d,e and f not typed please! foc in second pic For j = 1:1. Differentiating L1 with respect to C11:8L1dc110.40- λ11 = 0C112. Differentiating L₁ with respect to C12:JL100120.60-1=0C12For j = 2:1. Differentiating L2 with respect to C21:მL2дом0.60>2p1 = 0C212. Differentiating L2 with respect to C22:მL2доп0.40 - X2 = 0C22 Choose and c to maximizeU (c₁, c²) = In ((ci)ª³ (c₁₂)¹¯ª³) for j = 1,2subject to: pie+2 – pic - ² = 0. Let a¹ = .10, a² = .60, e₁ = 8, e₁ = 6, e² = 14 ande = 18.(a) Set up Lagrangian L = In(b) Take FOCS(c) Set ³ equal and find c (p₁) and c^2(p1)+³ [p₁e + e − p₁c - c₁] for j = 1,2(d) Substitute c(p₁) and c½ (p₁) into market clearing condition c₁ + c² = e₁ + e² to findPi(e) Using p solve for optimal consumptionau()(f) Check MRS;=is the same for j = 1,2AU()ac

Given,Maximization problem,Sub toAnd,

Choose c₁ and c₁₂ to maximize U(c₁, c²) = ln ((c²)ª³ (c²)¹¯ª³) for j = 1,2 subject to: pie² + e² - pic - c2 = 0. Let a¹ = .40, a² = .60, e₁ = 8, e₁ = 6, e² = 14 and epic e² = 18. (a) Set up Lagrangian £ = In ((ci)" (ci)+¯a³) + \\me{ + e − mic{ − c)] for j = 1,2 (b) Take FOCS (c) Set equal and find c (p₁) and 2 (p1) - (d) Substitute (p₁) and c2(p₁) into market clearing condition c₁ + c² = e₁ + e to find Pi (e) Using p solve for optimal consumption JU() ac (f) Check MRS; = = is the same for j = 1,2 oU) ac

Choose c₁ and c₁₂ to maximize U(c₁, c²) = ln ((c²)ª³ (c²)¹¯ª³) for j = 1,2 subject to: pie² + e² - pic - c2 = 0. Let a¹ = .40, a² = .60, e₁ = 8, e₁ = 6, e² = 14 and epic e² = 18. (a) Set up Lagrangian £ = In ((ci)" (ci)+¯a³) + \\me{ + e − mic{ − c)] for j = 1,2 (b) Take FOCS (c) Set equal and find c (p₁) and 2 (p1) - (d) Substitute (p₁) and c2(p₁) into market clearing condition c₁ + c² = e₁ + e to find Pi (e) Using p solve for optimal consumption JU() ac (f) Check MRS; = = is the same for j = 1,2 oU) ac

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter2: Mathematics For Microeconomics

Section: Chapter Questions

Problem 2.6P

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