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)

Answered: Image /qna-images/answer/76794696-ea30-419f-b637-9fa55abbd29d.jpg

1 Example 1: Let y = F(l, k) = 13k2 be the production function, p = 30, w = 10, and r = 5. maximizes the profit. Find the optimum input combination (l*, k*) that This question can be formulated as max M(1, k) = 30 - l¾kź – (101 + 5k). {l,k} At the optimum (l*, k*), the F.O.C. must be satisfied. That is, 1 30. · (1*)−¾(k*)} – 10 = 0 . - 3 30 - 1/2 · (²*) }(k*)———5 = 0. - Equation (2) implies (k*)} = 3 ⋅ (1*)¾. Plug it into equation (1), 10 () 3.3 (1) 10 · ³ = . ⇒ 1* = 27. · Since (k*)¹ = 3 ⋅ (1*)¾, k* = 81. (1) (2)

1 Example 1: Let y = F(l, k) = 13k2 be the production function, p = 30, w = 10, and r = 5. maximizes the profit. Find the optimum input combination (l, k) that This question can be formulated as max M(1, k) = 30 - l¾kź – (101 + 5k). {l,k} At the optimum (l, k), the F.O.C. must be satisfied. That is, 1 30. · (1)−¾(k)} – 10 = 0 . - 3 30 - 1/2 · (²) }(k)———5 = 0. - Equation (2) implies (k)} = 3 ⋅ (1)¾. Plug it into equation (1), 10 () 3.3 (1) 10 · ³ = . ⇒ 1* = 27. · Since (k)¹ = 3 ⋅ (1)¾, k* = 81. (1) (2)

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.7P

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