Transcript Econ 160 Ch 04



An increase in the price of one good –
holding tastes, income, and the price of other
goods constant – causes a movement along
the demand curve.
We use consumer theory to show how a
consumer’s choice changes as the price
changes, thereby tracing out the demand
curve.



In the previous chapter, we used calculus to
maximize utility subject to a budget
constraint.
We solved for the optimal quantities that a
consumer chooses as a functions of prices
and income.
We solved for the consumer’s system of
demand functions for these goods.

For example, Lisa chooses between pizzas,
q1, and burgers, q2, so her demand functions
are of the form
q1  q1  p1, p2,Y

q2  q2  p1, p2,Y 

where p1 is the price of pizza, and p2 is the
price of burger, and Y is her income.

We showed that if a consumer has a CobbDouglas utility function
U  q1aq21a

such demand functions are given by
Y
Y
q1  a
and q2  1 a 
p1
p2

Thus the Cobb-Douglas utility function has
the unusual property that the demand
function for each good depends only on its
own price and not the price of the other
good.
Illustration:
Consider Michael, who consumes only beers,
q1, and wines, q2. Let p1 be the price of beers,
p2 be the price of wines, and Y is his income.
We can derive his demand curve for beer by
showing the quantities of beer he will purchase
for some alternative prices of beer with price of
wine and his income constant.
Suppose that p2 = 35 and Y = 420. Let us find
q1 for p1 = 12, 6, and 4.
Wine (q2)
p2 = 35 and Y = 420
12.0
5.5
4.5
3.0
0
p1
12
e1
27
I2
I1 1
L (p1 =12)
45
Price-consumption curve
I3
L2
(p1 =6)
L3 (p1 =4)
Beer (q1)
59
E1
E2
6
4
0
e3
e2
27
45
E3
59
D1
Beer (q1)



An increase in an individual’s income, holding
tastes and prices constant, causes a shift of
the demand curve.
An increase in income causes a parallel shift
of the budget constraint away from the
origin, prompting a consumer to choose a
new optimal bundle with more of some or all
goods.
With price of beers fixed at p1 = 12, and price
of wines fixed at p2 = 35, let us find q1 for
incomes, Y = 420, 630, and 840.
Wine (q2)
p1 = 12 and p2 = 35
e3
7
5
3
0
p1
12
e2
e1
Income-consumption curve
I3
I2
I1
27
E1
38
E2
Beer (q1)
49
E3
D3
D2
0
D1
27
38
49
Beer (q1)
Wine (q2)
p1 = 12 and p2 = 35
e3
7
5
3
0
e2
e1
Y
27
I2
38
49
Engel curve
Beer (q1)
E3
630
0
I3
I1
840
420
Income-consumption curve
E2
E1
27
38
49
Beer (q1)
Wine (q2)
Income-consumption curve
p1 = 12 and p2 = 35
e3
20.5
I3
e2
11.5
if beer is an inferior good
I2
e1
3.0
0
840
I1
Y
10
19
27
Beer (q1)
E3
E2
630
420
E1
Engel curve
0
10
19
27
Beer (q1)
Holding tastes, other prices, and income
constant, an increase in a price of a good has
two effects on an individual’s demand.
1. Substitution Effect
2. Income Effect



The change in the quantity of a good that a
consumer demands when the good’s price
rises, holding other prices and the
consumer’s utility constant.
If utility is held constant as the price of the
good increases, consumers substitute other,
now relatively cheaper goods for that one.


The change in the quantity of a good a
consumer demands because of a change in
income, holding prices constant.
An increase in price reduces a consumer’s
buying power, effectively reducing the
consumer’s income or opportunity set and
causing the consumer to buy less of at least
some goods.
q2
e*
e2
e1
I2
L2
0
Income
effect
6
10
16
Total effect
L*
Substitution
effect
I1
L1
q1

The total effect from the price change is the
sum of the substitution and income effects.
total effect = substitution effect + income effect



Because indifference curves are convex to the
origin, the substitution effect is
unambiguous.
Less of a good is consumed when its price
rises.
A consumer always substitutes a less
expensive good for a more expensive one,
holding utility constant.





The substitution effect causes a movement
along an indifference curve.
The income effect causes a shift to another
indifference curve due to a change in the
consumer’s opportunity set.
The direction of the income effect depends
upon the type of good.
Since the good is normal, the income effect is
negative with respect to price increase.
Thus, both the substitution and income effect
go in the same direction, so the total effect of
the price increase must be negative.
q2
Assume q1 is an inferior good
e*
e1
e2
I1
L2
0
Income
effect
10 12
16
Substitution
effect
Total
effect
L*
I2
L1
q1




If a good is inferior, the income effect goes in
the opposite direction from the substitution
effect.
For most inferior goods, the income effect is
smaller than the substitution effect.
The total effect moves in the same direction
as the substitution effect, but the total effect
is smaller.
However, the income effect can more than
offset the substitution effect in extreme
cases.
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

A good is called a Giffen good if an increase
in its price causes the quantity demanded to
rise.
Thus, the demand curve for a Giffen good
slopes upward.
It was named after Robert Giffen, a 19th
century British economist who argued that
poor people in Ireland increased their
consumption of potatoes when the price rose
because of a potato blight.
q2
L*
Assume q1 is a Giffen good
L1
e*
L2
e1
I1
e2
0
Substitution
effect
8
14 16
Income
effect
I2
Total
effect
q1



We could derive a compensated demand
curve, where we determine how the quantity
demanded changes as the price rises, holding
utility constant.
The change in the quantity demanded reflects
only pure substitution effects when the price
changes.
It is called the compensated demand curve
because we would have to compensate an
individual – give the individual extra income –
as the price rises so as to hold the
individual’s utility constant.
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

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
It is also called the Hicksian demand curve,
after John Hicks, who introduced the idea.
The compensated demand function for q1 is
q1  H p1, p2,U


where we hold utility constant at U .
We cannot observe the compensated demand
curve directly because we do not observe
utility levels.
Because the compensated demand curve
reflects only substitution effects, the Law of
Demand must hold: A price increase causes
the compensated demand for a good to fall.
q2
p2 = 35 and Y = 420
12.0
e3
e2
0
p1
12
L2
(p1 =12)
27
E2
I2
27
I1
L*
41 45
L1 (p1 =6)
q1
E3
E1
6
0
e1
41 45
Uncompensated Demand Curve (D)
Compensated Demand Curve (H)
q1

We can also derive the compensated demand
curve by using the expenditure function.

E  E p1, p2,U


Differentiating the expenditure function with
respect to p1, we obtain the compensated
demand function for q1.
E
 H p1, p2,U  q1
p1


Illustration:
Find the compensated demand function for q1
given a Cobb-Douglas utility function below
with a = 0.6.
U  q1 q
a
1a
2
The expenditure function for this CobbDouglas utility function is
a
1a
 p1   p2 
E U   

a
1

a
  

Differentiating the expenditure function with
respect to p1 we have the compensated
demand function given as
1a
 a p2 


 1 a p1 
Given that a = 0.6, then the expenditure
function becomes
E
q1 
U
p1
0.6
 p1 
E U 

0.6


0.4
 p2 
 0.4 


 1.96Up10.6p20.4
The compensated demand function for q1 is
0.4
 0.6 p2 
q1  U 

 0.4 p1 
0.4
 p2 
 1.18U  
 p1 