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Chapter 4

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Economics

Economics 2150A/B

Prof

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P a g e | 1
Ch. 4
Learning Objectives:
1) Budget constraint
1. Effect of price change
2. Effect of income change
2) Indifference curve (IC)
1. Represents consumer preferences.
2. MRS (marginal rate of substitution) = MUx/MUy = (-)slope of the IC = (-) Δy/Δx
3) Consumer maximization problem
1. Maximize utility subject to a budget constraint.
2. Two types of solutions:
Interior solution – optimum bundle lies on B.C.
Corner solution –optimum bundle lies on a corner of B.C.
3. Optimization rule
1. At interior optimum, the slope of IC = slope of the budget constraint.
2. MUx/Px = MUy/Py (interior solution only)
At the optimum, the marginal utility of the last dollar spent on good X must
equal the marginal utility of the last dollar spent on good Y.
4) Solve for an interior solution.
Two methods:
1. Tangency condition plus the budget constraint.
2. Lagrange Multiplier method
6) Identify a corner point solution.
5) Optimal consumption basket solves both a utility maximization problem and an expenditure
minimization problem.
7) Applications of consumer theory :
-Coupons versus Cash subsidies
-Joining a club
-Borrowing and Lending
-Understand Future value, present value, and the marginal rate of time
preference.
-Quantity Discounts
(8) Revealed Preference theory
Consumer Problem:
- Maximize utility subject to an income constraint. P a g e | 2
This chapter discusses the theory behind consumer decision-making. The consumer chooses
how much of good X and how much of good Y he/she can consume given their current income.
In other words, the consumer tries to pick a consumption bundle of X and Y that maximizes
his/her satisfaction (utility) given a budget constraint.
1. The budget constraint
- Consume on or inside B.C.
The budget constraint represents all of the possible combinations of X and Y that the
consumer can consume given his/her income I and the market prices Px and Py of goods X
and Y. The concept of the budget constraint is similar to the concept of the production
possibilities frontier.The consumer can only consume combinations of X and Y that lie either
on or inside the budget constraint.
-Depends on Prices and Income
The budget constraint depends upon the current level of (1) income and the (2) prices of
X and Y. If one of these items changes, then the budget constraint and, consequently, the
consumption possibilities change. The consumer will need to choose a new bundle of
goods X and Y that maximizes satisfaction given the new budget constraint.
-Formula for B.C.
PxX + PyY ≤ I
PxX + PyY = I because maximize U somewhere on the B.C.
Y = (I/Py) +(-Px/Py)X point –slope form
Y-intercept (I/Py)
Slope = -Px/Py relative market prices
X-intercept (I/Px)
Example 1: affordable consumption bundles
A consumer has an income of $1,000 per month to spend on pizza and Pepsi. The price of a pizza is $10 and the price
of a litre of Pepsi is $2.
1) If the consumer spends all of his income on pizza, he can buy 100 pizzas consumer spends e
all of his income on litres of Pepsi, he can buy 500 litres per month. P a g e | 3
Example 2: Change in Px
If the price of pizza increases to $20, then he can only buy 50 pizzas if he spends
all of his income on pizza. The budget constraint pivots inward.
Example 3: Change in Income
When the consumer’s income doubles to $2000 and the prices stay the same, he can
consume double the amount of pizza if he spends all of his income on pizza or double the
amount of Pepsi if he spends all of his income on Pepsi. The budget constraint shifts
outward in a parallel fashion. The slope doesn’t change because the relative price (-Px/Py) is
unchanged. P a g e | 4
-Slope of the budget line = Relative MARKET prices
=how many units of the good on the vertical axis the consumer must give up to purchase
one unit of the good on the x-axis given the current market prices, Px and Py.
-Question 1: If the slope of the B.C. = -5/8, how much good Y must be traded at the
current market prices to get one unit of good X?
-Question 2: What happens to his budget constraint if his income doubles and the
prices both double?
2. Indifference Curves
-Shape represents consumer preferences
-Bundles on same IC are equally preferred
-Higher IC represent higher levels of Utility
-MRS = (-) slope of the IC
= rate at which a consumer is willing to trade one good for another.
3. Optimum
-Maximize utility subject to a budget constraint.
The consumer will choose the consumption bundle (X,Y) that maximizes satisfaction
given the budget constraint. This means that he/she will choose a consumption bundle on
the highest possible indifference curve that still touches the budget constraint (i.e. is still
affordable).
Can be expressed as:
-Two solutions possible:
1. Interior solution P a g e | 5
-An interior solution means that the consumer consumes positive amounts of
both goods at the optimum.
-An optimal interior solution satisfies the condition that slope of B.C. = slope
of IC.
MUx = MUy
Px Py
Meaning: This means that marginal satisfaction from the last dollar spent on
each good in the consumption basket must be equal across all
goods consumed.
MUx Px MUx MUy
- If this were not the case and > ∨¿ > , then
MUy Py Px Py
the consumer is not at an interior optimum. At this basket the
consumer gets greater utility for every dollar spent on good x
than on good y. The consumer can increase utility by taking the last
dollar spent on good y and spending it on another unit of good x.
2. Corner solution
- At a corner solution, the consumer consumes 0 units of one good and a
positive amount of the other good. P a g e | 6
MUx Px MUx Px
MUy < Py∨¿ MUy > Py∨¿
MUx MUy MUx MUy
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