Lecture 2(b) Lecture 2(b) Rational Choice Rational Choice

and Demandand Demand

Why It Would Probably Be Why It Would Probably Be Ok to Sleep Through This Ok to Sleep Through This

Part of the LecturePart of the Lecture The previous lecture described almost The previous lecture described almost

everything you need to know to everything you need to know to understand demand. You know what understand demand. You know what demand functions are about, what demand demand functions are about, what demand elasticity means and why it matters.elasticity means and why it matters.

What comes next is a formalization of the What comes next is a formalization of the theory of demand that doesn’t really theory of demand that doesn’t really extend your understanding of these things.extend your understanding of these things.

But Why You Should Pay But Why You Should Pay Attention AnyhowAttention Anyhow

The previous lecture did not explicitly consider The previous lecture did not explicitly consider howhow a rational consumer would elect to act. a rational consumer would elect to act. This section will model rational consumer This section will model rational consumer choice—the result of which is the demand for choice—the result of which is the demand for some goods.some goods.

This is worth learning both to confirm the This is worth learning both to confirm the intuitive results from the previous lecture but, intuitive results from the previous lecture but, more importantly, to better understand the more importantly, to better understand the nature of optimization.nature of optimization.

As an added bonus, this same model will be As an added bonus, this same model will be used when we look at production theory (hint: used when we look at production theory (hint: firms will be treated as “consumers” of inputs.)firms will be treated as “consumers” of inputs.)

Two Equivalent Ways to Describe Two Equivalent Ways to Describe What the Consumer Wants to What the Consumer Wants to

AchieveAchieve Objective:Objective:

Maximal happinessMaximal happiness Control variablesControl variables

Quantities of goods Quantities of goods consumedconsumed

ConstraintsConstraints Prices and incomePrices and income

Objective:Objective: Minimize Minimize

ExpenditureExpenditure Control variablesControl variables

Quantities of goods Quantities of goods consumedconsumed

ConstraintsConstraints Achieve a “target Achieve a “target

level” of happinesslevel” of happiness

Modeling Preferences (The really tough part Modeling Preferences (The really tough part of the exercise since we’re actually trying to of the exercise since we’re actually trying to

quantify something as complex as a quantify something as complex as a consumer’s tastes)consumer’s tastes)

Marginal Rate of Substitution:Marginal Rate of Substitution: The maximum The maximum amount of one good you would be willing to give amount of one good you would be willing to give up to get an extra unit of the other goodup to get an extra unit of the other good MRS = change Y/ change X (approximation)MRS = change Y/ change X (approximation) MRS = dY/dX (precise)MRS = dY/dX (precise)

The MRS is Often Best Understood by Imagining The MRS is Often Best Understood by Imagining anan “Indifference Curve”: “Indifference Curve”: Combination of Goods Combination of Goods about Which The Consumer is Indifferentabout Which The Consumer is Indifferent MRS = slope of indifference curve (geometric)MRS = slope of indifference curve (geometric)

Example: Suppose you’ve received five job offers to Example: Suppose you’ve received five job offers to work for companies that offer some combination of two work for companies that offer some combination of two perks: Company Jet (let X = days per month) Golfing at perks: Company Jet (let X = days per month) Golfing at Pebble Beach (let Y = days per month) and that you’re Pebble Beach (let Y = days per month) and that you’re completely indifferent between each point (e.g., you are completely indifferent between each point (e.g., you are as happy with A as with B).as happy with A as with B).

Offer X Y MRS

A 1 10  

B 2 6 4

C 3 3 3

D 4 1 2

E 5 0 1

Optimization Problem Optimization Problem ResolvedResolved

Imagine the points in the previous Imagine the points in the previous example just represent 5 different example just represent 5 different packages, each of which contain packages, each of which contain different quantities of an X and Y.different quantities of an X and Y.

Suppose also that the X good costs Suppose also that the X good costs $5 and the Y good costs $2$5 and the Y good costs $2

Problem: Minimize the cost Problem: Minimize the cost of achieving the level of of achieving the level of

“happiness” generated by “happiness” generated by one of the these fiveone of the these five

Package X Y MRS Expenditure

A 1 10   $ 25.00

B 2 6 4 $ 22.00

C 3 3 3 $ 21.00

D 4 1 2 $ 22.00

E 5 0 1 $ 25.00

Package C Minimizes

Expenditure

The Principle (Margins again):The Principle (Margins again):Think about the ratio of price as the marginal Think about the ratio of price as the marginal

cost of one good expressed in terms of the cost of one good expressed in terms of the other good (e.g., the marginal cost of x is 2 other good (e.g., the marginal cost of x is 2

units of y).units of y).

Package X Y MRS Expenditure

A 1 10   $ 25.00

B 2 6 4 $ 22.00

C 3 3 3 $ 21.00

D 4 1 2 $ 22.00

E 5 0 1 $ 25.00

At these points the value of one more x is greater than the

cost of one more X

At the points the value of one more x is less than the cost of an x

Conclusion: The ideal choice for the Conclusion: The ideal choice for the consumer is one where the price ratio is as consumer is one where the price ratio is as close as possible to the MRSclose as possible to the MRS

Observations:Observations: It is easy to see that, at least most of the time, It is easy to see that, at least most of the time,

the law of demand holds—that is an increase in the law of demand holds—that is an increase in the price of x causes the consumer to buy less x.the price of x causes the consumer to buy less x.

Although there is an interesting exception that we’ll Although there is an interesting exception that we’ll talk about if we have time.talk about if we have time.

The consumer problem is exactly the same as a The consumer problem is exactly the same as a firm trying to decide what mixture of inputs to firm trying to decide what mixture of inputs to buy in order to produce a certain amount of buy in order to produce a certain amount of output. We’ll exploit this similarity in the next output. We’ll exploit this similarity in the next section.section.