Modern Consumer Theory:Ordinal Utility, Preferences and

Indifference CurvesSignificance: Dispenses entirely with concept of “utility” and

depends only on observable quantitiesLearn:

• Assumptions about consumer’s behavior• Properties of indifference curves• Representing the consumer’s budget constraint• Equilibrium Condition and how consumer gets there.• How to represent changes in prices or income• Constructing the demand curve from indifference map• How to decompose a change in purchases into substitution and income effects• Definition and illustration of indexation

• Consumer wishes to choose between alternate “market baskets” of goods

• Assumptions:I. Consumer knows own preferences: for any

baskets A and B, A P B, B P A, or A I B

II. Transitivity: if A P B and B P C, then A P C (or I)

III. For any good, more is better than less

IV. Variety in consumption: a market basket with some X and some Y is preferred to all X or all Y

Y

X

B

A F

C D

Y

X

B

A F C D II I

Indifference Curves:

Since F P C every point on II must be preferred to every point on I points on curves to right are preferred to points on curves to left.

Shape: reflects assumption IV above.

Non-Intersection Property

A B

C

Y

X

Since B P A and B I C, we must have C P A, but C and A are on same indifference curve, a logical contradiction.

• Marginal rate of substitution of X for Y: slope of the indifference curve or |Y/ X|

• MRSXY is the rate at which consumer is willing to give up Y for additional X

X

Y

Y

X

• The Budget Constraint depends on – prices– how much the consumer has to spend

Y

X

B/pY

B/pX

Slope of the Budget Constraint is the price ratio –pX/pY. The absolute value px/py is called the marginal

rate of exchange

• Marginal Rate of Exchange of X for Y: The absolute value of the slope of the budget line. MREXY gives the terms on which the consumer can exchange Y for X.

• To buy an extra X, consumer must reduce purchases of Y by pX/pY.

• Or, giving up one Y allows the consumer to obtain px/py of X

• Example: suppose pV = $2 and pB = $3 and consumer has $18. Max videotapes = 9 and max beer = 6. Slope = 9/6 = 3/2 = 1.5. Sandy must give up 1.5 videotapes to get an additional 6-pack.

V

9

B

6

Suppose that Sandy initially finds herself at this

position. Note that MRSXY > MREXY

The slope of the budget line = rise/run. In rising nine Y, the line runs -6

X.

Y

X

dY

To obtain X, consumer is willing to give up Y. He has to give up only dY however, so moving to the right along B-B is a bargain.

Consumer need only know that he’s willing to give up more Y than he has to.

B

B

V

9

B

6

E

Consumer is in equilibrium at E, where MRSXY = MREXY. At any other point on budget line, consumer will find his willingness and ability are not equal. Above E, he’ll give up more Y to get X than he has to. Below E, he’ll give up more X to get Y than he has to.

V

9

B

6

At equilibrium, we have

MRSXY = pX/pY. Since MRSXY is roughly equivalent to MUX/MUY, this is equivalent to condition found in equilbrium with cardinal utility.

EXAM THURSDAY

• Coverage as noted in Syllabus• Study Questions Sets 2, 3 & 4 through question

23• Newspaper readings as posted• Format and length as first exam• Bring

– number 2 pencil– calculator (NOT cell ‘phone)

• Bubble in your name Last Name First Name• I will use PIN from first exam; there’s no reason

to repeat it

V

B

B

4 6 B B’

II

I

Establishing Demand Curves: When the price of beer falls from $3 to $2, the budget line rotates from B-B to B-B’. Sandy’s purchases increase from 4 to 6

Price of Beer

D

3

2

D

Quantity of Beer

4 6

Sandy’s demand for beer can be established by presenting him with different prices and observing how much he buys. The points 3,4 and 2,6 are two points on his demand curve D-D.

V

9

B

4 5

II

I

Establishing Income Effects: When Sandy’s Budget increases from $18 to $24, his purchases of both goods increase.

• Demand: when p, q– substitution effect– income effect

• How much of change in q is due to which• Decomposing change into substitution and

income effects• In principle

– Observe change as price rises– Restore original income and observe new

purchase; any difference must be substitution effect

V

B

B

4 B’ 6 7 B

II

I

Decomposing Substitution and Income Effects: The Hicks Decomposition.

“Same income” is defined as being on the same indifference curve. E is the original consumer equilibrium; E’ is the equilibrium after price increase.

H

H

EH

E

E’

Giving the consumer additional income creates the budget line H-H; the “compensated” equilibrium is at EH.

The substitution effect is 1 or 7 – 6; the income effect is 2 or 6 – 4.

Y

B

4 6 B 8 B’

II

I

Hicks Decomposition in reverse: When the price of X falls, budget line rotates to B-B’ and consumer’s purchases increase from 4 to 8. The line H-H reduces income back to the original indifference curve but with new price ratio.

X

H

H

Sir John Hicks, 1904 – 1989

Hicks was said to be mystified by the difference in treatment accorded himself vs. John Maynard Keynes. Keynes was a public figure, widely known for his economic theory and praised for the elegance of his writing. On top of that, Keynes was wealthy and even married a Russian ballerina, an exotic beauty, while Hicks got by with a professor’s salary and a frumpy, dowdy professor’s wife.

The fact is – Keynes was oriented to policy and reveled in public attention, while Hicks was an “economist’s economist” who wrote for other professionals. Of the two, Hicks surely made the greater and more lasting contribution to economic theory. But Keynes had a far greater impact on political and social thought.

• Example: Suppose that the U.S. levied a tax of $3 a gallon on gasoline while simultaneously cutting income taxes, so that tax revenues remained constant – in effect compensating consumers by giving them more money. – What would happen to sales of gasoline? – Would anyone be worse off?

• Definition of “real income”• Hicks: same indifference curve. Interpreted as same

level of utility• Slutsky: enough money to buy same market basket

V

B

B

4 B’ 6 7 B

III

I II

Decomposing Substitution and Income Effects: The Slutsky Decomposition. The consumer is compensated for higher prices by giving him enough additional money to buy the original market basket. But he will instead buy ES.

S

S

ES

E

E’

The original equilbrium is at E; when PB rises, consumer moves to E’. The line S-S represents new price ratio with enough money to buy E.

Compensated equilibrium is at ES.

• Advantage of Slutsky approach: involves observable quantities.

• Led to statistical estimation of societal indifference curves.

• Note: after being compensated in the Slutsky manner is consumer as well off or better off?

Eugene Slutsky, 1880 – 1948. Slutsky was Russian, but his path-breaking paper was published in Italian, a language little spoken in Britain or the United States. The paper was discovered, and Slutsky rescued from obscurity, by Paul Samuelson in the 1930’s.

• Indexation: The process of tying a payment or other value to a price index, increasing the value at the same rate as the price index. (Also called a “Cost of Living Adjustment” or COLA.)– Social Security payments are indexed by the

Consumer Price Index– Personal Exemption in federal income tax is indexed

• Social Security is similar to Slutsky decomposition: if cost of market basket increases 10%, Granny gets 10% more dollars – enough to buy original market basket– But Granny won’t

• Conclusion: indexation makes Granny better off year-to-year