1、Chapter OneThe MarketThe Theory of Economics does notfurnish a body of settled conclusionsimmediately applicable to policy.It isa method rather than a doctrine,anapparatus of the mind,a technique ofthinking which helps its possessor todraw correct conclusions-John Maynard KeynesEconomic ModelinguWha
2、t causes what in economic systems?uAt what level of detail shall we model an economic phenomenon?uWhich variables are determined outside the model(exogenous)and which are to be determined by the model(endogenous)?Modeling the Apartment MarketuHow are apartment rents determined?uSuppose apartments ar
3、e close or distant,but otherwise identicaldistant apartments rents are exogenous and knownmany potential renters and landlordsModeling the Apartment MarketuWho will rent close apartments?uAt what price?uWill the allocation of apartments be desirable in any sense?uHow can we construct an insightful m
4、odel to answer these questions?Economic Modeling AssumptionsuTwo basic postulates: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.Modeling Apartment DemanduDemand:Suppose the mo
5、st any one person is willing to pay to rent a close apartment is$500/month.Thenp=$500 QD=1.uSuppose the price has to drop to$490 before a 2nd person would rent.Thenp=$490 QD=2.Modeling Apartment DemanduThe lower is the rental rate p,the larger is the quantity of close apartments demandedp QD .uThe q
6、uantity demanded vs.price graph is the market demand curve for close apartments.Market Demand Curve for ApartmentspQDModeling Apartment SupplyuSupply:It takes time to build more close apartments so in this short-run the quantity available is fixed(at say 100).Market Supply Curve for ApartmentspQS100
7、Competitive Market Equilibriumu“low”rental price quantity demanded of close apartments exceeds quantity available price will rise.u“high”rental price quantity demanded less than quantity available price will fall.Competitive Market EquilibriumuQuantity demanded=quantity available price will neither
8、rise nor falluso the market is at a competitive equilibrium.Competitive Market EquilibriumpQD,QS100Competitive Market EquilibriumpQD,QSpe100Competitive Market EquilibriumpQD,QSpe100People willing to pay pe for close apartments get closeapartments.Competitive Market EquilibriumpQD,QSpe100People willi
9、ng to pay pe for close apartments get closeapartments.People not willing to pay pe for close apartments get distant apartments.Competitive Market EquilibriumuQ:Who rents the close apartments?uA:Those most willing to pay.uQ:Who rents the distant apartments?uA:Those least willing to pay.uSo the compet
10、itive market allocation is by“willingness-to-pay”.Comparative StaticsuWhat is exogenous in the model?price of distant apartmentsquantity of close apartmentsincomes of potential renters.uWhat happens if these exogenous variables change?Comparative StaticsuSuppose the price of distant apartment rises.
11、uDemand for close apartments increases(rightward shift),causingua higher price for close apartments.Market EquilibriumpQD,QSpe100Market EquilibriumpQD,QSpe100Higher demandMarket EquilibriumpQD,QSpe100Higher demand causes highermarket price;same quantitytraded.Comparative StaticsuSuppose there were m
12、ore close apartments.uSupply is greater,so uthe price for close apartments falls.Market EquilibriumpQD,QSpe100Market EquilibriumpQD,QS100Higher supplypeMarket EquilibriumpQD,QSpe100Higher supply causes alower market price and alarger quantity traded.Comparative StaticsuSuppose potential renters inco
13、mes rise,increasing their willingness-to-pay for close apartments.uDemand rises(upward shift),causinguhigher price for close apartments.Market EquilibriumpQD,QSpe100Market EquilibriumpQD,QSpe100Higher incomes causehigher willingness-to-payMarket EquilibriumpQD,QSpe100Higher incomes causehigher willi
14、ngness-to-pay,higher market price,andthe same quantity traded.Taxation Policy AnalysisuLocal government taxes apartment owners.uWhat happens topricequantity of close apartments rented?uIs any of the tax“passed”to renters?Taxation Policy AnalysisuMarket supply is unaffected.uMarket demand is unaffect
15、ed.uSo the competitive market equilibrium is unaffected by the tax.uPrice and the quantity of close apartments rented are not changed.uLandlords pay all of the tax.Imperfectly Competitive MarketsuAmongst many possibilities are:a monopolistic landlorda perfectly discriminatory monopolistic landlorda
16、competitive market subject to rent control.A Monopolistic LandlorduWhen the landlord sets a rental price p he rents D(p)apartments.uRevenue=pD(p).uRevenue is low if p 0uRevenue is low if p is so high that D(p)0.uAn intermediate value for p maximizes revenue.Monopolistic Market EquilibriumpQDLowprice
17、Low price,high quantitydemanded,low revenue.Monopolistic Market EquilibriumpQDHighpriceHigh price,low quantitydemanded,low revenue.Monopolistic Market EquilibriumpQDMiddlepriceMiddle price,medium quantitydemanded,larger revenue.Monopolistic Market EquilibriumpQD,QSMiddlepriceMiddle price,medium quan
18、titydemanded,larger revenue.Monopolist does not rent all theclose apartments.100Monopolistic Market EquilibriumpQD,QSMiddlepriceMiddle price,medium quantitydemanded,larger revenue.Monopolist does not rent all theclose apartments.100Vacant close apartments.Perfectly Discriminatory Monopolistic Landlo
19、rduImagine the monopolist knew everyones willingness-to-pay.uCharge$500 to the most willing-to-pay,ucharge$490 to the 2nd most willing-to-pay,etc.Discriminatory Monopolistic Market EquilibriumpQD,QS100p1=$5001Discriminatory Monopolistic Market EquilibriumpQD,QS100p1=$500p2=$49012Discriminatory Monop
20、olistic Market EquilibriumpQD,QS100p1=$500p2=$49012p3=$4753Discriminatory Monopolistic Market EquilibriumpQD,QS100p1=$500p2=$49012p3=$4753Discriminatory Monopolistic Market EquilibriumpQD,QS100p1=$500p2=$49012p3=$4753peDiscriminatory monopolistcharges the competitive marketprice to the last renter,a
21、ndrents the competitive quantityof close apartments.Rent ControluLocal government imposes a maximum legal price,pmax 20.Shapes of Budget Constraints-Quantity DiscountsuSuppose p2 is constant at$1 but that p1=$2 for 0 x1 20 and p1=$1 for x120.Then the constraints slope is -2,for 0 x1 20-p1/p2=-1,for
22、x1 20and the constraint isShapes of Budget Constraints with a Quantity Discountm=$1005010020Slope=-2/1=-2 (p1=2,p2=1)Slope=-1/1=-1 (p1=1,p2=1)80 x2x1Shapes of Budget Constraints with a Quantity Discountm=$1005010020Slope=-2/1=-2 (p1=2,p2=1)Slope=-1/1=-1 (p1=1,p2=1)80 x2x1Shapes of Budget Constraints
23、 with a Quantity Discountm=$100501002080 x2x1Budget SetBudget ConstraintShapes of Budget Constraints with a Quantity Penaltyx2x1Budget SetBudget ConstraintShapes of Budget Constraints-One Price NegativeuCommodity 1 is stinky garbage.You are paid$2 per unit to accept it;i.e.p1=-$2.p2=$1.Income,other
24、than from accepting commodity 1,is m=$10.uThen the constraint is -2x1+x2=10 or x2=2x1+10.Shapes of Budget Constraints-One Price Negative10Budget constraints slope is-p1/p2=-(-2)/1=+2x2x1x2=2x1+10Shapes of Budget Constraints-One Price Negative10 x2x1 Budget set is all bundles for which x1 0,x2 0 andx
25、2 2x1+10.More General Choice SetsuChoices are usually constrained by more than a budget;e.g.time constraints and other resources constraints.uA bundle is available only if it meets every constraint.More General Choice SetsFoodOther Stuff10At least 10 units of foodmust be eaten to surviveMore General
26、 Choice SetsFoodOther Stuff10Budget SetMore General Choice SetsFoodOther Stuff10Choice is further restricted by a time constraint.More General Choice SetsMore General Choice SetsFoodOther Stuff10More General Choice SetsFoodOther Stuff10More General Choice SetsFoodOther Stuff10The choice set is thein
27、tersection of all ofthe constraint sets.Chapter ThreePreferences Rationality in Economicsu Behavioral Postulate:A decisionmaker always chooses its most preferred alternative from its set of available alternatives.uSo to model choice we must model decisionmakers preferences.Preference RelationsuCompa
28、ring two different consumption bundles,x and y:strict preference:x is more preferred than is y.weak preference:x is as at least as preferred as is y.indifference:x is exactly as preferred as is y.Preference RelationsuStrict preference,weak preference and indifference are all preference relations.uPa
29、rticularly,they are ordinal relations;i.e.they state only the order in which bundles are preferred.Preference Relationsu denotes strict preference;x y means that bundle x is preferred strictly to bundle y.p pp pPreference Relationsu denotes strict preference;x y means bundle x is preferred strictly
30、to bundle y.u denotes indifference;x y means x and y are equally preferred.p pp pPreference Relationsu denotes strict preference so x y means that bundle x is preferred strictly to bundle y.u denotes indifference;x y means x and y are equally preferred.u denotes weak preference;x y means x is prefer
31、red at least as much as is y.f ff fp pp pPreference Relationsux y and y x imply x y.f ff fPreference Relationsux y and y x imply x y.ux y and(not y x)imply x y.f ff ff ff fp pAssumptions about Preference RelationsuCompleteness:For any two bundles x and y it is always possible to make the statement t
32、hat either x y or y x.f ff fAssumptions about Preference RelationsuReflexivity:Any bundle x is always at least as preferred as itself;i.e.x x.f fAssumptions about Preference RelationsuTransitivity:Ifx is at least as preferred as y,andy is at least as preferred as z,thenx is at least as preferred as
33、z;i.e.x y and y z x z.f ff ff fIndifference CurvesuTake a reference bundle x.The set of all bundles equally preferred to x is the indifference curve containing x;the set of all bundles y x.uSince an indifference“curve”is not always a curve a better name might be an indifference“set”.Indifference Cur
34、vesxIndifference Curves p pp pxyzIndifference Curvesx2x1xAll bundles in I1 arestrictly preferred to all in I2.yzAll bundles in I2 are strictly preferred to all in I3.I1I2I3Indifference Curvesx2x1I(x)xI(x)WP(x),the set of bundles weakly preferred to x.Indifference Curvesx2x1WP(x),the set of bundles w
35、eakly preferred to x.WP(x)includes I(x).xI(x)Indifference Curvesx2x1SP(x),the set of bundles strictly preferred to x,does not include I(x).xI(x)Indifference Curves Cannot IntersectI2Indifference Curves Cannot IntersectI2p pSlopes of Indifference CurvesuWhen more of a commodity is always preferred,th
36、e commodity is a good.uIf every commodity is a good then indifference curves are negatively sloped.Slopes of Indifference CurvesSlopes of Indifference CurvesuIf less of a commodity is always preferred then the commodity is a bad.Slopes of Indifference CurvesExtreme Cases of Indifference Curves;Perfe
37、ct SubstitutesuIf a consumer always regards units of commodities 1 and 2 as equivalent,then the commodities are perfect substitutes and only the total amount of the two commodities in bundles determines their preference rank-order.Extreme Cases of Indifference Curves;Perfect SubstitutesI2I1Extreme C
38、ases of Indifference Curves;Perfect ComplementsuIf a consumer always consumes commodities 1 and 2 in fixed proportion(e.g.one-to-one),then the commodities are perfect complements and only the number of pairs of units of the two commodities determines the preference rank-order of bundles.Extreme Case
39、s of Indifference Curves;Perfect ComplementsI1Each of(5,5),(5,9)and(9,5)contains5 pairs so each is equally preferred.Extreme Cases of Indifference Curves;Perfect ComplementsI2I1Since each of(5,5),(5,9)and(9,5)contains 5 pairs,each is less preferred than the bundle(9,9)which contains 9 pairs.Preferen
40、ces Exhibiting SatiationuA bundle strictly preferred to any other is a satiation point or a bliss point.uWhat do indifference curves look like for preferences exhibiting satiation?Indifference Curves Exhibiting SatiationIndifference Curves Exhibiting SatiationIndifference Curves Exhibiting Satiation
41、Indifference Curves for Discrete CommoditiesuA commodity is infinitely divisible if it can be acquired in any quantity;e.g.water or cheese.uA commodity is discrete if it comes in unit lumps of 1,2,3,and so on;e.g.aircraft,ships and refrigerators.Indifference Curves for Discrete CommoditiesuSuppose c
42、ommodity 2 is an infinitely divisible good(gasoline)while commodity 1 is a discrete good(aircraft).What do indifference“curves”look like?Indifference Curves With a Discrete Good3Well-Behaved PreferencesuA preference relation is“well-behaved”if it ismonotonic and convex.uMonotonicity:More of any comm
43、odity is always preferred(i.e.no satiation and every commodity is a good).Well-Behaved PreferencesuConvexity:Mixtures of bundles are(at least weakly)preferred to the bundles themselves.E.g.,the 50-50 mixture of the bundles x and y is z=(0.5)x+(0.5)y.z is at least as preferred as x or y.Well-Behaved
44、Preferences-Convexity.xyz=x+y2Well-Behaved Preferences-Convexity.xyz=(tx1+(1-t)y1,tx2+(1-t)y2)is preferred to x and y for all 0 t U(x”)x x”U(x)U(4,1)=U(2,2)=4.uCall these numbers utility levels.p pUtility Functions&Indiff.CurvesuAn indifference curve contains equally preferred bundles.uEqual prefere
45、nce same utility level.uTherefore,all bundles in an indifference curve have the same utility level.Utility Functions&Indiff.CurvesuSo the bundles(4,1)and(2,2)are in the indiff.curve with utility level U 4 4uBut the bundle(2,3)is in the indiff.curve with utility level U 6.uOn an indifference curve di
46、agram,this preference information looks as follows:Utility Functions&Indiff.CurvesU 6U 4(2,3)(2,2)(4,1)x1x2p pUtility Functions&Indiff.CurvesuAnother way to visualize this same information is to plot the utility level on a vertical axis.U(2,3)=6U(2,2)=4 U(4,1)=4Utility Functions&Indiff.Curves3D plot
47、 of consumption&utility levels for 3 bundlesx1x2UtilityUtility Functions&Indiff.CurvesuThis 3D visualization of preferences can be made more informative by adding into it the two indifference curves.Utility Functions&Indiff.CurvesU 4 4U 6 6Higher indifferencecurves containmore preferredbundles.Utili
48、tyx2x1Utility Functions&Indiff.CurvesuComparing more bundles will create a larger collection of all indifference curves and a better description of the consumers preferences.Utility Functions&Indiff.CurvesU 6U 4U 2x1x2Utility Functions&Indiff.CurvesuAs before,this can be visualized in 3D by plotting
49、 each indifference curve at the height of its utility index.Utility Functions&Indiff.CurvesU 6U 5U 4U 3U 2U 1x1x2UtilityUtility Functions&Indiff.CurvesuComparing all possible consumption bundles gives the complete collection of the consumers indifference curves,each with its assigned utility level.u
50、This complete collection of indifference curves completely represents the consumers preferences.Utility Functions&Indiff.Curvesx1x2Utility Functions&Indiff.Curvesx1x2Utility Functions&Indiff.Curvesx1x2Utility Functions&Indiff.Curvesx1x2Utility Functions&Indiff.Curvesx1x2Utility Functions&Indiff.Curv
