Intermediate Microeconomics - PowerPoint Presentation

Slide1

Intermediate Microeconomics

Part I

CONSUMER THEORY

Laura SochatSlide2

Budget constraint I

Income is one of the factors affecting the quantity demanded by consumers.

I like to spend money on food and on clothes. Assume they cost £5/g and £10/unit respectively. Also assume that my weekly income is £200.

if I decide to only consume food. if I decide to only buy clothes.

 Slide3

Budget constraint II

Given

my income

, I can afford to buy 40g of food if I do not buy any clothes. Given my income, I can afford to buy 20 units of clothes if I do not buy any food.Food (g)

Clothes (unit)

40

20Slide4

If instead, I want to balance my consumption between the two, it must be true that I do not spend more than my income

:

We know the respective prices, so we can re-write the budget constraint such as:

We have drawn the budget constraint with food on the vertical axis. Rewrite the budget constraint such as: Budget Constraint IIISlide5

The feasible set

Given my income, any bundle below the budget constraint is affordable. Any bundle

on

the budget constrain is just affordableFoodClothes4020Slide6

Budget constraint- shifts and movement

We saw earlier that the slope of the budget constraint depends only on relative prices:

A change in the price of one of the good will lead to a rotation of the budget constraint

A change in the income of the consumer will lead to a shift of the budget constraint What if both prices change by the same proportion? Slide7

The effect of a change in the price of one good

Given the price of clothing, if

to £10

 Food (g)Clothes (units)40

20

2

0

1

0

Given the price of food, if

to £20

 Slide8

Budget constraint

Let’s go further… Suppose two goods, x (food) and y (coffee)

What would the budget constraint look like, if the consumer was to be given:

An in kind transfer of 40g of coffee?What would the budget constraint look like if the government imposes:A quantity tax (t) on coffee?A subsidy (s) on food?Slide9

Preferences

Preferences will tell us more about a consumer’s choice.

Preference ordering; for any bundle

:Strict preferencesWeak preferencesIndifference These are ordinal relationsWhile preferences will differ between individuals, there are some properties we assume to be shared by all regarding preference ordering. Some of those will ensure rationality of the choice made by the consumers. Slide10

Properties of preference ordering

Completeness

The consumer can always rank between a choice of bundles. Either the consumer prefers X to Y, Y to X, or is indifferent between the two.

TransitivityThis assumption helps with the consistency of preference ordering. ContinuousIf X is preferred to Y, and there is a third bundle Z which lies within a small radius of Y, then X will be preferred to Z. Non- satiation- More is betterSuppose two bundles, X and Y such that X: (10,15) and Y: (12,15). It must be true that B is preferred to A. Slide11

Monotonicity and Convexity

Those two axioms are needed to define “well behaved preferences”

Monotonicity

Consider two bundles x and y, if bundle y has at least as much of both goods, and more of one, then it must be true that ConvexityConsider bundle x, comprising of a mixture of bundles x and y. It must be true that that z is (at least weakly) preferred to x and y, for any

 Slide12

Preference map

More is better tells us that B is preferred to A, and A is preferred to D.

There must be a point C equally likeable to A on [DB]

FoodClothesABD

C

5

15Slide13

Indifference curve

Food

Clothes

ABDC

5

15Slide14

Indifference map

Food

Clothes

515

B

C

A

D

E

What about point E?

E has more clothes than C, but C has more food than E, how can we tell whether E is preferred to C?Slide15

Properties of indifference curves

Bundles on indifference curves further from the origin are preferred to ones on indifference curves closer to the origin

Follows from the monotonicity assumption.

Indifference curves are downward sloping Follows from the more is better- Every commodity is a goodIndifference curves cannot crossFollows from more is better and transitivity assumptionsIndifference curves are continuousFollows from the completeness assumption Indifference curves are convex to the originPreferences are convex Slide16

Utility

Working

with preference relations is not always convenient.

Economists like to work with Utility Functions, which are simple and easy way of summarizing preferences.If a preference relation is complete, transitive and (continuous) it can be represented by a (continuous) utility function (sufficient condition for the existence of a utility function).People are able to rank all possible situations from the least desirable to the most. Economists call this ranking utilityIf x is preferred to y, then the utility assigned to x exceeds the utility assigned to y:  Slide17

Monotonic transformations of utility functions

Consider a utility function

, representing specific preferences. Then we know that any monotonic transformations of this utility function will represent the same preferences. Some examples of monotonic transformations:

 Slide18

Trade offs

We know that one is indifferent between two bundles on the same indifference curve. The rate at which a consumer is willing to substitute one good for another is represented by the slope of the IC, and is called the

Marginal rate of substitution.

It is the slope of the indifference curve at that point Slide19

Marginal utility

AB

From point A to point B, the consumer loses

and gains

. We also know that both A and B give the consumer the same utility

Marginal utility lost from less

must be offset by marginal utility gained from more

 Slide20

Marginal rate of substitution

To obtain the expression for the marginal rate of substitution, consider implicit differentiation

Consider a change in

and which keeps utility constant: Consider a different representation of the utility function:

Show that the marginal rate of substitution does not depend on the utility representation

 Slide21

Different preferences

Bread (piece)

Pasta (kg)

Pasta (kg)Bread (piece)

5

4

4

5

7

6

7

5Slide22

Some utility functions examples

Perfect substitutes

Consider the folder example above. All the consumer cares about is the overall number of folders, not how many red/blue folders are in the mix. Considering the one-to-one relationship from above, the utility function would take the form

In general, the utility function will take the formPerfect complementsWe looked above at the right earring/left earring where the relationship is one to one. The right earring will not provide any utility without a left earring. Considering this one-to-one relationship we obtain the following utility function

.

In general (not a one to one relationship), we would have

 Slide23

Perfect complements/Perfect substitutes

Red folders

Blue folders

Left earringRight earring

Constant MRS

MRS=

if

MRS=

if

MRS=

if

 Slide24

Cobb-

D

ouglas preferences

Very commonly used (also for production functions). Takes the general following form: , where a and b represent the consumers preferences. We will assume that and rewrite  Some utility functions examples

 Slide25

Linking MRS to the slope of budget constraint

Slope of the budget constraint: For a given income (expenditure), how much of one good does one have to give up to purchase an extra unit of the other good

Slope of the indifference curve: How much of one good is one willing to give up to obtain an extra unit of the other good, to be as well as off as before.

The slope of the budget constraint give us the marginal cost of clothes in terms of food. The slope of the indifference curve give us the marginal benefit of clothes in terms of food. Slide26

Optimal choice

Food (g)

Clothes (unit)

4020

A

B

O

C

Which point will be the optimal choice for the consumer?

Remember the assumptions we made about preference ordering, and the properties of indifference curves that follow from those.Slide27

Optimal choice

The optimal choice for the consumer is the tangency point between the budget constraint and an indifference curve.

If

, the consumer gets less food (1) for giving up a unit of clothing than the amount of food the consumer could buy by not buying any clothes (2)The consumer will clearly be better off buying more food, and less clothes. Can you think of examples where the tangency condition might not hold?The tangency condition is necessary, but not necessarily sufficient  Slide28

Corner solution

Food

Clothes

4020

At point A the marginal rate of substitution is lower than the slope of the budget constraint, with diminishing marginal rate of substitution, the two never reach equality.

With MRS < slope of BC at every point, the best the consumer can do is to buy food only: For an extra unit of clothing, the consumer will have to give up more food than what he could buy, by not buying clothes. Slide29

Revealed preferences

Use the consumer’s demand to discover his preferences- we need to observe the consumer’s behaviour

Assume behaviour doesn’t change over

time; Economists use monthly, or quarterly time spans depicts the optimising bundle. What can we say about bundle ?Have we made any assumptions about preferences to make this analysis easier? Slide30

Weak Axiom of Revealed P

references

Weak Axiom of Revealed Preferences

If is directly revealed preferred to , and the two bundles are not the same, then it cannot happen that is directly revealed preferred to Algebraically, we can say that if it is true that

Then, it cannot be true that

 Slide31

Strong Axiom of Revealed Preferences

Looks at indirect revealed preferences as well

If

if revealed preferred to , either directly or indirectly, and if is different than , then cannot be directly, or indirectly revealed preferred to . Let’s look at how we can check SARP Slide32

Homothetic tastes

A situation where the consumer’s preferences depend solely on the ratio of good 1 to good 2

Homothetic tastes give rise to indifference maps where is MRS is constant along any ray from the

origin. Can you say whether examples of preferences shown above are homothetic preferences (perfect substitutes, perfect complements, Cobb-Douglas)? Slide33

Quasilinear tastes

Tastes are linear in one good, but may not be in the other good:

With quasilinear tastes, indifference curves are vertical translates of one another.

In this case, the MRS is constant along any vertical line from the x-axis.