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-DouglasMRTSKL, the cost-minimizing input quantities L* and K*, and minimum total costC*.The Jabot company's production function is:Q(L, K) = L½KThe target level of output is:Q = QoThe Jabot company's total cost function is:C(L, K) = wL + rKsubstitution, MRTSKL.K1/½MPL = &MRTSKL =MPK =7,7.: MRTS ELD. Write the tangency condition for a minimum of long run total cost, LTCmin.C= 'WL+ rk%3DC. Use the tangency condition and the cost function to solve for optimal L* and K* asfunctions of C*= LTCmin, W, and r.K* =*,

Given production function Q=L1/2K1/2 .... (1) Isocost line equation: C=wL+rK

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* =

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 =

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

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* =
*,

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