Suppose that you have five consumption choices: good ₁ 5. 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.
Suppose that you have five consumption choices: good ₁ 5. 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.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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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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