CDAE 254 - Class 5 Sept. 11
Last class:
2. Preferences and choice
Today:
2. Preferences and choice
Quiz 1 (Chapter 1)
Next class:
2. Preferences and choice
Important date:
Problem set 2: due Thursday, Sept. 20
2. Utility and choice
2.1.
2.2.
2.3.
2.4.
2.5.
2.6.
2.7.
2.8.
2.9.
Basic concepts
Assumptions about rational choice
Utility
Indifference curve and substitution
Marginal utility and MRS
Special utility functions
Budget constraints
Utility maximization
Applications
2.2. Assumptions about rational choice:
A and B are two bundles of goods and services:
(1) Completeness:
A  B or B  A or A  B
(2) Transitivity of preferences
If A  B and B  C, then A  C
(3) Economic goods: More is better
2.4. Indifference curve and substitution
(1) What is an indifference curve?
A curve that represents all the combinations of
goods or services that provide the same level
of utility.
(2) A graphical presentation
(3) Marginal rate of substitution (MRS):
The negative of the slope of an indifference
curve:
MRS =
Interpretation:
Marginal Rate of Substitution
Y, Burritos
per semester
a
8
–3
5
b
1
–2
3
1
–1
2
0
c
d
1
3
4 5
I
6
X, Pizzas per semester
2.4. Indifference curve and substitution
(4)
(5)
(6)
(7)
Indifference curve maps
Indifference curves do not intersect
An indifference curve should be “thin”
Convex indifference curve
-- Diminishing MRS: MRS decreases when X increases
-- Relatively balanced bundles are preferred to
relatively unbalanced bundles
2.5. Marginal utility and MRS
(1) Marginal utility:
Change in utility associated with a one-unit
change in the consumption of a good, holding
other goods unchanged.
e.g., Utility = U(X1, X2, …, Xn)
MU X 1
U

X 1
Economic goods: MU > 0
Economic bads: MU < 0
A useless product: MU = 0
2.5. Marginal utility and MRS
(2) Marginal utility and MRS
U= U(X, Y)
dY

dX
MU X
 MRS
U constant 
MU Y
2.6. Special utility functions
(1)
(2)
(3)
(4)
Perfect substitutes
Perfect complements
A useless good
An economic bad
Perfect substitutes

straight line indifference curves
Perfect Substitutes
Coke, Cans
per week
4
3
2
1
I1
0
I2
I3
I4
1
2
3
4
Pepsi, Cans per week
Perfect complements

right-angle indifference curves
 MRS = 0 (Coffee-Cream)
Perfect Complements
Ice cream,
Scoops per week
e
3
d
2
a
1
0
1
c
b
I3
I2
I1
2
3
Pie, Slices per week
A useless good

Horizontal or vertical indifference curves
An economic bad

Utility decreases when the quantity
increases
Practice problem
Mr. Smith does not watch any TV without
popcorn and he eats popcorn only when he
watches TV. Draw an indifference curve to show
his preference for popcorn and watching TV.
2.7. Budget constraint
(1) Budget constraint: total expenditure should be
less than or equal to the available income.
e.g., Helen has $20 to buy candies (X) and/or
soda (Y):
Px X + Py Y < 20
where Px and Py are the corresponding prices
In general:
P1 X1 + P2 X2 + P3 X3 + …+ Pn Xn < I
where I is the available income
2.7. Budget constraint
(2) A graphic analysis of two goods (X and Y)
-- Budget constraint  feasible (affordable) vs.
infeasible (not affordable) regions
e.g., 1X + 2Y < 50
-- What is the slope of the budget line?
Slope = - (I/Py) / (I/Px) = - Px / Py
-- Impacts of a change in income (I)
-- An increase in income expand the feasible region
-- A decrease in income reduce the feasible region
-- Impacts of a change in one price (e.g, an increase in Px)
-- Impacts of a change in both prices
Budget Constraint 1 X + 2 Y < 50
Y
25
20
a
b
Infeasible (not affordable) region
c
10
Feasible (affordable) region
d
0
10
30
Slope of the budget line = -0.5
In general: slope = - Px / Py
50
X
Budget Constraint: an increase in income
Y
50
L new (I = $100)
25
Gain
L (I = $50)
0
50
100
X
A change in income does not change the slope of the budget line
Budget Constraint: an increase in Px
Y
25
L (Px = $1)
Loss
New
L (Px = $2)
0
25
50
X
Class exercise 2
(Tuesday, Sept. 11)
Ms Johnson has $10 to buy beer and/or popcorns
and the price of beer is $2 per bottle and the
price of popcorn is $1 per bag.
Draw a graph to show her budget constraint
What is the slope of the budget line?
What is the interpretation of the slope?
When one price rises

price of pizza doubles: Px = $2 (up from
$1)
 price of burritos and income unchanged
 slope of the new budget line:
 budget constraint swings in toward origin
 opportunity set shrinks
Changes in the Budget Constraint
(a) Price of Pizza Doubles
Y, Burritos
per semester
25
Loss
0
25
50
X, Pizzas per semester
2.7. Budget constraint
(3) Applications and special cases:
-- Consumption quota
-- China’s double price system
-- Electricity pricing
-- A minimum charge for taxi service
-- A company requires its workers to purchase
its product