The Jabot company's production function is: Q(L, K) = L½K½ The target level of output is: Q = Qo The Jabot company's total cost function is: C(L, K) = wL + rK %3D a. Find and simplify expressions for MPL, MPK, and the marginal rate of technical substitution, MRTSKL. K MPL = &Lk's -'2 2 と MRTSKL = LM MPK = %3D IC = MRTSEL と,7 b. Write the tangency condition for a minimum of long run total cost, LTCmin. C= WL+rk %3D WK ol bns 81 bis St.0- ニ . Use the tangency condition and the cost function to solve for optimal L* and K* as functions of C*= LTCmin, W, and r.
The Jabot company's production function is: Q(L, K) = L½K½ The target level of output is: Q = Qo The Jabot company's total cost function is: C(L, K) = wL + rK %3D a. Find and simplify expressions for MPL, MPK, and the marginal rate of technical substitution, MRTSKL. K MPL = &Lk's -'2 2 と MRTSKL = LM MPK = %3D IC = MRTSEL と,7 b. Write the tangency condition for a minimum of long run total cost, LTCmin. C= WL+rk %3D WK ol bns 81 bis St.0- ニ . Use the tangency condition and the cost function to solve for optimal L* and K* as functions of C*= LTCmin, W, and r.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Could I have help or explanation on how to find the LTC min and L* and k*
![The Jabot company's production function is:
Q(L, K) = L'¼K½
The target level of output is:
Q = Qo
The Jabot company's total cost function is:
C(L, K) = wL + rK
%3D
a. Find and simplify expressions for MPL, MPK, and the marginal rate of technical
substitution, MRTSKL.
MPL
MPK
MRTSKL =
%3D
7,73
1/2
- MRTS KL
b. Write the tangency condition for a minimum of long run total cost, LTCmin.
C= WL+ rk
%3D
C. Use the tangency condition and the cost function to solve for optimal L* and K* as
functions of C*= LTCmin, W, and r.
L* =
K* =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1f061069-91e6-48ee-985f-f8d5b158cf5c%2Ff3ec180e-fce9-4695-833c-ef9989e629e7%2Fvwzl7o6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The Jabot company's production function is:
Q(L, K) = L'¼K½
The target level of output is:
Q = Qo
The Jabot company's total cost function is:
C(L, K) = wL + rK
%3D
a. Find and simplify expressions for MPL, MPK, and the marginal rate of technical
substitution, MRTSKL.
MPL
MPK
MRTSKL =
%3D
7,73
1/2
- MRTS KL
b. Write the tangency condition for a minimum of long run total cost, LTCmin.
C= WL+ rk
%3D
C. Use the tangency condition and the cost function to solve for optimal L* and K* as
functions of C*= LTCmin, W, and r.
L* =
K* =
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