Review
1
Main Goal
Derive the demand curve
from preferences
Consumer’s
problem
Optimal
bundle
Individual
demand
curve
For given prices and income
we can solve for the
consumer’s optimal bundle
Change only the price of x and
see how optimal choice changes
Review
2
Y: Composite good
Price Consumption
PX1
X1
PX2
X2
PX3
X3
•A
•B
x1
x2
I/PX1
•C
x3
I/PX2
I/PX3
X
Review
Price Consumption
Price
•
PX1
X1
PX2
X2
PX3
X3
•
•
PX1
•
PX2
•
PX3
•
•
0
X1
X2
X3
Quantity
Review
Y: Composite good
How does the consumption of x change with
income?
I3/Py
Income
Consumption
I1
X1
I2
X2
I3
X3
I2/Py
I1/Py
•
A
x1
•
B •C
x2 x3
I1/PX I2/PX
I3/PX
X
Review
Key definition: The Engel curve for good x is the
quantity consumed of good x for any income level.
I ($)
Engel Curve
92
68
40
0
10
18
24
X (units)
Change in price of x
6
The plan: Understand how a change in
price influences demand.
Question:
Price
Why does a decrease in price from
PX1 to PX2 lead to a consumption
increase of:
X2-X1,
whereas a decrease in price from
PX2 to PX3 lead to a consumption
increase of:
•
•
•
PX1
•
PX2
X3-X2
•
PX3
?
•
•
0
X1
X2
X3
Quantity
Change in price
7
Decompose the effect that a price change has on
demand:
1. Substitution effect: the effect that the change in relative
prices only has on demand.
2. Income effect: the effect that the change in purchasing
power (real income) only has on demand.
Example
8
Suppose the price of x is PX =2 and the price of y is Py =1, both Daniel and Isabel have
the same income I=12
For Daniel the goods are perfect substitutes: U=x+y
For Isabel the goods are perfect complements: U=min{x,y}
Question: What is Daniel’s optimal bundle? What is Isabel's optimal bundle?
- Daniel would spend his entire income on good y, consuming 12 units of y
- Isabel purchases and equal amount of both goods, consuming 4 units of x and 4
units of y
Question: Suppose price of y increases from 1 to 4, Py2 =4. How do Daniel and Isabel
adjust their consumption?
- Daniel would now spend his entire income on good x, consuming 6 units of x
- Isabel would still spend her income equally on both goods, consuming 2 units of x
and 2 units of y
Example
9
Daniel substitutes all 12 units of y for 6 units of x.
Y: Composite good
Isabel decreases both x and y proportionately.
12 •
Key point: When price of y increases
two things happen:
Daniel
1. Good x is cheaper compared to good y,
pushes towards more x (Think of Daniel)
4
•
3
2
Isabel
•
2
4
•
6
2. Consumer has less money to spend,
and can afford to purchase less of x and y
(Think of Isabel)
X
Change in price of x
10
Key point:
Y: Composite good
When price of x falls, consumption changes from x1 to
x2. Two things happen:
1. x becomes cheaper relative to y. So the consumer
substitutes y for more x.
2. Purchasing power (“real income”) increases: the
consumer can buy the same amount and still have
money left.
x2 –x1
•A
We want to know how much of the consumption
change is due to the change in relative prices and how
much is due to the increase in purchasing power.
•B
x1
x2
I/PX1
I/PX2
X
The substitution and income effects
11
Initially, optimal bundle is A. Now price of x drops and bundle B becomes optimal.
How much is due to substitution and how much due to income effect?
Idea: use a decomposition basket.
Y: Composite good
“Suppose that under the new prices income
adjusts to keep the consumer just as well off as
initially (that is, on the initial IC). What would be
the optimal basket?”
Decomposition
basket
The answer is the decomposition basket, C. The
difference between the amount of x consumed in
A and C is the substitution effect. The rest is the
income effect.
•A
Income effect
C
•
•B
Substitution effect
x1
x3
x2
I/PX1
X
I/PX2
The substitution and income effects
12
Y: Composite good
Substitution effect
Income effect
A
•
•B
C
•
x1
I/PX1
x2
X
I/PX2
The substitution and income effects
13
Y: Composite good
Main points
1. The income effect can either be
positive or negative depending on
whether the good is normal or inferior.
Substitution effect
Income effect
A
•
•B
C
•
x1
I/PX1
x2
2. The substitution effect is always
negative: A decrease in the price of x
always increases the amount
consumed.
X
I/PX2
Example 1
14
Suppose that price of x is Px1 = 9 € and price of y is Py = 1 € and income I=72 €.
The utility function is U(x,y) = xy
a. What is the (initial) optimal consumption basket?
b. Suppose that price of x falls and Px2 = 4 €. What is the (final) optimal
consumption basket?
c. Find the decomposition basket. What is the substitution effect? What is the
income effect?
Example 1
15
a. When Px1 = 9 € the optimal consumption is x = 4 and y = 36
b. When price of x falls to Px2 = 4, we have that x = 9 and y = 36
c. How to find the decomposition basket?
1. Figure out the utility level of the original basket (4,36):
Since u(x,y)=xy, u(4,36)=4*36=144
2. The decomposition basket lies on an adjusted budget line with the new price ratio
Px2 /Py that is tangent to the original indifference curve.
The tangency condition: MRS= Px2 /Py , or y=4x
3. Solve for the decomposition bundle using 1 and 2:
xy = 146 and y=4x which implies that: x=6 and y=24
Example 1
16
We have that:
-The original basket A is: (4,36)
-The final basket B is: (9,36)
-The decomposition basket C is: (6,24)
Y: Composite good
Substitution effect
A
Income effect
•
C
•
x1
-When price of x decreases from 9 to
4, consumption of x increases by 5
units (from 4 to 9).
- The substitution effect is 6-4=2.
- The income effect is 9-6=3.
•B
x2
X
Example 2
17
Suppose the price of x is PX =2 and the price of y is Py =4, income I=12.
For Daniel the goods are perfect substitutes: U=x+y
Y: Composite good
12 •
The price of y goes down to Py =1, what are the income and
substitution effects?
B
Daniel
3
A
•
6
X
Example 3
18
Suppose the price of x is PX =2 and the price of y is Py =4, income I=12
For Isabel the goods are perfect complements: U=min{x,y}
Y: Composite good
The price of y goes down to Py =1, what are the income and
substitution effects?
12
Isabel
•
B=(4,4)
3
•
A=(2,2)
6
X
Example 5: labor supply curve
Think of leisure (free time) as good x and all other products
(“consumption”) as good y. Let py=1, the hourly wage be w and assume the
person can work 24 hours per day if he wants to.
1. Draw the person’s daily budget line.
2. What happens to the budget line if w increases?
3. What is the “price” of leisure?
Example 5: labor supply curve
Trade-off between leisure and consumption.
Wage as the price of leisure.
Budget line:
Consumption
I = (24 - L) w
where L = leisure hours and w = hourly wage
C
A•
B •
•
L1 L2 L3
L (hours of leisure)
Example 5: labor supply curve
21
PL=w
PL=w
Supply of labour
Demand for leisure
w2
w2
w1
w1
0
L1
L2
L
0
24-L
Change in prices
22
Example of positive income effect (x is a normal good)
Change in prices
23
Example of negative income effect (x is an inferior good)
Giffen good
24
A good is called a Giffen good if it is an inferior good and a price increase leads
to an increase in the consumption of the good. That is, demand slopes upwards.
This happens when the good is inferior and the income effect dominates the
substitution effect.
Giffen good
25
Consumer Surplus
26
When the price is PX1 the consumer’s optimal bundle is X1 and
when she consumes X1 units, the most she is willing to pay PX1 for
an additional unit of x is PX1 .
Price
•
Why?
•
•
PX1
•
PX2
•
PX3
•
•
0
X1
X2
X3
Quantity of x
Consumer Surplus
27
Y: Composite good
•A
•B
x1
x2
I/PX1
•C
x3
I/PX2
I/PX3
X
Consumer Surplus
The consumer’s surplus is the net economic
benefit to the consumer from a purchase.
Price
•
10
It is measured by the difference between
the price that the consumer is willing to pay
and the price that she actually pays.
•
7
•
6
The consumer’s surplus is the area between
the market price and the demand curve.
•
5.5
5
•
•
2
0
1 2
3
4
5
10
Quantity
Consumer Surplus: example
CS3 = 0.5 (10-3)(28) = 98
CS2 = 0.5 (10-2)(32) = 128
CSP = (10-P)(40-4P)/2
Generally for linear
demand
Q= a/b – P/b or P = a-bQ:
CSP = (a-P)(a/b – P/b)/2
= (a-P)2/2b
Market Demand
The market demand function is the horizontal sum of the individual demands.
P
P
10
P
10
Q = 10 - P
10
Q = 20 – 5P
4
4
Segment 1
Q
4
Segment 2
Q
Market demand
Q
Consumers’ Surplus
Consumers’ surplus is the sum of all the consumers’ consumer surpluses.
P
P
P
10
Q = 10 - P
Q = 20 – 5P
1
Segment 1
Q
Segment 2
Q
Market demand
Q
Market demand
32
Many buyers and uniformly
distributed WTPs
Price
1000 Eu
Q = 2000- 2P
500 Eu
•
Demand
0
1000
Quantity
Review example
33
Mike and Flora like tennis and yoga classes.
Their utilities are: Mike’s is UM(t,y)= t1/2 y and Flora’s is UF(t,y)= min{2t, y}.
Each has 60 € per week to spend on these lessons. The price of a tennis class
is 10 € and of a yoga class is 5 €.
1. Suppose that initially each consumes bundle A=(tA,yA)=(4,4). Is it the optimal
bundle for Mike? For Flora? If not, what is the direction of improvement: more
tennis or more yoga?
2. What is the optimal bundle of each?
3. Derive and plot each person’s demand for yoga lessons.
4. Derive Mike’s and Flora’s joint demand. Plot it.
5. Suppose that the price of tennis increases to 20 €. What is Flora’s new
optimal bundle? What are the substitution and income effects on tennis and
yoga classes?
Outlook: paradox of value
34
Adam Smith:
Why is water so much cheaper than diamonds if water has many more uses for
many more people?
Outlook
35
Price
Supply
Demand
0
Quantity