1 the market molly w. dahl georgetown university econ 101 – spring 2009

1

The Market

Molly W. DahlGeorgetown UniversityEcon 101 – Spring 2009

2

Economic Modeling

Construct a model Choose simplifications

Solve the model Come up with a prediction Set S = D, etc.

Evaluate the model Was it too simple? Do we learn anything about the real world?

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Modeling the Apartment Market How are apartment rents determined? Suppose

apartments are close or distant, but otherwise identical

distant apartments rents are exogenous (determined outside the model) and known

many potential renters and landlords

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Modeling the Apartment Market

Who will rent close apartments? At what price? Will the allocation of apartments be

desirable in any sense?

How can we construct an insightful model to answer these questions?

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Economic Modeling Assumptions

Two basic assumptions:Rational Choice: Each person tries to choose

the best alternative available to him or her.Equilibrium: Market price adjusts until

quantity demanded equals quantity supplied.

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Modeling Apartment Demand

Demand: Suppose the most any one person is willing to pay to rent a close apartment is $500/month. Then

p = $500 QD = 1. Suppose the price has to drop to $490

before a 2nd person would rent. Thenp = $490 QD = 2.

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Modeling Apartment Demand

The lower is the rental rate p, the larger is the quantity of close apartments demanded

p QD . The quantity demanded vs. price graph is

the market demand curve for close apartments.

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Market Demand Curve for Apartments

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Market Demand Curve for Apartments

p

QD

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Modeling Apartment Supply

Supply: It takes time to build more close apartments so in this short-run the quantity available is fixed (at say 100).

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Market Supply Curve for Apartments

p

QS100

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Competitive Market Equilibrium

“low” rental price quantity demanded of close apartments exceeds quantity available price will rise.

“high” rental price quantity demanded less than quantity available price will fall.

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Competitive Market Equilibrium Quantity demanded = quantity available

price will neither rise nor fallso the market is at a competitive equilibrium.

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Competitive Market Equilibriump

QD,QS

pe

100

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Competitive Market Equilibrium

Q: Who rents the close apartments? A: Those most willing to pay.

Q: Who rents the distant apartments? A: Those least willing to pay.

So the competitive market allocation is by “willingness-to-pay”.

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Comparative Statics

What is exogenous in the model?price of distant apartmentsquantity of close apartments incomes of potential renters.

What happens if these exogenous variables change?

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Comparative Statics

Suppose the price of distant apartment rises.

Demand for close apartments increases (rightward shift), causinga higher price for close apartments.

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Market Equilibriump

QD,QS

pe

100

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Market Equilibriump

QD,QS

pe

100

Higher demand

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Market Equilibriump

QD,QS

pe

100

Higher demand causes highermarket price; same quantitytraded.

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Comparative Statics

Suppose there were more close apartments.

Supply is greater, so the price for close apartments falls.

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Market Equilibriump

QD,QS

pe

100

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Market Equilibriump

QD,QS100

Higher supply

pe

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Market Equilibriump

QD,QS

pe

100

Higher supply causes alower market price and alarger quantity traded.

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Comparative Statics

Suppose potential renters’ incomes rise, increasing their willingness-to-pay for close apartments.

Demand rises (upward shift), causinghigher price for close apartments.

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Market Equilibriump

QD,QS

pe

100

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Market Equilibriump

QD,QS

pe

100

Higher incomes causehigher willingness-to-pay

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Market Equilibriump

QD,QS

pe

100

Higher incomes causehigher willingness-to-pay,higher market price, andthe same quantity traded.

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Market Equilibriump

QD,QS

pe

100

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Budget Constraints

Molly W. DahlGeorgetown UniversityEcon 101 – Spring 2009

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Consumption Choice Sets

A consumption choice set is the collection of all consumption choices available to the consumer.

What constrains consumption choice?Budgetary, time and other resource

limitations.

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Budget Constraints

A consumption bundle containing x1 units of commodity 1, x2 units of commodity 2 and so on up to xn units of commodity n is denoted by the vector (x1, x2, … , xn).

Commodity prices are p1, p2, … , pn.

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Budget Constraints

Q: When is a bundle (x1, … , xn) affordable at prices p1, … , pn?

A: When p1x1 + … + pnxn mwhere m is the consumer’s (disposable) income.

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Budget Constraints

The bundles that are only just affordable form the consumer’s budget constraint. This is the set

{ (x1,…,xn) | x1 0, …, xn and p1x1 + … + pnxn m }.

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Budget Constraints

The consumer’s budget set is the set of all affordable bundles;B(p1, … , pn, m) ={ (x1, … , xn) | x1 0, … , xn 0 and p1x1 + … + pnxn m }

The budget constraint is the upper boundary of the budget set.

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Budget Set and Constraint for Two Commodities

x2

x1

Budget constraint isp1x1 + p2x2 = m.

m /p1

m /p2

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Budget Set and Constraint for Two Commodities

x2

x1

Budget constraint isp1x1 + p2x2 = m.

m /p2

m /p1

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Budget Set and Constraint for Two Commodities

x2

x1

Budget constraint isp1x1 + p2x2 = m.

m /p1

Just affordable

m /p2

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Budget Set and Constraint for Two Commoditiesx2

x1

Budget constraint isp1x1 + p2x2 = m.

m /p1

Just affordable

Not affordable

m /p2

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Budget Set and Constraint for Two Commoditiesx2

x1

Budget constraint isp1x1 + p2x2 = m.

m /p1

Affordable

Just affordable

Not affordable

m /p2

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Budget Set and Constraint for Two Commodities

x2

x1

Budget constraint isp1x1 + p2x2 = m.

m /p1

BudgetSet

the collection of all affordable bundles.

m /p2

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Budget Set and Constraint for Two Commodities

x2

x1

p1x1 + p2x2 = m is x2 = -(p1/p2)x1 + m/p2

so slope is -p1/p2.

m /p1

BudgetSet

m /p2

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Budget Constraints

For n = 2 and x1 on the horizontal axis, the constraint’s slope is -p1/p2. What does it mean?

21

2

12 p

mx

p

px

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Budget Constraints

For n = 2 and x1 on the horizontal axis, the constraint’s slope is -p1/p2. What does it mean?

Increasing x1 by 1 must reduce x2 by p1/p2.

21

2

12 p

mx

p

px

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Budget Constraintsx2

x1

Slope is -p1/p2

+1

-p1/p2

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Budget Constraintsx2

x1

+1

-p1/p2

Opp. cost of an extra unit of commodity 1 is p1/p2 units foregone of commodity 2.

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Budget Constraintsx2

x1

Opp. cost of an extra unit of commodity 1 is p1/p2 units foregone of commodity 2. And the opp. cost of an extra unit of commodity 2 is p2/p1 units foregone of commodity 1.

-p2/p1

+1

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Budget Sets & Constraints; Income and Price Changes

The budget constraint and budget set depend upon prices and income. What happens as prices or income change?

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How do the budget set and budget constraint change as income m

increases?

Originalbudget set

x2

x1

50

Higher income gives more choice

Originalbudget set

New affordable consumptionchoices

x2

x1

Original andnew budgetconstraints areparallel (sameslope).

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How do the budget set and budget constraint change as income m

decreases?

Originalbudget set

x2

x1

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How do the budget set and budget constraint change as income m

decreases?x2

x1

New, smallerbudget set

Consumption bundlesthat are no longeraffordable.Old and new

constraintsare parallel.

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Budget Constraints - Income Changes

Increases in income m shift the constraint outward in a parallel manner, thereby enlarging the budget set and improving choice.

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Budget Constraints - Income Changes

Increases in income m shift the constraint outward in a parallel manner, thereby enlarging the budget set and improving choice.

Decreases in income m shift the constraint inward in a parallel manner, thereby shrinking the budget set and reducing choice.

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Budget Constraints - Income Changes

No original choice is lost and new choices are added when income increases, so higher income cannot make a consumer worse off.

An income decrease may (typically will) make the consumer worse off.

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Budget Constraints - Price Changes

What happens if just one price decreases? Suppose p1 decreases.

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How do the budget set and budget constraint change as p1 decreases from

p1’ to p1”?

Originalbudget set

x2

x1

m/p2

m/p1’ m/p1”

-p1’/p2

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How do the budget set and budget constraint change as p1 decreases from

p1’ to p1”?

Originalbudget set

x2

x1

m/p2

m/p1’ m/p1”

New affordable choices

-p1’/p2

59

How do the budget set and budget constraint change as p1 decreases from

p1’ to p1”?

Originalbudget set

x2

x1

m/p2

m/p1’ m/p1”

New affordable choices

Budget constraint pivots; slope flattens from -p1’/p2 to -p1”/p2

-p1’/p2

-p1”/p2

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Budget Constraints - Price Changes

Reducing the price of one commodity pivots the constraint outward. No old choice is lost and new choices are added, so reducing one price cannot make the consumer worse off.

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Budget Constraints - Price Changes

Similarly, increasing one price pivots the constraint inwards, reduces choice and may (typically will) make the consumer worse off.

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The Food Stamp Program

Food stamps are coupons that can be legally exchanged only for food.

How does a commodity-specific gift such as a food stamp alter a family’s budget constraint?

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The Food Stamp Program

Suppose m = $100, pF = $1 and the price of “other goods” is pG = $1.

The budget constraint is then F + G =100.

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The Food Stamp ProgramG

F100

100

F + G = 100; before stamps.

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The Food Stamp ProgramG

F100

100

F + G = 100: before stamps.

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The Food Stamp ProgramG

F100

100

F + G = 100: before stamps.

Budget set after 40 foodstamps issued.

14040

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The Food Stamp ProgramG

F100

100

F + G = 100: before stamps.

Budget set after 40 foodstamps issued.

140

The family’s budgetset is enlarged.

40

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The Food Stamp Program

What if food stamps can be traded on a black market for $0.50 each?

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The Food Stamp ProgramG

F100

100

F + G = 100: before stamps.

Budget constraint after 40 food stamps issued.

140

120

Budget constraint with black market trading.

40

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The Food Stamp ProgramG

F100

100

F + G = 100: before stamps.

Budget constraint after 40 food stamps issued.

140

120

Black market trading makes the budget set larger again.

40

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Shapes of Budget Constraints

Q: What makes a budget constraint a straight line?

A: A straight line has a constant slope and the constraint is p1x1 + … + pnxn = mso if prices are constants then a constraint is a straight line.

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Shapes of Budget Constraints

But what if prices are not constants? E.g. bulk buying discounts, or price

penalties for buying “too much”. Then constraints will be curved or kinked.

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Shapes of Budget Constraints - Quantity Discounts

Suppose p2 is constant at $1 but that p1=$2 for 0 x1 20 and p1=$1 for x1>20.

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Shapes of Budget Constraints - Quantity Discounts

Suppose p2 is constant at $1 but that p1=$2 for 0 x1 20 and p1=$1 for x1>20. Then the constraint’s slope is - 2, for 0 x1 20-p1/p2 = - 1, for x1 > 20and the constraint is

{

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Shapes of Budget Constraints with a Quantity Discount

m = $100

50

100

20

Slope = - 2 / 1 = - 2 (p1=2, p2=1)

Slope = - 1/ 1 = - 1 (p1=1, p2=1)

80

x2

x1

76

Shapes of Budget Constraints with a Quantity Discount

m = $100

50

100

20

Slope = - 2 / 1 = - 2 (p1=2, p2=1)

Slope = - 1/ 1 = - 1 (p1=1, p2=1)

80

x2

x1

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Shapes of Budget Constraints with a Quantity Discount

m = $100

50

100

20 80

x2

x1

Budget Set

Budget Constraint

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Shapes of Budget Constraints with a Quantity Penalty

x2

x1

Budget Set

Budget Constraint