This is not a graded question. Kindly help me solve. This is a question from my lecture notes. I want to understand the steps involed in arriving at the anwer shown. Kindly explain all steps showing details of how the answer was arrived at. Please don't use langrangian law. Thanks a lot. Example 1: Let y = : F(l, k) = l¾kỄ be the production function, p = 30,w = 10, and r = 5. Find the optimum input combination (1*, k*) thatmaximizes the profit. This question can be formulated asmax П(l, k) = 30 · l¾kź – (101 + 5k).{l,k}At the optimum (1*, k*), the F.O.C. must be satisfied. That is,130. · (1*) −¾ (k*) ¾ — 10330. • 1/2 · (²*) ³} (x^³*) — — — 5 = 0.Equation (2) implies (k*)= 0= 3 ⋅ (1*)³. Plug it into equation (1),.10 · (1*)−³ · 3 · (1*) — 10⇒ 1* = 27.Since (k*) = 3 ⋅ (1*)³, k* = 81.(1)(2)

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Answered: 1 Example 1: Let y = F(l, k) = 13k2 be…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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This is not a graded question. Kindly help me solve.

This is a question from my lecture notes. I want to understand the steps involed in arriving at the anwer shown. Kindly explain all steps showing details of how the answer was arrived at. Please don't use langrangian law. Thanks a lot.

Example 1: Let y = : F(l, k) = l¾kỄ be the production function, p = 30,
w = 10, and r = 5. Find the optimum input combination (1*, k*) that
maximizes the profit. This question can be formulated as
max П(l, k) = 30 · l¾kź – (101 + 5k).
{l,k}
At the optimum (1*, k*), the F.O.C. must be satisfied. That is,
1
30. · (1*) −¾ (k*) ¾ — 10
3
30. • 1/2 · (²*) ³} (x^³*) — — — 5 = 0.
Equation (2) implies (k*)
= 0
= 3 ⋅ (1*)³. Plug it into equation (1),
.
10 · (1*)−³ · 3 · (1*) — 10
⇒ 1* = 27.
Since (k*) = 3 ⋅ (1*)³, k* = 81.
(1)
(2)

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