ECON2913 (Spring 2012)
21 & 24.2.2012 (Tutorial 2)
Chapter 3 Consumer Behavior
An Application of Indiffernce Curve Analysis: Labor Supply
 Given,
Utility function: U(x, l)
Potential income: I = wh + m
Time available: T = h + l
 Budget Constraint: Pxx + wl = wT + m or

How would (1) a change in w, (2) minimum wage, (3) a change in m and (4) maximum
working hour (5) Unemployment allowance (6) Transportation allowance affect people’s
optimal choice? Will people be better off or worse off?

Possibility of backward banding labor supply curve?
Good x
Good x
(1)Minimum wage
(2) Change in w
(w’T + m)/Px
(wT + m)/Px
(wT + m)/Px
Slope = -w’/Px
Slope = -w/Px
m/Px
m/Px
Leisure
T
Leisure
(wT + m)/w
T
Good x
Good x
(3) Change in m
(4) Maximum working hours
(wT + m’)/Px
(wT + m)/Px
(wT + m)/w
(wT + m)/Px
Slope = -w/Px
m’/Px
(whma x + m)/Px
m/Px
Slope = -w/Px
m/Px
Leisure
T
(wT + m)/w
Leisure
(T  h
max
) T
(wT + m)/w
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Example: (Utility Maximization)
Assume that there are two goods in the world: apples and raspberries. Say that Geoffrey has a
utility function for these goods of the following type, where r denotes the quantity of
raspberries and a the quantity of apples.
U  ra
a) Draw the indifference curve that is defined by the utility function and has a utility level of
a
2500.
50
U = 2500
r
50
b) What is the marginal rate of substitution of raspberries for apples when Geoffrey
consumes 50 raspberries and 50 apples? What is the marginal rate of substitution between
these two goods when Geoffrey consumes 100 raspberries and 50 apples?
MUr a
MRS ra 
 . MRSra when Geoffrey has 50r and 50a = 1 , MRSra when Geoffrey
MU a r
has 100r and 50a = 1
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c) If the price of raspberries is $1 per unit and the price of apples is $1 per unit and Geoffrey
has $100 to spend, what bundle of raspberries and apples would he buy? Is the marginal
rate of substitution be equal to the ratio of the prices of these goods in the optimal bundle?
If not, why not?
a
a
Optimal condition: MRSra = Pr/Pa    1 --- (1)
r
100
Budget constraint: Prr + Paa = 100
 1r + 1a = 100 --- (2)
MRS = -1
50
Slope of BL = -1
r
50
Solving (1) and (2), a* = r* = 50
This optimal bundle is an interior solution, and
marginal rate of substitution equals the price ratio.
100
d) If the unit prices of raspberries and the apples are $4 and $3, respectively, what bundle of
raspberries and apples would Geoffrey buy with his income of $100?
a
a
4
  --- (1)
r
3
33⅓
Optimal condition: MRSra = Pr/Pa  
16.67
Budget constraint: Prr + Paa = 100
 4r + 3a = 100 --- (2)
MRS = -4/3
Solving (1) and (2), a* = 16.67 and r* = 12.50
Slope of BL = -4/3
r
12.5
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2
Example: (Utility Maximization)
Assume that there are two goods in the world: apples and raspberries. Say that Geoffrey has a
utility function for these goods of the following type, where r denotes the quantity of
raspberries and a the quantity of apples.
U  4r  3a
a) Draw the indifference curves that are defined by the utility function.
a
Slope of IC = 
4
3
r
b) What is the marginal rate of substitution between raspberries and the apples when
Geoffrey consumes 50 raspberries and 50 apples? What is the marginal rate o substitution
between these two goods when Geoffrey consumes 100 raspberries and 50 apples? What
do the answers to these questions imply about the type of goods the apples and raspberries
are for Geoffrey?
MRSra when Geoffrey has 50r and 50a = 4
3
MRSra when Geoffrey has 100r and 50a = 4
3
As MRS remains constant over all consumption bundles, apples and raspberries are
perfect substitutes.
c) If the price of raspberries is $1 per unit and the price of apples is $1 per unit and Geoffrey
has $100 to spend, what bundle of raspberries and apples would he buy? Would the
marginal rate of substitution be equal to the ratio of the prices of these goods in the
optimal bundle? If not, why not?
a
100
Slope of BL = -1
Slope of IC = 
4
3
r
100
Optimal bundle: (100r, 0a)
MRS is not equal to the relative price in the optimal bundle. As indifference curves are
linear functions, it ends up in corner solutions. MRS is not equal to the relative price
because in the optimal bundle, MRSra is greater than the relative price, Geoffrey should
further reduce the consumption of apple in order to equalize MRS and the relative price.
However, consumption of apple in the optimal bundle is already 0.
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d) If the unit prices of raspberries and the apples are $4 and $3, respectively, what bundle of
raspberries and apples would Geoffrey buy with his income of $100?
a
33⅓
Slope of BL = 
4
3
Optimal bundle: any bundle on BL
(Since, BL and IC coincide)
Slope of IC = 
r
4
3
25
Example: (From individual demand to market demand)
Given there are 2 individuals, person A and B in the economy. Their demand functions for
good X are given by the following equations:
Person A: p = 20 – qA
Person B: p = 15 – 2qB
Find the market demand curve (Equation and diagram).
Person A: qA = 20 – P
Person B: qB = 7.5 – 0.5P
The market demand could be obtained by adding up the quantity demanded of person A and
person B at all price levels (Horizontal summation). (Q = 27.5 – 1.5P)
However, at P >15, the demand for person B is 0. Therefore the market demand will have a
kink. The equation for the market demand function will be:
Rearrange the terms,
P
20
p = 20 – Q
1 2
p  18  Q
3 3
Market demand
15
if P  15
if P  15
Slope = -2/3
Slope = -1
Slope = -2
7.5
DB
DA
Q
20
27.5
4
Chapter 3, Problem 15
Jane receives utility from days spent traveling on vacation domestically (D) and days spent
traveling on vacation in a foreign country (F), as given by the utility function U(D, F) = 10DF.
In addition, the price of a day spent traveling domestically is $100, the price of a day spent
traveling in a foreign country is $400, and Jane’s annual travel budget is $4,000.
Foreign (Days)
U(1200)
U(1000)
U(800)
Domestic
(Days)
(a) Illustrate the indifference curve associated with a utility of 800 and the indifference
curve associated with a utility of 1200.
The indifference curve with a utility of 800 has the equation 10DF=800, or DF=80
The indifference curve with a utility of 1200 has the equation 10DF=1200, or DF=120
(b) Graph Jane’s budget line on the same graph
If Jane spends all of her budget on domestic travel she can afford 40 days. If she spends
all of her budget on foreign travel she can afford 10 days.
(c) Can Jane afford any of the bundles that give her a utility of 800? What about a utility of
1200?
Yes she can afford some of the bundles that give her a utility of 800 as part of this
indifference curve lies below the budget line. She cannot afford any of the bundles
that give her a utility of 1200 as this whole indifference curve lies above the budget
line.
(d) Find Jane’s utility maximizing choice of days spent traveling domestically and days
spent in a foreign country.
The optimal condition for utility maximization:
MRS 
MU D 10F F


MU F 10D D
and
PD 1 ,

PF 4
thus
4F  D
MRS
PD
PF
--- (1)
Budget Constraint: 100 D  400 F  4000 --- (2)
Solving (1) and (2) gives D = 20 and F = 5. Utility is 1000
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