L'a i a b. Write the tangency condition for a minimum of long run total cost, LTCmin- C= 'WL+ rk ( W o el bns 82 bns SIa 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* =

Microeconomic Theory
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Chapter11: Profit Maximization
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Problem 11.9P
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Im a bit confused on finding a tangencial condition for LTCmin and how to use the tangency condition and the cost function for l* k*
Company I: LR Cobb-Douglas
MRTSKL, the cost-minimizing input quantities L* and K*, and minimum total cost
C*.
The Jabot company's production function is:
Q(L, K) = L½K
The target level of output is:
Q = Qo
The Jabot company's total cost function is:
C(L, K) = wL + rK
substitution, MRTSKL.
K
1/½
MPL = &
MRTSKL =
MPK =
7,7.
: MRTS EL
D. 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.
K* =
*,
Transcribed Image Text:Company I: LR Cobb-Douglas MRTSKL, the cost-minimizing input quantities L* and K*, and minimum total cost C*. The Jabot company's production function is: Q(L, K) = L½K The target level of output is: Q = Qo The Jabot company's total cost function is: C(L, K) = wL + rK substitution, MRTSKL. K 1/½ MPL = & MRTSKL = MPK = 7,7. : MRTS EL D. 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. K* = *,
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