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

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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QUESTION 1 For the utility function U = Qx0.50Qy(1-0.50) and the budget 122 = 8Qx + 14Qy find the CHANGE in optimal consumption of Y if the price of Xincreases by a factor of 1.7. Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 1.2, 1.14 = 1.1).