Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
1. Suppose that a producer has the following production function: Where Q is output, and L and K are man-bours and machine-hour the tvo inputs used in the production procesS. 1A) Set up the cost minimization problem as shonn in class In the cost minimization problem, the cost is minimized subject to constraint production fnction. It is indieated as follows: Minimize wL + IK subject to constraint Q = K L A=wL+rK + (Q-K-L") The Lagrange f unction is differentiated by K and L to caleulate the minimize the cost, and W=wage rate L= Labor R=real interest rate K = capital Q = output A= parameter coefficient %3D 1B) Determine the cost-minmize ratio of iEputs where capital costa 31 per mackine-bour and labor osts 34 per lab- hour -Marginal Rate of technical substitution is the ratio of marginal product of labor to capital. 吉PE MRTS = MPK MPL is the marginal product of labor, calculated by differentiating production function with respect to Labor. MPK 1s the marginal product of capital, calculated by difterentiating production fonetionm with respect to Capital. The exponential power of L and K are the elasticities of labor and capital Factor Elasticity Vhere a s elasticty of Laber And Dis elastich of capitel Factor intensty ato= MRTS =Fector elasticihFnor intens R MRIS =

1. Suppose that a producer has the following production function: Where Q is output, and L and K are man-bours and machine-hour the tvo inputs used in the production procesS. 1A) Set up the cost minimization problem as shonn in class In the cost minimization problem, the cost is minimized subject to constraint production fnction. It is indieated as follows: Minimize wL + IK subject to constraint Q = K L A=wL+rK + (Q-K-L") The Lagrange f unction is differentiated by K and L to caleulate the minimize the cost, and W=wage rate L= Labor R=real interest rate K = capital Q = output A= parameter coefficient %3D 1B) Determine the cost-minmize ratio of iEputs where capital costa 31 per mackine-bour and labor osts 34 per lab- hour -Marginal Rate of technical substitution is the ratio of marginal product of labor to capital. 吉PE MRTS = MPK MPL is the marginal product of labor, calculated by differentiating production function with respect to Labor. MPK 1s the marginal product of capital, calculated by difterentiating production fonetionm with respect to Capital. The exponential power of L and K are the elasticities of labor and capital Factor Elasticity Vhere a s elasticty of Laber And Dis elastich of capitel Factor intensty ato= MRTS =Fector elasticihFnor intens R MRIS =

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 23EQ: 23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes...
See similar textbooks
icon
Related questions
Question
1. Suppose that a producer has the following production function: Where Q is output, and L and K are man-bours and machine-hour the two inputs used in the production procesS. 1A) Set up the cost minimization problem as shown in class In the cost mimimization problem, the cost is minimized subject to constraint production fimction. It is indicated as follows: Minimize wL rK subject to constraint Q =K L" A=wL+K+(Q-K-L") The Lagrangefunction is differentiated by K and L to calculate the minımize the cost, and W= waee rate L=Labor R=real interest rate K= capital Q= output N=parameter coefficient 1B) Determine the cost-minimize ratio of input: where capital costa 30 per macline-bour and abor costs 34 per lab- hour -Marginal Rate of technical substitution is the ratio of marginal product of labor to capital. MPE MRTS = MPK MPL is the marginal product of labor, calculated by differentiating productior function with respect to Labor. MPK 1s the marginal product of eapital, caleulated by difterentiating production fonetron vith respect to Capital. The exponentLal power of L and K are the elasticities of labor and capita Factor Elasticity = = Where &Belasbat of Laber And Dis elastiat of capiel Factor istensiry DD = NRTS =
Transcribed Image Text:1. Suppose that a producer has the following production function: Where Q is output, and L and K are man-bours and machine-hour the two inputs used in the production procesS. 1A) Set up the cost minimization problem as shown in class In the cost mimimization problem, the cost is minimized subject to constraint production fimction. It is indicated as follows: Minimize wL rK subject to constraint Q =K L" A=wL+K+(Q-K-L") The Lagrangefunction is differentiated by K and L to calculate the minımize the cost, and W= waee rate L=Labor R=real interest rate K= capital Q= output N=parameter coefficient 1B) Determine the cost-minimize ratio of input: where capital costa 30 per macline-bour and abor costs 34 per lab- hour -Marginal Rate of technical substitution is the ratio of marginal product of labor to capital. MPE MRTS = MPK MPL is the marginal product of labor, calculated by differentiating productior function with respect to Labor. MPK 1s the marginal product of eapital, caleulated by difterentiating production fonetron vith respect to Capital. The exponentLal power of L and K are the elasticities of labor and capita Factor Elasticity = = Where &Belasbat of Laber And Dis elastiat of capiel Factor istensiry DD = NRTS =
Cost minimizing ratio of imputs is IC) |How many worker-hours are used to produce 100 units of output at these prices? 8.
Transcribed Image Text:Cost minimizing ratio of imputs is IC) |How many worker-hours are used to produce 100 units of output at these prices? 8.
Expert Solution
steps

Step by step

Solved in 5 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra for College Students
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
SEE MORE TEXTBOOKS