, th cheaper capital, thereby keeping the increase in tota than doubled. This is the expected result. If a firm su duced with the expenditure of C, dollars. We lea labor, it would substitute away from labor and em choices. To get you started, note that the Lagran 1. qf the following production functions, which exhibit 2. The production function for a product is given by q : number of computerized stitching-machine hours, bns 9ohun show that equations (A7.24) and (A7.25) descrit = AK“L- ulwL + rK Co). MF (L,L) >con stont 1, PFlukiML). returi (uk u)> MF (K,) n うincreasi Flu.Liu Eしうdecs Flv. EXERCISES a. F(K, L) = K²L b. F(K, L) = 10K + 5L c. F(K, L) = (KL)5 to capital and labc in the production areesingstelefodea. By minimizing %3D Vorl wore tion, derive the as a function rates on mac %3D total cost fune price of labor $30 per day, what is the minimum cost of producing 1000 units of output? 3. Suppose a production function is given by F(K, L) KL?; the price of capital is $10 and the price of labor $15. What combination of labor and capital minimizes the cost of producing any given output? 4. Suppose the process of producing lightweight parkas by Polly's Parkas is described by the function and the cons b. This process per hour. T the process what are to technology ing returns c. Polly's Pa week. At workers q = 10K*(L – 40)² and how machine and ave where q is the number of parkas produced, K the
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