Lecture 10 slide 1

A primer on

Consumer ChoicePreferences, Indifference Curves and

Utility

Lecture 10 slide 2

INTRODUCTION

PreferencesIndifference CurvesUtility

Lecture 10 slide 3

The problem

Simplify the consumer’s choice problem into her making the best she can to maximize her satisfaction

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Preferences

What is best? We assume that what is best for the consumer

should be left to her to decide (we want to be positive, not normative)

And that her preferences, how much she enjoys the consumption of goods can be described by using indifference maps

Lecture 10 slide 5

Preferences

Define a consumption bundle (or basket) as a combination of quantities of different goods (for simplicity 2 goods)

Say we use goods X and Y so the basket is (x,y)

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Properties of Preferences

We assume preferences to be:complete: any bundle (x,y) can be compared to any

other bundle (x’,y’), the consumer can rank them or know that she is indifferent between both

This might seem rational…but not always, …like when you are 4 years old and your brother is 5 or so :)

- Ýx,yÞ, Ýxv,yvÞ Ýx,yÞOÝxv,yvÞ or Ýxv,yvÞOÝx,yÞ or both: Ýxv,yvÞ i Ýx,yÞ

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Properties of Preferences

We assume preferences to be:transitive: if (x,y) is weakly preferred to (x’,y’) and

(x’,y’) is weakly preferred to (x”,y”) then the consumer must weakly prefer (x,y) to (x”,y”)

- Ýx,yÞ, Ýxv,yvÞ,Ýxvv,yvvÞÝx,yÞP Ýxv,yvÞ , Ýxv,yvÞP Ýxvv,yvvÞ => Ýx,yÞP Ýxvv,yvvÞ

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Properties of Preferences

We assume preferences to respect the non-satiation property (for the case of goods) or free disposability

- Ýx,yÞ,Ýxv,yvÞx > xv,y ³ yv=> Ýx,yÞÉ Ýxv,yvÞ

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Indifferences curves

We can represent the preferences of consumers by using indifference curves

These show in the x, y space those consumption bundles about which the consumer is indifferent

Indifference curve: combinations of goods that give the same level of satisfaction

We are going to think of X and Y as pizzas and burritos and of x and y as pizzas per semester and burritos per semester

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Indifferences curves

Using the property of nonsatiation, we can work out the green area of preferred bundles and the orange area of dominated bundles

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Indifferences curves

The indifference curve passing through e might well look like this (it respects the nonsatiation property)

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Indifferences curves

The further from the origin, the more utility the indifference curves show

y

x

Better

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Indifferences curves

There is an indifference curve through all possible bundles

y

x

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Indifferences curves

Indifference curves cannot cross!

y

x

eb

a

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Indifferences curves

Indifference curves cannot be any thick!

y

x

eb

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Indifferences curves

Indifference curves for goods should slope downwards

y

x

e

b

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Marginal Rate of SubstitutionIndifference curves tell us about the willingness of the consumer to substitute one good for the other

y

x

e

b

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Marginal Rate of Substitution

The Marginal Rate of Substitution is the maximum amount of one good the consumer is willing to sacrifice to obtain a marginal unit of the other good

y

x

e

b

MRS is the slope of the indifference curve

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The curvature of indifference curves

Most indifference curves are convex to the origin, exhibiting decreasing MRS between the goods

y

x

e

b

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The curvature of indifference curves

But other possibilities exist: concave curves (increasing MRS!!!) => you prefer the extremes to the mixing, perhaps you hate the combination of both goods! Or they are individually addictive…

y

x

e

b

Ice-cream

anchovies

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The curvature of indifference curves

But other possibilities exist: straight lines =>what kind of preferences do they represent?

y

x

e

b

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The curvature of indifference curves

Check the slope…constant what does it show?

y

x

e

bGo to hidden slide

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The curvature of indifference curves

What about this slope?

y

x

e

bGo to

hidden slide

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The curvature of indifference curves

What about this shape?

y

x

e

bGo to

hidden slide

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The curvature of indifference curves

These goods have A different complementarily ratio

Sugarcubes

Tea cups

e

b

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The curvature of indifference curves

What about this shape? Could happen with food and clothes

y

x

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Next

Utility and Budget Constraints