microeconomics and financecermsem.univ-paris1.fr/davila/teaching/sbs/ch03_pindyck...microeconomics...
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Microeconomics and Finance
Solvay Business School 08/09
Julio DAVILA
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Microeconomics and Finance
Textbook:
Microéconomie, Pindyck & Rubinfeld Prentice Hall, 6th ed.
Part 1 : Demand Part 2 : Introduction to finance Part 3 : Supply Part 4 : Competitive equilibrium Part 5 : Non-competitive markets
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Microeconomics and Finance
Teaching Assistant: Ritha Sukadi [email protected]
Office hours: by appointment (e-mail Ritha)
Slides: http://cermsem.univ-paris1.fr/davila/microfinance.html
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Consumer behavior
Microéconomie, chapter 3
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Consumer behavior
Consumer behavior theory explains how the consumer chooses to spend his income in different goods and services
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Consumer behavior
The consumer’s choice depends on: his preferences
They describe how the consumer ranks different bundles of goods or commodities
his budget constraint The consumer has limited resources
the optimization of his preferences given his budget constraint
The consumer seeks to maximize the «utility» he derives from consumption given his resources
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Consumer preferences
Assumptions
1. his preferences are complete he is able to rank any two bundles of goods
2. his preferences are transitive if he prefers A to B, and B to C, then he must prefer
A to C 3. his preferences are monotone
he always prefers more to less
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Consumer preferences
Preferences can be represented graphically by means of indifference curves
An indifference curve contains all the bundles of goods that satisfy equally the consumer He is indifferent between any of two them
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Indifference curves: example
bundles food clothes
A 20 30
B 10 50
D 40 20
E 30 40
G 10 20
H 10 40
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Indifference curves: example
The assumptions on preferences translate into graphical properties of the indifference curves
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A is preferred to any bundle in the yellow box,
but any bundle in the pink box is preferred to A.
Indifference curves: example
food
10
20
30
40
10 20 30 40
clothes 50
G
A
E H
B
D
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Indifference curves: example
The indifference curve through A cannot intersect the areas to the NE and SW of point A
It must be contained in the areas to the NW and SE of point A
Conclusion: indifference curves must be decreasing Otherwise they are not monotone:
The consumer would be indifferent to a bundle having less of both goods!!!
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• B, A, and D are indifferent • E is preferred to any bundle in U1 • Any bundle in U1 is preferred to H and G
Indifference curves: example
food
10
20
30
40
10 20 30 40
clothes 50
U1 G D
A
E H
B
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Indifference curves
Bundles to the NE of an indifference curve are preferred to those on the curve
Bundles on the curve are preferred to those to the SW of the indifference curve
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Indifference curves
Indifference curves cannot cross Crossings are incompatible with monotonicity
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Indifference curves
food
clothes • A and B are indifferent • A and C are indifferent • B and C should be indifferent • but B is preferred to C!!
U1
U1
U2
U2
A
B
C
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Indifference curves
Through every bundle goes an indifference curve
A consequence of preferences being complete
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U2
U3
Indifference curves
food
clothes
U1
A B C
• Through every bundle goes just one indifference curve • A is preferred to B, and B to C.
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Indifference curves
The shape of indifference curves conveys the consumer willingness to trade one good for the other good
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the number of clothes required to compensate for the loss of one unit of food increases from 1 to 6
Indifference curves
food
clothes
2 3 4 5 1
2
4
6
8
10
12
14
16 A
B
C
D E
6
-1
-1
4
-1 2
-1 1
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Indifference curves
The shape of indifference curves conveys the consumer willingness to trade one good for the other e.g., from A to B, 6 units of clothes for 1 unit of food but from C to D, only 2 units of clothes for 1 unit of
food
The more clothes one has, the more one is ready to trade clothes for food
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Indifference curves
The consumer willingness to trade goods is measured by his marginal rate of substitution (MRS) It provides the amount of a good that he is
ready to trade for one more unit of the other good
It is given by the slope of the indifference curve
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Marginal rate of substitution
food 2 3 4 5 1
clothes
2
4
6
8
10
12
14
16 A
B
C
D E
6
-1
-1
-1 -1
4
2 1
MRS = 6
MRS = 2 €
MRS = −ΔcΔf
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Marginal rate of substitution
Indifference curves are convex The more one consumes of a good, the less
one is ready to give up other goods to increase additionally its consumption
Consumers usually do prefer balanced bundles
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Marginal rate of substitution
food 40 80 20
clothes
20
30
40
0
U1
A
B
• The bundles between A and B are preferred to these two
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Marginal rate of substitution
Decreasing marginal rate of substitution The MRS decreases along the indifference
curve In the example, the MRS goes down from 6
to 4, then to 2, and finally to 1
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Marginal rate of substitution
different shapes for an indifference curve represent different attitudes to substituting one good for another
Special cases: Perfect substitutes Perfect complements
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Marginal rate of substitution
Perfect substitutes The MRS is constant Example: some may consider orange juice
and apple juice perfect substitutes They would always be ready to exchange 1
glass of orange juice for 1 glass of apple juice
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Consumer preferences
Apple juice
Orange juice
2 3 4 1
1
2
3
4
0
Perfect substitutes
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Consumer preferences
Perfect complements The indifference curbes are L-shaped Example: left and right shoes are used in
pairs (additional units of, say, just left shoes leave us indifferent)
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Consumer preferences
Right shoes
Left shoes
2 3 4 1
1
2
3
4
0
Perfect complements
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Consumer preferences
Explaining the consumer behavior does not require an index measuring the consumer’s satisfaction
A ranking suffices, but utility indexes are useful, mainly to represent attitudes towards risk
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Consumer preferences
Utility A numerical value representing the level of
satisfaction derived from consuming a particular bundle of goods
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Utility
Utility function A formula assigning a utility level to each
bundle of goods Example 1: given the utility function
U(f,c) = f + 2c the bundle (8 units of food, 3 units of clothes)
provides a utility 14 = 8 + 2x3
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Utility – Example 1
bundles food clothes utility
A 8 3 8 + 2x3 = 14
B 6 4 6 + 2x4 = 14
C 4 4 4 + 2x4 = 12
The consumer is indifferent between A and B but prefers both to C
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Utility – Example 2
food
10 15 5
5
10
15
0
clothes
U1 = 25
U2 = 50
U3 = 100
bundle U = f x c A 25 = 2,5 x 10 B 25 = 5 x 5 C 25 = 10 x 2,5
B
C
A
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Utility
Ordinal utility function Ranks bundles from less to more preferred
but does not convey any sense of intensity of preferences
Cardinal utility function It describes how much more is a bundle
preferred to another
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Utility
An ordinal utility sufices to explain most individual decisions
A cardinal ranking is needed to explain decisions under uncertainty and risk
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The budget constraint
Preferences alone do not explain consumers’ choices
The budget constraint limits the consumer’s decisions
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The budget constraint
The budget line It contains all the bundles of goods whose
cost equals the consumer’s income or wealth
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The budget line
If f is the amount of food purchased c is the amount of clothes, Pf is the price for food, Pc is the price for clothes then Pf f is the expenditure in food, and Pc c is the expenditure in clothes Pf f + Pc c is the total expenditure
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Pf f + Pcc = I
The budget line
The equation of the budget line is:
It says that the entire income is spent either on food or clothes
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The budget constraint
bundles food Pf = €1
clothes Pc = €2
income I = Pf f + Pc c
A 0 40 €80
B 20 30 €80
C 40 20 €80
D 60 10 €80
E 80 0 €80
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€
slope = - ΔcΔf
= - 12
= - Pf
Pc
The budget line
10
-20
A
B
C
D
E
I/Pc = 40
food
40 60 80 = I/Pf 20
10
20
30
0
clothes
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The budget line
Along the budget line any increase in the consumption of a good implies a decrease in the consumption of the other good
The slope the negative of the ratio of the goods prices
The slope is the rate at which goods can be substituted between them without changing the cost of the bundle
The slope measures also the relative price of one good in terms of the other
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The budget line
€
Pf f + Pcc = I
€
c =IPc−Pf
Pcf
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The budget line
The intersection I/Pc with the vertical axis is the maximum quantity of clothes c that can be purchased with an income I
The interection I/Pf with the horizontal axis is the maxmum quantity of food f that can be purchased with an income I
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€
slope = ΔcΔf
= - 12
= - Pf
Pc
The budget line
10
-20
A
B
C
D
E
I/Pc = 40
food
40 60 80 = I/Pf 20
10
20
30
0
clothes
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The budget line
Income and prices can change Changes in prices and income shift the
budget line Shifts in the budget line change the
consumer’s choice
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The budget line
An increase of income shifts the budget line
outwards
food
clothes
80 120 160 40
20
40
60
80
0
I = €160 D2
I = €80 D1
D3
I = €40
An decrease of income shifts the budget line
inwards
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The budget line
Impact of a change in income: An increase in income shifts outwards the
budget line (keeping the slope constant) With the additional income one can buy more
of both goods
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The budget line
Impact of a change in income: A decrease in income shifts inwards the
budget line (keeping the slope constant) One cannot buy as much as before with the
smaller income
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The budget line
Pf = 1
D1
An increase in the price of food to € 2
makes the budget line pivot inwards around 40
D2
Pf = 2 Pf = 0,50
D3
A decrease in the price of food to € 0,50 makes the budget line
pivot outwards around 40
40 food
clothes
80 120 160
40
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The budget line
Impact of changes in prices: If the price of a good increases, the budget line pivots
inwards around its crossing with the axis of the other good
e.g. if the price of food increases:
If the consumer only buys food he cannot buy as much as before (the intersection with the axis of food shifts leftwards)
If the consumer only buys clothes he can still by the same amount (the intersection with the axis of clothes stays put)
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The budget line
Impact of changes in prices: If the price of a good decreases, the budget line
pivots outwards around its crossing with the axis of the other good
e.g. if the price of food decreases:
If the consumer only buys food he can buy even more than before (the intersection with the axis of food shifts rightwards)
If the consumer only buys clothes he can still by the same amount (the intersection with the axis of clothes stays put)
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The budget line
Impact of changes in prices: If all prices increase in the same proportion,
then the slope does not change The budget line shifts inwards
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The budget line
Impact of changes in prices: If all prices decrease in the same proportion,
then the slope does not change The budget line shifts outwards
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Consumer’s choice
Given his preferences and budget constraint, how does the consumer choose a bundle of goods?
The consumer chooses the bundle on the budget line that maximizes his utility
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Consumer’s choice
The consumer’s choice: 1. is on the budget line
The consumer spends all his income (since his preferences are monotone)
2. gives the consumer his most preferred bundle on the budget line
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Consumer’s choice
Graphically, the consumer tries to reach the highest indifference curve on his budget line
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Consumer’s choice
U3
D
U2
A
food 40 80 20
clothes
20
30
40
0
U1
B
C
• D give a higher utility than A, but it is too expensive • B and C are affordable, but they are less preferred than A • A gives the highest attainable utility • A is the consumer’s choice
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Consumer’s choice
Graphically, the consumer tries to reach the highest indifference curve on his budget line
The highest attainable indifference curve is tangent to the budget line
The slope of the budget line is equal to the slope of the indifference curve at the consumer’s choice
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Consumer’s choice
The slope of an indifference curve is:
€
slopeIC = −MRS
€
slopeBL = −Pf
Pc
the slope of the budget line is:
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Consumer’s choice
therefore, at the consumer’s chosen bundle:
€
MRS =Pf
Pc
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Consumer’s choice
Utility is maximized on the budget line when the marginal rate of substitution is equal to the relative price
This happens ONLY at the optimal consumption bundle
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Consumer’s choice
food
clothes
40 80 20
20
30
40
0
bundle B does not maximize the utility
since the MRS = -(-10/10) = 1 Is bigger than the relative price = 1/2
+10f U1
-10c
B
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Consumer’s choice
If MRS ≠ Pf /Pc the consumer can increase his utility spending his income differently
If MRS > Pf /Pc He will increase his consumption of food and
decrease his consumption of clothes until MRS = Pf /Pc holds
If MRS < Pf /Pc He will decrease his consumption of food and
increase his consumption of clothes until MRS = Pf /Pc holds
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Consumer’s choice
U3
D
U2
A
food 40 80 20
clothes
20
30
40
0
U1
B
C
• at B the MRS> Pf/Pc and the utility increases as more food and less clothes are consumed • at C the MRS< Pf/Pc and the utility increases as less food and more clothes are consumed
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Consumer’s choice
A corner solution happens when the consumer does not buy one of the goods In that case MRS needs not be equal to the
relative price Pf /Pc
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Corner solution
food
clothes
B
A
U2 U3 U1
bundle B is a corner solution
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Corner solution
At bundle B, the MRS of clothes for food is bigger than the slope of the budget line
The consumer would like to give up clothes in exchange for additional food
But he has no more clothes to exchage
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Corner solution
When the optimal choice is located at the border of the budget constraint, the MRS needs not be equal to the relative price
In this case:
€
MRS ≥Pf
Pc
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Corner solution
When the MRS is much bigger than the the relative price, a small change in the price for clothes will have no impact on the consumer’s choice
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Revealed preferences
If the consumer’s choices before many different prices and incomes are known, then the consumer preferences can be recovered
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Revealed prices
D1
D2
B
A
• D1: chooses A instead of B • A is revealed preferred to B
• D2: chooses B instead of C • B is revealed preferred to C
food
clothes
C
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Revealed preferences
D1
D2
B
A
food
clothes
C
All pink bundles are preferred
to A.
A is preferred to any yellow bundle
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Revealed preferences
As the budget line changes, the consumer’s choice changes
The more the consumer reveals his choices, the more his preferences can be identified
In the limit, the indifference curves can be obtained
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All pink bundles are Preferred to A
food
Revealed preferences
clothes
L1
L2
L3
L4
A is preferred to any yellow bundle
D B
A
C
L3: C is revealed preferred to A
L4: D reveled preferred to A
L2: A revealed preferred to B
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Marginal utility and the consumer’s choice
Marginal utility mesures the additional satisfaction from the consumption of one more unit of a good How much happier is a consumer due to an
additional unit of food?
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Marginal utility - example
Let 9 be the marginal utility from increasing the consumption of food from 0 to 1 units
from 1 to 2, let the marginal utility be 7 from 2 to 3, let the marginal utility be 5 remark: marginal utility decreases as
consumption increases
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Marginal utility
Principle decreasing marginal utility: the more a good is consumed, the smaller the marginal utility of an additional unit of the good
Total utility increases monotonically nonetheless, since preferences are monotone
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Marginal utility and the consumer’s choice
Along an indifference curve: The increase in utility from the additional
consumption of a good must compensate for the decrease of utility from the smaller consumption of the other good
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Marginal utility and the consumer’s choice
formally:
€
0 = MgUf ⋅ Δf + MgUc ⋅ Δc
Total utility does not change along the indifference curve. The compensation leaves the consumer indifferent.
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Marginal utility and the consumer’s choice
That is to say:
€
− ΔcΔf
=MgU f
MgUc
and since MRS = −ΔcΔf
then MRS =MgU f
MgUc
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Marginal utility and the consumer’s choice
When the consumer maximizes his utility:
€
MRS = Pf
Pc
€
MgU f
MgUc
= Pf
Pc
Since the MRS equals also the ratio of marginal utilities from consuming f et c
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Marginal utility and the consumer’s choice
Condition for the utility maximization:
€
MgUf
Pf
=MgUc
Pc
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Marginal utility and the consumer’s choice
Equal marginal utilities principle: utility is maximized only if the marginal utility from spending an additional euro is the same for both goods