microeconomics and financecermsem.univ-paris1.fr/davila/teaching/sbs/ch03_pindyck...microeconomics...

1 Solvay Business School – Université Libre de Bruxelles

Microeconomics and Finance

Solvay Business School 08/09

Julio DAVILA

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

  Teaching Assistant: Ritha Sukadi Ritha.Sukadi.Mata@ulb.ac.be

  Office hours: by appointment (e-mail Ritha)

  Slides: http://cermsem.univ-paris1.fr/davila/microfinance.html

Consumer behavior

Microéconomie, chapter 3

Consumer behavior

 Consumer behavior theory explains how the consumer chooses to spend his income in different goods and services

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

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

 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

Indifference curves: example

bundles food clothes

A 20 30

B 10 50

D 40 20

E 30 40

G 10 20

H 10 40

 The assumptions on preferences translate into graphical properties of the indifference curves

A is preferred to any bundle in the yellow box,

but any bundle in the pink box is preferred to A.

10 20 30 40

clothes 50

  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!!!

• B, A, and D are indifferent • E is preferred to any bundle in U1 • Any bundle in U1 is preferred to H and G

10 20 30 40

clothes 50

U1 G D

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

Indifference curves

 Indifference curves cannot cross  Crossings are incompatible with monotonicity

Indifference curves

clothes • A and B are indifferent • A and C are indifferent • B and C should be indifferent • but B is preferred to C!!

Indifference curves

 Through every bundle goes an indifference curve

 A consequence of preferences being complete

Indifference curves

clothes

• Through every bundle goes just one indifference curve • A is preferred to B, and B to C.

Indifference curves

  The shape of indifference curves conveys the consumer willingness to trade one good for the other good

the number of clothes required to compensate for the loss of one unit of food increases from 1 to 6

Indifference curves

clothes

2 3 4 5 1

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

  The more clothes one has, the more one is ready to trade clothes for food

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

Marginal rate of substitution

food 2 3 4 5 1

clothes

MRS = 6

MRS = 2 €

MRS = −ΔcΔf

 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

food 40 80 20

clothes

• The bundles between A and B are preferred to these two

 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

 different shapes for an indifference curve represent different attitudes to substituting one good for another

 Special cases:  Perfect substitutes  Perfect complements

 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

Apple juice

Orange juice

2 3 4 1

Perfect substitutes

 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)

Right shoes

Left shoes

2 3 4 1

Perfect complements

 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

 Utility  A numerical value representing the level of

satisfaction derived from consuming a particular bundle of goods

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

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

Utility – Example 2

10 15 5

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

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

Utility

 An ordinal utility sufices to explain most individual decisions

 A cardinal ranking is needed to explain decisions under uncertainty and risk

The budget constraint

 Preferences alone do not explain consumers’ choices

 The budget constraint limits the consumer’s decisions

 The budget line  It contains all the bundles of goods whose

cost equals the consumer’s income or wealth

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

42 €

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

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

slope = - ΔcΔf

= - 12

= - Pf

The budget line

I/Pc = 40

40 60 80 = I/Pf 20

clothes

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

The budget line

Pf f + Pcc = I

c =IPc−Pf

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

slope = ΔcΔf

= - 12

= - Pf

The budget line

I/Pc = 40

40 60 80 = I/Pf 20

clothes

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

The budget line

An increase of income shifts the budget line

outwards

clothes

80 120 160 40

I = €160 D2

I = €80 D1

I = €40

An decrease of income shifts the budget line

inwards

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

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

The budget line

Pf = 1

An increase in the price of food to € 2

makes the budget line pivot inwards around 40

Pf = 2 Pf = 0,50

A decrease in the price of food to € 0,50 makes the budget line

pivot outwards around 40

40 food

clothes

80 120 160

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)

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)

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

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

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

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

Consumer’s choice

 Graphically, the consumer tries to reach the highest indifference curve on his budget line

Consumer’s choice

food 40 80 20

clothes

• 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

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

Consumer’s choice

 The slope of an indifference curve is:

slopeIC = −MRS

slopeBL = −Pf

the slope of the budget line is:

Consumer’s choice

 therefore, at the consumer’s chosen bundle:

MRS =Pf

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

Consumer’s choice

clothes

40 80 20

bundle B does not maximize the utility

since the MRS = -(-10/10) = 1 Is bigger than the relative price = 1/2

+10f U1

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

Consumer’s choice

food 40 80 20

clothes

• 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

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

Corner solution

clothes

U2 U3 U1

bundle B is a corner solution

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

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

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

Revealed preferences

 If the consumer’s choices before many different prices and incomes are known, then the consumer preferences can be recovered

Revealed prices

• D1: chooses A instead of B • A is revealed preferred to B

• D2: chooses B instead of C • B is revealed preferred to C

clothes

All pink bundles are preferred

A is preferred to any yellow bundle

 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

All pink bundles are Preferred to A

clothes

A is preferred to any yellow bundle

L3: C is revealed preferred to A

L4: D reveled preferred to A

L2: A revealed preferred to B

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?

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

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

 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

 formally:

0 = MgUf ⋅ Δf + MgUc ⋅ Δc

Total utility does not change along the indifference curve. The compensation leaves the consumer indifferent.

 That is to say:

− ΔcΔf

=MgU f

and since MRS = −ΔcΔf

then MRS =MgU f

 When the consumer maximizes his utility:

MRS = Pf

Since the MRS equals also the ratio of marginal utilities from consuming f et c

 Condition for the utility maximization:

 Equal marginal utilities principle: utility is maximized only if the marginal utility from spending an additional euro is the same for both goods

microeconomics and financecermsem.univ-paris1.fr/davila/teaching/sbs/ch03_pindyck...microeconomics...

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