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 =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 =
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.
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