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**Molly W. Dahl Georgetown University Econ 101 – Spring 2009**

The Market Molly W. Dahl Georgetown University Econ 101 – Spring 2009

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**Economic Modeling Construct a model Solve the model Evaluate the 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. Then p = $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**

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**

100 QS

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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 fall so the market is at a competitive equilibrium.

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**Competitive Market Equilibrium**

100 QD,QS

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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 apartments quantity 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), causing a higher price for close apartments.

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Market Equilibrium p pe 100 QD,QS

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Market Equilibrium p Higher demand pe 100 QD,QS

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Market Equilibrium p Higher demand causes higher market price; same quantity traded. pe 100 QD,QS

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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 Equilibrium p pe 100 QD,QS

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Market Equilibrium p Higher supply pe 100 QD,QS

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Market Equilibrium p Higher supply causes a lower market price and a larger quantity traded. pe 100 QD,QS

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Comparative Statics Suppose potential renters’ incomes rise, increasing their willingness-to-pay for close apartments. Demand rises (upward shift), causing higher price for close apartments.

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Market Equilibrium p pe 100 QD,QS

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**Market Equilibrium p Higher incomes cause higher willingness-to-pay pe**

100 QD,QS

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Market Equilibrium p Higher incomes cause higher willingness-to-pay, higher market price, and the same quantity traded. pe 100 QD,QS

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Market Equilibrium p pe 100 QD,QS

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**Molly W. Dahl Georgetown University Econ 101 – Spring 2009**

Budget Constraints Molly W. Dahl Georgetown University Econ 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 £ m where 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 ³ 0, …, xn ³ 0 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 ³ 0, … , xn ³ 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 Budget constraint is p1x1 + p2x2 = m. m /p2 m /p1 x1

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**Budget Set and Constraint for Two Commodities**

x2 Budget constraint is p1x1 + p2x2 = m. m /p2 m /p1 x1

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**Budget Set and Constraint for Two Commodities**

x2 Budget constraint is p1x1 + p2x2 = m. m /p2 Just affordable m /p1 x1

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**Budget Set and Constraint for Two Commodities**

x2 Budget constraint is p1x1 + p2x2 = m. m /p2 Not affordable Just affordable m /p1 x1

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**Budget Set and Constraint for Two Commodities**

x2 Budget constraint is p1x1 + p2x2 = m. m /p2 Not affordable Just affordable Affordable m /p1 x1

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**Budget Set and Constraint for Two Commodities**

x2 Budget constraint is p1x1 + p2x2 = m. m /p2 the collection of all affordable bundles. Budget Set m /p1 x1

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**Budget Set and Constraint for Two Commodities**

x2 p1x1 + p2x2 = m is x2 = -(p1/p2)x1 + m/p2 so slope is -p1/p2. m /p2 Budget Set m /p1 x1

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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?

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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.

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Budget Constraints x2 Slope is -p1/p2 -p1/p2 +1 x1

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Budget Constraints x2 Opp. cost of an extra unit of commodity 1 is p1/p2 units foregone of commodity 2. -p1/p2 +1 x1

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Budget Constraints x2 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. +1 -p2/p1 x1

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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?**

x2 Original budget set x1

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**Higher income gives more choice**

x2 New affordable consumption choices Original and new budget constraints are parallel (same slope). Original budget set x1

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**How do the budget set and budget constraint change as income m decreases?**

x2 Original budget set x1

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**How do the budget set and budget constraint change as income m decreases?**

x2 Consumption bundles that are no longer affordable. Old and new constraints are parallel. New, smaller budget set x1

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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”?**

x2 m/p2 -p1’/p2 Original budget set m/p1’ m/p1” x1

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**How do the budget set and budget constraint change as p1 decreases from p1’ to p1”?**

x2 m/p2 New affordable choices -p1’/p2 Original budget set m/p1’ m/p1” x1

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**How do the budget set and budget constraint change as p1 decreases from p1’ to p1”?**

x2 m/p2 New affordable choices Budget constraint pivots; slope flattens from -p1’/p2 to -p1”/p2 -p1’/p2 Original budget set -p1”/p2 m/p1’ m/p1” x1

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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 Program G F + G = 100; before stamps. 100 F 100

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The Food Stamp Program G F + G = 100: before stamps. 100 F 100

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**The Food Stamp Program G F + G = 100: before stamps. 100**

Budget set after 40 food stamps issued. F 40 100 140

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**The Food Stamp Program G F + G = 100: before stamps. 100**

Budget set after 40 food stamps issued. The family’s budget set is enlarged. F 40 100 140

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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 Program G F + G = 100: before stamps. 120**

Budget constraint after food stamps issued. 100 Budget constraint with black market trading. F 40 100 140

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**The Food Stamp Program G F + G = 100: before stamps. 120**

Budget constraint after food stamps issued. 100 Black market trading makes the budget set larger again. F 40 100 140

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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 = m so 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 , for 0 £ x1 £ 20 -p1/p2 = , for x1 > 20 and the constraint is {

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**Shapes of Budget Constraints with a Quantity Discount**

x2 m = $100 Slope = - 2 / 1 = (p1=2, p2=1) 100 Slope = - 1/ 1 = (p1=1, p2=1) x1 20 50 80

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**Shapes of Budget Constraints with a Quantity Discount**

x2 m = $100 Slope = - 2 / 1 = (p1=2, p2=1) 100 Slope = - 1/ 1 = (p1=1, p2=1) x1 20 50 80

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**Shapes of Budget Constraints with a Quantity Discount**

x2 m = $100 100 Budget Constraint Budget Set x1 20 50 80

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**Shapes of Budget Constraints with a Quantity Penalty**

x2 Budget Constraint Budget Set x1

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