The rules of the game Lectures Seminars The marking: exams and exercises.

The rules of the game

Lectures

Seminars

The marking: exams and exercises

The lectures

12 weeks times 2 hours

Attendance to the lectures is compulsory Make sure you do the reading each week Prepare questions on lecture points or the

reading that seem unclear Do not hesitate to ask questions during the

lecture The course outline and lecture slides will

be made available on the ENTG

The seminars

A short seminar will be organised during the first half hour of each lecture.To go over the exercises for the weekTo clarify problematic points

Make sure you prepare the exercises, they are part of the learning process !

The exercises to be prepared for each week are given in the course outline

Exams and marks

The overall mark for the module is a weighted average: 2/3 given by the seminar marks 1/3 given by final exam

The final exam is composed of Multiple choice questions Review questions A standard exercise An applied exercise

Exams and marks

The seminar mark is composed of 50% : 2 « galops d’essai » (mock exams) 30% : average exercise mark 20% : personal mark, that takes into account

participation, turnout, etc.

The average exercise mark (incentives!) : You are free to hand in exercises every week The mark is the average of your best 6 results If you hand in less than 6 exercises, then your

average takes in the extra 0’s needed to make up the 6 marks...

Consumer preferences and utility

Modelling consumer preferences


How can we possibly model the decision of consumers ?What will they consume?How much of each good?

Actually, a very simple framework is enough !This framework can explain a lot of the

behaviour of people on markets.


Last week’s “general rule”: A rational consumer will always choose

the best basket of goods amongst all the ones it can afford

But we need to clarify :What we mean by rationalWhat we mean by bestWhat we mean by afford

Today

Next week


The utility function as a measure of satisfaction

Indifference curves as a representation of preferences

The marginal rate of substitution

The Utility function

Historically, utility as a measure of satisfaction is grounded in utilitarianism

Jeremy Bentham (1748-1831): “It is the property of an object to produce pleasure, well-being or happiness”

Stanley Jevons (1835-1882): The father of the “marginalist revolution”, who generalised this concept to consumer behaviour


Cardinal utility assigns a value to the level of satisfaction associated with the consumption of a basket of goods.

Total utility is the sum of the satisfactions derived from the consumption of several goods.

Marginal utility is the increase in utility following the consumption of an extra unit of a good.

Beers consumed

Total Utility

Marginal Utility

0 0 0

1 10 10

2 15 5

3 18 3

4 19 1


The marginal utility of a good (mU ) measures the increase (or decrease) in total utility (∂U) following a small variation in the quantity consumed (∂x)

Remember last week’s lecture:Marginal utility is the first derivative of the

utility function. It gives the slope of the utility function

UmU

x


mU = 10

mU = 5

mU = 3

mU = 1


The marginal utility of the good (beers) gets smaller as the quantity consumed increases.

This phenomenon is called the law of diminishing marginal utility


The initial, historical approach to consumer behaviour used this concept of cardinal utility

However, this is a problematic concept: Is it possible to quantify the satisfaction derived from

consuming a good ? Is it possible for the quantities of utility derived from 2 different

goods to be compared ? More importantly, do consumers actually think that way when

they choose goods ???

This problem was solved by the introduction of ordinal utility More general, more realistic and more powerful


Ordinal utility is a representation of preferences

What is important is not the ability to quantify « how much » utility is provided by a bundle, but the ability to rank bundles in order of increasing utility

This is much closer to the “real” behaviour of agents

1 2 11 22 1 2( ) ( ) if U( )y , y U( )x , x x , x y , y

1 2 11 22 1 2( ) ( ) if U( )x , x U( )x , xy , y y , y

1 2 11 22 1 2( ) ( ) if U( )y , y U( )x , x x , x y , y


Some types of preferences cannot be represented by an ordinal utility function

Some simplifying assumptions have to be made Preferences are complete :

Agents can always rank bundles (i.e. preferences exist for all possible bundles)

Preferences are transitive :

1 2 1 21

1

2

2

1

1

2

2

If ( ) ( ) and ( ) ( )

(

x , x

x , x

z ,y , y y

) ( )

y z

z

,

z ,


An example of non-transitive preferences

Your favourite childhood game:

Rock

Paper

Scissors


Such preferences cannot be represented by an ordinal utility function !! This is a first example of how consumer theory

simplifies a complex reality

Consumer theory (and economic theory in general) often “breaks down” in extreme situations People’s behaviour becomes governed by

different priorities





Indifference curves

Indifference curves represent preferences in “consumption space”

They are built from the ordinal utility function As seen above, an ordinal utility function can

represent preferences (under some conditions) The ranking of bundles in order of preference

corresponds to the ranking in order of increasing (or decreasing utility)

Good 1

Good 2

Indifference curves

Indifference curves

Utility function for a single good

Indifference curves

But how would you draw a utility function for the consumption of 2 goods ?

Indifference curves

Seen from above, the 3-D diagram looks like this...

Lines of constant utility

Indifference curves

This is the same “trick” as for this kind of diagram...

Indifference curves

Indifference curves are a graphical (2-D) representation of a 3-D utility function Just like the contour lines of a 2-D road map

represent the 3rd dimension (altitude)

A given indifference curve represents all the baskets of goods that provide the same utility to a consumer The consumer is therefore indifferent to all

these baskets

Indifference curves

Indifference curves further from the origin correspond to higher levels of utility

Good 1

Good 2

x1

x2

X U(x1,x2) < U(y1,y2)

y1

y2

Y

Indifference curves

Because they are derived from a utility function, indifference curves are a representation of preferences

However, at this point, indifference curves can still take a wide range of shapes Some examples are in the exercise for next week

For a general theory of choice, economists like “well-behaved” indifference curves 2 more simplifying assumptions need to be made

Indifference curves

Monotonicity (non-satiation)

In other words, “more is always preferred to less”

Extra units of a good always increase utility, so consumers always prefer to have more of a good

The implication is that regardless of which indifference curve you are on, there always exists a higher one right next to it.

Indifference curves

Convexity (preference for variety)

Good 1

Good 2

y1

y2

Y

x1

x2

XA combination z of extreme bundles x and y is preferred to x and yZ

Indifference curves

Example of concave preferencesGood 1

Good 2

y1

y2

Y

x1

x2

X The extreme bundles x and y are preferred to a combination z of x and yZ

What can we say about marginal utility?

Indifference curves

“Well-behaved” indifference curves don’t cross

Good 1

Good 2

Y

X

Let’s assume they can

Z

x y y z and , x z so but z x

This violates monotonicity (more is preferred to less)






What is a rate of substitution ?You currently have a bundle composed of 10

tubs of ice-cream and 3 DVDs.You want to keep your satisfaction the sameHow many tubs of ice-cream are you

prepared to give up to get some extra DVDs?

The rate at which you are prepared to exchange is known as the “rate of substitution”


Ice-cream

DVD

y1

y2

Y

x1

x2

X

DVD

(+)

IC(-)

ICRate of Substitution =

DVD


What is a marginal rate of substitution ?Exactly the same idea, but this time we are

talking about a tiny change in your bundle (∂x) instead of a large change (∆x)

You have 10 tubs of ice-cream and 3 DVDs.How many tubs of ice-cream are you

prepared to give up to get ONE extra DVD ?

This means that the marginal rate of substitution is the slope of the indifference curve


Ice-cream

DVD

y1

y2

Y

x1

x2

X

ICMRS =

DVD

∂IC

∂DVD

∂IC

∂DVD

The MRS is decreasing along the indifference curve


So the marginal rate of substitution is the slope of the indifference curve

The amount of ice-cream you are willing to give up for an extra DVD is lower the less ice-cream you haveThis suggests a link with the idea of

decreasing marginal utility

Is there a way of clarifying this link ?


Ice-cream

DVD

x1

x2

X

Let’s “zoom in” on the indifference curve until it looks flat

Giving up ∂IC ice-cream causes a loss of utility

ICmU IC

DVDmU DVD

Receiving ∂DVD DVDs causes a gain of utility

Because we are still on the same indifference curve, loss=gain


The loss of utility from giving up one good equals the gain from receiving the other good

Or equivalently:

Rearranging (dividing both sides by mUIC and ∂DVD):

The MRS is equal to the ratio of marginal utilities!

IC DVDmU IC mU DVD 0

IC DVDmU IC mU DVD

DVD

IC

mUICMRS

DVD mU


In general, with two goods x and y, we have :

Note: Economists typically “forget” about the minus sign and give the MRS as a positive number

This is result may seem a bit pointless, but it will become clear when we examine consumer choice next week

x

y

mUyMRS

x mU

The rules of the game Lectures Seminars The marking: exams and exercises.

Documents

total utility marginal

week slide

total utility u

consumer behaviour slide

entg slide

applied exercise slide

course outline slide

rational consumer