ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN: 9780190931919
Author: NEWNAN
Publisher: Oxford University Press
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Suppose that you have five consumption choices: good x₁ 5. An indifference surface is the set of consumption choices with ,5) = (2, 1, 1, 1, 1) gives the same utility as (x1, ,5) = (1, 1, 1, 1, 2) than these a CONSTANT utility. For example if (x₁, 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: U = ΣIn(ri-ai) Where (a₁,.., a5) = (7,3, 8,5,7) The budget constraint gives the set of possible consumption choices with a given income. If you have an income of $568 and the price of good , is given by pi. The equation for the budget line is given by: 568 = 5 x1 = (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: A(x₁,, x5, A) = U(x₁,, x5) - \ 5 i=1 i=1 Pixi - 568 Pixi. Utility is maximized when all of the partial derivatives of the Lagrange function are equal to 0.
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Transcribed Image Text:Suppose that you have five consumption choices: good x₁ 5. An indifference surface is the set of consumption choices with ,5) = (2, 1, 1, 1, 1) gives the same utility as (x1, ,5) = (1, 1, 1, 1, 2) than these a CONSTANT utility. For example if (x₁, 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: U = ΣIn(ri-ai) Where (a₁,.., a5) = (7,3, 8,5,7) The budget constraint gives the set of possible consumption choices with a given income. If you have an income of $568 and the price of good , is given by pi. The equation for the budget line is given by: 568 = 5 x1 = (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: A(x₁,, x5, A) = U(x₁,, x5) - \ 5 i=1 i=1 Pixi - 568 Pixi. Utility is maximized when all of the partial derivatives of the Lagrange function are equal to 0.
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