(1 point) Suppose that you have five consumption choices: good 1. ⚫ 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 Un(x-ai) Where (a1,, as) = (6,6,3,3,6) The budget constraint gives the set of possible consumption choices with a given income. If you have an income of $772 and the price of good x is given by pi. The equation for the budget line is given by: 772 Pixi 5 A utility maximizing combination of goods 1 Find ₁ as a function of P₁ ... Ps x1 (Use p1 for p₁ and likewise for P2, P3, P4, P5. 5 occurs when the surface given by the budget constraint is tangent to an indifference surface. The easiest way to solve this question is using Lagrange multiplier. We define the Lagrange function to be: 5 A(x1,5,A) = U(x₁,, x5) A Pixi 772 i=1 Utility is maximized when all of the partial derivatives of the Lagrange function are equal to 0.
(1 point) Suppose that you have five consumption choices: good 1. ⚫ 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 Un(x-ai) Where (a1,, as) = (6,6,3,3,6) The budget constraint gives the set of possible consumption choices with a given income. If you have an income of $772 and the price of good x is given by pi. The equation for the budget line is given by: 772 Pixi 5 A utility maximizing combination of goods 1 Find ₁ as a function of P₁ ... Ps x1 (Use p1 for p₁ and likewise for P2, P3, P4, P5. 5 occurs when the surface given by the budget constraint is tangent to an indifference surface. The easiest way to solve this question is using Lagrange multiplier. We define the Lagrange function to be: 5 A(x1,5,A) = U(x₁,, x5) A Pixi 772 i=1 Utility is maximized when all of the partial derivatives of the Lagrange function are equal to 0.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:(1 point) Suppose that you have five consumption choices: good 1. ⚫ 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
Un(x-ai)
Where (a1,, as) = (6,6,3,3,6)
The budget constraint gives the set of possible consumption choices with a given income. If you have an income of $772 and the price of good x is given by pi. The equation for the budget line is given by:
772 Pixi
5
A utility maximizing combination of goods 1
Find ₁ as a function of P₁ ... Ps
x1
(Use p1 for p₁ and likewise for P2, P3, P4, P5.
5 occurs when the surface given by the budget constraint is tangent to an indifference surface.
The easiest way to solve this question is using Lagrange multiplier.
We define the Lagrange function to be:
5
A(x1,5,A) = U(x₁,, x5) A
Pixi
772
i=1
Utility is maximized when all of the partial derivatives of the Lagrange function are equal to 0.
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