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

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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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3 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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4 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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5 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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6 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 Q D = 1. Suppose the price has to drop to $490 before a 2nd person would rent. Then p = $490 Q D = 2.

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7 Modeling Apartment Demand The lower is the rental rate p, the larger is the quantity of close apartments demanded p Q D. The quantity demanded vs. price graph is the market demand curve for close apartments.

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8 Market Demand Curve for Apartments

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9 p QDQD

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10 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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11 Market Supply Curve for Apartments p QSQS 100

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12 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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13 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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14 Competitive Market Equilibrium p Q D,Q S pepe 100

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15 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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16 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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17 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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18 Market Equilibrium p Q D,Q S pepe 100

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19 Market Equilibrium p Q D,Q S pepe 100 Higher demand

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20 Market Equilibrium p Q D,Q S pepe 100 Higher demand causes higher market price; same quantity traded.

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21 Comparative Statics Suppose there were more close apartments. Supply is greater, so the price for close apartments falls.

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22 Market Equilibrium p Q D,Q S pepe 100

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23 Market Equilibrium p Q D,Q S 100 Higher supply pepe

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24 Market Equilibrium p Q D,Q S pepe 100 Higher supply causes a lower market price and a larger quantity traded.

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25 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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26 Market Equilibrium p Q D,Q S pepe 100

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27 Market Equilibrium p Q D,Q S pepe 100 Higher incomes cause higher willingness-to-pay

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28 Market Equilibrium p Q D,Q S pepe 100 Higher incomes cause higher willingness-to-pay, higher market price, and the same quantity traded.

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29 Market Equilibrium p Q D,Q S pepe 100

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30 Budget Constraints Molly W. Dahl Georgetown University Econ 101 – Spring 2009

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31 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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32 Budget Constraints A consumption bundle containing x 1 units of commodity 1, x 2 units of commodity 2 and so on up to x n units of commodity n is denoted by the vector (x 1, x 2, …, x n ). Commodity prices are p 1, p 2, …, p n.

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33 Budget Constraints Q: When is a bundle (x 1, …, x n ) affordable at prices p 1, …, p n ? A: When p 1 x 1 + … + p n x n m where m is the consumers (disposable) income.

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34 Budget Constraints The bundles that are only just affordable form the consumers budget constraint. This is the set { (x 1,…,x n ) | x 1 0, …, x n and p 1 x 1 + … + p n x n m }.

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35 Budget Constraints The consumers budget set is the set of all affordable bundles; B(p 1, …, p n, m) = { (x 1, …, x n ) | x 1 0, …, x n 0 and p 1 x 1 + … + p n x n m } The budget constraint is the upper boundary of the budget set.

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36 Budget Set and Constraint for Two Commodities x2x2 x1x1 Budget constraint is p 1 x 1 + p 2 x 2 = m. m /p 1 m /p 2

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37 Budget Set and Constraint for Two Commodities x2x2 x1x1 Budget constraint is p 1 x 1 + p 2 x 2 = m. m /p 2 m /p 1

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38 Budget Set and Constraint for Two Commodities x2x2 x1x1 Budget constraint is p 1 x 1 + p 2 x 2 = m. m /p 1 Just affordable m /p 2

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39 Budget Set and Constraint for Two Commodities x2x2 x1x1 Budget constraint is p 1 x 1 + p 2 x 2 = m. m /p 1 Just affordable Not affordable m /p 2

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40 Budget Set and Constraint for Two Commodities x2x2 x1x1 Budget constraint is p 1 x 1 + p 2 x 2 = m. m /p 1 Affordable Just affordable Not affordable m /p 2

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41 Budget Set and Constraint for Two Commodities x2x2 x1x1 Budget constraint is p 1 x 1 + p 2 x 2 = m. m /p 1 Budget Set the collection of all affordable bundles. m /p 2

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42 Budget Set and Constraint for Two Commodities x2x2 x1x1 p 1 x 1 + p 2 x 2 = m is x 2 = -(p 1 /p 2 )x 1 + m/p 2 so slope is -p 1 /p 2. m /p 1 Budget Set m /p 2

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43 Budget Constraints For n = 2 and x 1 on the horizontal axis, the constraints slope is -p 1 /p 2. What does it mean?

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44 Budget Constraints For n = 2 and x 1 on the horizontal axis, the constraints slope is -p 1 /p 2. What does it mean? Increasing x 1 by 1 must reduce x 2 by p 1 /p 2.

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45 Budget Constraints x2x2 x1x1 Slope is -p 1 /p p 1 /p 2

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46 Budget Constraints x2x2 x1x1 +1 -p 1 /p 2 Opp. cost of an extra unit of commodity 1 is p 1 /p 2 units foregone of commodity 2.

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47 Budget Constraints x2x2 x1x1 Opp. cost of an extra unit of commodity 1 is p 1 /p 2 units foregone of commodity 2. And the opp. cost of an extra unit of commodity 2 is p 2 /p 1 units foregone of commodity 1. -p 2 /p 1 +1

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48 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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49 How do the budget set and budget constraint change as income m increases? Original budget set x2x2 x1x1

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50 Higher income gives more choice Original budget set New affordable consumption choices x2x2 x1x1 Original and new budget constraints are parallel (same slope).

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51 How do the budget set and budget constraint change as income m decreases? Original budget set x2x2 x1x1

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52 How do the budget set and budget constraint change as income m decreases? x2x2 x1x1 New, smaller budget set Consumption bundles that are no longer affordable. Old and new constraints are parallel.

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53 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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54 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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55 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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56 Budget Constraints - Price Changes What happens if just one price decreases? Suppose p 1 decreases.

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57 How do the budget set and budget constraint change as p 1 decreases from p 1 to p 1? Original budget set x2x2 x1x1 m/p 2 m/p 1 -p 1 /p 2

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58 How do the budget set and budget constraint change as p 1 decreases from p 1 to p 1? Original budget set x2x2 x1x1 m/p 2 m/p 1 New affordable choices -p 1 /p 2

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59 How do the budget set and budget constraint change as p 1 decreases from p 1 to p 1? Original budget set x2x2 x1x1 m/p 2 m/p 1 New affordable choices Budget constraint pivots; slope flattens from -p 1 /p 2 to -p 1 /p 2

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60 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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61 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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62 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 familys budget constraint?

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63 The Food Stamp Program Suppose m = $100, p F = $1 and the price of other goods is p G = $1. The budget constraint is then F + G =100.

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

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

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66 The Food Stamp Program G F 100 F + G = 100: before stamps. Budget set after 40 food stamps issued

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67 The Food Stamp Program G F 100 F + G = 100: before stamps. Budget set after 40 food stamps issued. 140 The familys budget set is enlarged. 40

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68 The Food Stamp Program What if food stamps can be traded on a black market for $0.50 each?

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69 The Food Stamp Program G F 100 F + G = 100: before stamps. Budget constraint after 40 food stamps issued Budget constraint with black market trading. 40

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70 The Food Stamp Program G F 100 F + G = 100: before stamps. Budget constraint after 40 food stamps issued Black market trading makes the budget set larger again. 40

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71 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 p 1 x 1 + … + p n x n = m so if prices are constants then a constraint is a straight line.

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72 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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73 Shapes of Budget Constraints - Quantity Discounts Suppose p 2 is constant at $1 but that p 1 =$2 for 0 x 1 20 and p 1 =$1 for x 1 >20.

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74 Shapes of Budget Constraints - Quantity Discounts Suppose p 2 is constant at $1 but that p 1 =$2 for 0 x 1 20 and p 1 =$1 for x 1 >20. Then the constraints slope is - 2, for 0 x p 1 /p 2 = - 1, for x 1 > 20 and the constraint is {

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75 Shapes of Budget Constraints with a Quantity Discount m = $ Slope = - 2 / 1 = - 2 (p 1 =2, p 2 =1) Slope = - 1/ 1 = - 1 (p 1 =1, p 2 =1) 80 x2x2 x1x1

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76 Shapes of Budget Constraints with a Quantity Discount m = $ Slope = - 2 / 1 = - 2 (p 1 =2, p 2 =1) Slope = - 1/ 1 = - 1 (p 1 =1, p 2 =1) 80 x2x2 x1x1

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77 Shapes of Budget Constraints with a Quantity Discount m = $ x2x2 x1x1 Budget Set Budget Constraint

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78 Shapes of Budget Constraints with a Quantity Penalty x2x2 x1x1 Budget Set Budget Constraint

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