Read Chapter 4
Ch 4. How
Consumers Make
Choice
The Budget Constraint
 Budget constraint:
The set of baskets that a consumer can
purchase with a limited amount of
income.
 Budget line:
The set of baskets that a consumer can
purchase when spending all of his or her
available income.
The Budget Line
 Example:
Px X + Py Y = I
Px = price of food
Py = price of clothing
X = number of food purchased
Y = number of clothing purchased
I = income
The Budget Line
(continued)
 Example:
I = 800
Px = 20
Py = 40
Budget line Figure 4.1. Page 99
Slope budget line = - (Px/Py)
Effect Of A Change In
Income On The Budget Line
 Px = 20
Py = 40
I1 = 800
Budget line when I1?
Budget line when I2 = 1000?
Figure 4.2. Page 101.
Note: - an increase in income shifts the budget
line
outward in parallel fashion.
How Does A Change In Price
Affect The Budget Line?
 Px1 = 20
Py1 = 40
I1 = 800
What happened:
Px2 = 25
Py2 = 40
I2 = 800
Figure 4.3. Page 102
Optimal Choice
 Optimal choice:
Consumer choice of a basket of goods
that:
1. maximize satisfaction (utility) while
2. allowing him to live within his budget
constraint.
Optimal Choice
(continued)
 Let:
U (x, y) : represent the consumer’s utility
from purchasing x units of food
and y units of clothing.
with the budget constraint:
Px X + Py Y equals or less than I
Optimal Choice
(continued)
 The optimal choice:
Max U(x,y)
subject to: Px X + Py Y equals or less I
Figure 4.4. Page 104.
Optimal Choice
(continued)
 - MUx / MUy = - MRS
 MUx / MUy = Px / Py
 MRS x,y = Px / Py
 MUx / Px = MUy / Py
Finding Optimum
 U(x,y) = XY
I = 800
Px = 20
Py = 40
Find optimal consumption bundle?
MUx = ?
MUy = ?
Finding Optimum
(continued)
 Px X + Py Y = I
20X + 40Y = 800
MUx / MUy = Px / Py
Two Ways Of Thinking
1. Max Utility = U(x,y)
subject to: Px X + Py Y equals or less I
2. Min Expenditure = Px X + Py Y
subject to: U(x,y) = U2
Exercise:
 The utility that Ann receives by consuming food (F) and
clothing (C) is given by:
U(F,C) = FC + F
The marginal utilities of food and clothing are:
MUf = ?
MUc = ?
Food cost $ 1 a unit, and clothing costs $ 2 a unit.
Ann’s income is $ 22.
a. Ann is currently spending all of her income. She is
buying 8 units of food. How many units of clothing is
she consuming?
Exercise (continued):
b. Graph her budget line. Place the
number of units of clothing on the
vertical axis, and the number of units of
food on the horizontal axis. Plot her
current consumption basket.
c. Find the utility maximizing choice of
food and clothing.
Homework:
 4.3. Page 129