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Suppose that you have five consumption choices: good #15. An indifference surface is the set of consumption choices with a CONSTANT utility. For example if (x₁, ,5) = (2, 1, 1, 1, 1) gives the same utility as (₁, ..,5) = (1, 1, 1, 1, 2) than these are both points on the same indifference surface. An indifference map is the set of all indifference surface for EVERY given utility. Consider the following utility map: 5 U = In(r; - ai) Where (a1,.., a5) = (4, 3, 6, 8, 6) The budget constraint gives the set of possible consumption choices with a given income. If you have an income of $920 and the price of good ** is given by p₁. The equation for the budget line is given by: 920 Pizi. 5 21 = (Use p1 for p₁ and likewise for P2, P3, P4, P5. A utility maximizing combination of goods 15 occurs when the surface given by the budget constraint is tangent to an indifference surface. Find 1 as a function of p₁ P5 The easiest way to solve this question is using Lagrange multiplier. We define the Lagrange function to be: 5 * (₂ = A(x₁, , 25, A) = U(£₁, · ·, 5) — A Pii -920 i-1 Utility is maximized when all of the partial derivatives of the Lagrange function are equal to 0.

Suppose that you have five consumption choices: good #15. An indifference surface is the set of consumption choices with a CONSTANT utility. For example if (x₁, ,5) = (2, 1, 1, 1, 1) gives the same utility as (₁, ..,5) = (1, 1, 1, 1, 2) than these are both points on the same indifference surface. An indifference map is the set of all indifference surface for EVERY given utility. Consider the following utility map: 5 U = In(r; - ai) Where (a1,.., a5) = (4, 3, 6, 8, 6) The budget constraint gives the set of possible consumption choices with a given income. If you have an income of $920 and the price of good ** is given by p₁. The equation for the budget line is given by: 920 Pizi. 5 21 = (Use p1 for p₁ and likewise for P2, P3, P4, P5. A utility maximizing combination of goods 15 occurs when the surface given by the budget constraint is tangent to an indifference surface. Find 1 as a function of p₁ P5 The easiest way to solve this question is using Lagrange multiplier. We define the Lagrange function to be: 5 * (₂ = A(x₁, , 25, A) = U(£₁, · ·, 5) — A Pii -920 i-1 Utility is maximized when all of the partial derivatives of the Lagrange function are equal to 0.

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Suppose that you have five consumption choices: good ₁5. An indifference surface is the set of consumption choices with a CONSTANT utility. For example if (x₁,...,x5) = (2, 1, 1, 1, 1) gives the same utility as (x1, ,5) = (1, 1, 1, 1, 2) than these are both points on the same indifference surface. An indifference map is the set of all indifference surface for EVERY given utility. Consider the following utility map: 5 U=In(xi -ai) Where (a₁, ... , a5) = (4,3, 6, 8,6) - The budget constraint gives the set of possible consumption choices with a given income. If you have an income of $920 and the price of good i is given by p. The equation for the budget line is given by: 920 = Pixi. i=1 A utility maximizing combination of goods 15 occurs when the surface given by the budget constraint is tangent to an indifference surface. Find 1 as a function of p₁ P5 C1 = (Use p1 for p₁ and likewise for P2, P3, P4, P5. The easiest way to solve this question is using Lagrange multiplier. We define the Lagrange function to be: A(x₁, ,5, ) = U(x₁,. 5 5 -1 Σφιπι – 920) (²² i=1 Utility is maximized when all of the partial derivatives of the Lagrange function are equal to 0.
Transcribed Image Text:Suppose that you have five consumption choices: good ₁5. An indifference surface is the set of consumption choices with a CONSTANT utility. For example if (x₁,...,x5) = (2, 1, 1, 1, 1) gives the same utility as (x1, ,5) = (1, 1, 1, 1, 2) than these are both points on the same indifference surface. An indifference map is the set of all indifference surface for EVERY given utility. Consider the following utility map: 5 U=In(xi -ai) Where (a₁, ... , a5) = (4,3, 6, 8,6) - The budget constraint gives the set of possible consumption choices with a given income. If you have an income of $920 and the price of good i is given by p. The equation for the budget line is given by: 920 = Pixi. i=1 A utility maximizing combination of goods 15 occurs when the surface given by the budget constraint is tangent to an indifference surface. Find 1 as a function of p₁ P5 C1 = (Use p1 for p₁ and likewise for P2, P3, P4, P5. The easiest way to solve this question is using Lagrange multiplier. We define the Lagrange function to be: A(x₁, ,5, ) = U(x₁,. 5 5 -1 Σφιπι – 920) (²² i=1 Utility is maximized when all of the partial derivatives of the Lagrange function are equal to 0.
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