CHAPTER 2 UTILITY AND CHOICE

Objective• Build a model to understand how a consumer makes

decisions under scarcity.

• To understand his choice we need to know:1. Preferences2. Constraints

• Consumer makes a choice that results in the maximum satisfaction or UTILITY.

• Two goods available: X1 and X2.• Utility = U(X1, X2; other things)

• Utility depends on the amount of X1 and X2 consumed and other things.

• Assume other things are held constant.

Utility

Three Assumptions About Preferences

We make the following assumptions about preference so we can represent preferences by a utility function• Completeness

• Given two options, A and B, a person can state which option they prefer or whether they find both options equally attractive.

• Transitivity• Preferences are internally consistent.• If I prefer A to B, and prefer B to C, then I must prefer A to C.

• More is Better• Economic “goods”• What’s an economic “bad”?

Quantity of Y

per week

Y*

Quantity of Xper week

?

?

X*

More is Better GraphicallyCombinations of X and Y in the green area are preferred to (X*, Y*)

(X*, Y*) is preferred to combinations of X an Y in the red area.

Can’t say about the other points.

Indifference Curves• We want to find a way to compare points in the two ?

regions from the last picture.

• Two goods: soft drinks and hamburgers.

• Indifference curve• A curve that shows all the combinations of two goods that give the

same level of utility

• If you get the same utility you must be indifferent.

Hamburgersper week

6 A

B

CD

U1

4

3

2

Soft drinksper week2 3 4 5 6

Indifference CurveLet’s say you are indifferent between A, B, C and D.

Draw a curve through those points.

Every point gives the same level of utility.

Hamburgersper week

6 A

B

CD

U1

4

3

2

Soft drinksper week2 3 4 5 6

Indifference Curve

E

What can we say about combination E?

What about F?

F

Hamburgersper week

6 A

B

CD

U1

4

3

2

Soft drinksper week2 3 4 5 6

Indifference Curve

E

F

Why does the indifference curve have a negative slope?

Because, if you give up hamburgers, you need to get more soft drinks to still get the same level of utility.

Hamburgersper week

Soft drinksper week

Indifference Curve Maps

U1

U2

U3

An indifference curve map shows the utility a person gets from all possible combinations of two goods.

As you move to the northwest, utility increases: U3 > U2 > U1

Marginal Rate of Substitution (MRS)

• The absolute value of the slope of the indifference curve

• The MRS measures the rate at which you are willing to reduce the consumption of one good to get one more unit of another good and still remain indifferent.

Hamburgersper week

6 A

B

CD

U1

4

3

2

Soft drinksper week2 3 4 5 6

MRS

E

F

From A to B: the person is willing to give up 2 burgers to get 1 more soda.

From B to C: the person is willing to give up 1 burger to get 1 more soda.

From C to D: the person is willing to give up ½ burger to get 1 more soda.

Diminishing MRS

• As you consume more and more soda, the number of burgers you are willing to give up to get one more soda gets smaller and smaller.

• This is known as diminishing marginal rate of substitution.

• People prefer balanced consumption to extremes.• From convexity• Move along the indifference curve

• Same utility level• MRS decreases

Calculating MRS• MRS=-MU1/MU2• Calculate Mui, where i =1 or 2, from utility function

Hamburgersper week

6 A

G

DU1

4

2

Soft drinksper week2 3 4 60

Convexity of Preferences

You would prefer 4 burgers and 4 sodas to 6 of one good and 2 of the other good.

Suppose we create a basket that is ½ of A and ½ of D: point G.

Representing Preferences Graphically

16

• Upward sloping indifference curves• A good and a bad

• Flat indifference curves• Goods that yield no utility • Useless goods

• Straight-line indifference curves• Goods that are perfect substitutes

• MRS - constant along an indifference curve• In a two-good world

• Indifference curve - straight line

17

Good 1 (x 1)

0

Good 2 (x 2)

(a) Flat indifference curves. The good measured on the horizontal axis is yielding no utility for the consumer.

(b) Straight-line indifference curves: perfect substitutes. The same amount of good 2 is always needed to compensate the consumer for the loss of one unit of good 1.

(a) (b)

a

Good 1 (x 1)

0 3 8 11

Good 2 (x 2)

9

54

10

+∆x2-∆x1

+∆x2

-∆x1

Representing Preferences Graphically

18

• Right-angle indifference curves• Goods that are perfect complements

• Must be consumed in a fixed ratio to produce utility

• Bowed-out indifference curves• Nonconvex preferences

I1

19

Good 1 (x 1)0

Good 2 (x 2)

(c) Right-angle indifference curves: perfect complements. Adding any amount of only one good to bundle a yields no additional utility.

(d) Bowed-out indifference curves: non-convex preferences and the MRS. As the consumer gets more of good 2, he values it more.

(c) (d)Good 2 (x 2)

1011

-∆x1-∆x1

Good 1 (x 1)

0 5 6

bc

a-∆x1

b

a

+∆x2+∆x2

+∆x2

Perfect substitutes

20

Coke0

Pepsi

Mary’s marginal rate of substitution is constant at any bundle of Pepsi and Coke.

Budget line

21

Points on the budget line indicate all the bundles of goods that the consumer can afford.

Good 2

150

50

100

Good 11501000 50

Budget Line and Government PolicyWhat is the effect of the following on the budget line?

• Quantity tax• Value tax• Lump sum tax• Voucher• rationing

Optimal Consumption Bundle

23

• Optimal consumption bundle• Maximize consumer’s utility

• Within the economically feasible set• Best bundle

• According to consumer’s preferences

• Characteristics of optimal bundles• Indifference curve tangent to budget line

• Slope of indifference curve = MRS = -∆x2/∆x1

• Slope of budget line = price ratio = p1/p2

• MRS = p1/p2

The optimal consumption bundle

24

At the optimal point e, the indifference curve is tangent to the budget line

Good 1 (x 1)0

Good 2 (x 2)

x

ez

B

B’

F

+1

+1

-4

-3

mn

k