1、Chapter OneThe Market - Appreciating Economic ModelingThe Purpose of this ChapteruTo begin to understand the art of building an economic modeluTo begin to understand three basic elements of modeling in economics:PurposeSimplification through assumptionsValue judgmentThe Purpose of an Economic Modelu
2、 The purpose of an economic model is to help provide precise insights (精精确的洞察力）确的洞察力）on a specific economic phenomenon.uThus:Different phenomena needs different model;Simplification by assumption is necessaryAn Illustration: Modeling the Apartment MarketuPurpose: How are apartment rents determined?
3、Are rents “desirable”?uSimplifying assumptions: apartments are close or distant, but otherwise identicaldistant apartments rents are exogenous (外生变量）外生变量） and knownmany potential renters and landlordsTwo Very Common Modeling AssumptionsRational Choice (理性选择）理性选择）: Each person tries to choose the bes
4、t alternative available to him or her.Equilibrium （均衡）均衡）: economic agents interact with each other, resulting in an equilibrium, in which each person reaches an optimal decision given others decisions.Modeling Apartment DemanduDemand: Suppose the most any one person is willing to pay to rent a clos
5、e 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 quantity demanded vs. price graph is t
6、he 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 ApartmentspQS100Competitive Market Equilibrium(竞争性
7、市场均衡）uQuantity demanded = quantity available price will neither rise nor falluso the market is at a competitive equilibrium.Competitive Market EquilibriumpQD,QSpe100People willing to pay pe for close apartments get closeapartments.People not willing to pay pe for close apartments get distant apartme
8、nts.Comparative Statics（静态比较分析）uWhat is exogenous in the model? price of distant apartments quantity of close apartments incomes of potential renters.uWhat happens if these exogenous variables change?uNote： We are not analyzing the transition process or dynamic process.Comparative StaticsuSuppose th
9、e price of distant apartment rises.uDemand for close apartments increases (rightward shift), causinguA higher price for close apartments.Market EquilibriumpQD,QSpe100Higher demand causes highermarket price; same quantitytraded.More Comparative Statics (Do Them Yourself)uSuppose there were more close
10、 apartments.uOr, renters income rises;Elaboration of the Basic Model: 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 i
11、s unaffected.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 MarketCase 1： A Monopolistic LandlorduLandlord sets a rental price p he rents D(p) apartments.uRevenue
12、 = pD(p).uHe chooses p to maximizes p D(p), subject to D(p) = S (total number of apartments in his hands)uTypically, his optimal p is such thatD(p) S, that is, there are vacant apartments.Monopolistic Market EquilibriumpQD,QSMiddlepriceMiddle price, medium quantitydemanded, larger revenue.Monopolist
13、 does not rent all theclose apartments.100Vacant close apartments.Imperfectly Competitive Market Case 2： Perfectly Discriminatory Monopolistic LandlorduImagine the monopolist knew willingness-to-pay of everybody,uCharge $500 to the most willing-to-pay,ucharge $490 to the 2nd most willing-to-pay, etc
14、.Discriminatory Monopolistic Market EquilibriumpQD,QS100p1 =$5001Discriminatory Monopolistic Market EquilibriumpQD,QS100p1 =$500p2 =$49012Discriminatory Monopolistic Market EquilibriumpQD,QS100p1 =$500p2 =$49012p3 =$4753Discriminatory Monopolistic Market EquilibriumpQD,QS100p1 =$500p2 =$49012p3 =$47
15、53Discriminatory Monopolistic Market EquilibriumpQD,QS100p1 =$500p2 =$49012p3 =$4753peDiscriminatory monopolistcharges the competitive marketprice to the last renter, andrents the competitive quantityof close apartments.Rent Control(房租管制）uLocal government imposes a maximum legal price, pmax 20.Shape
16、s 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 x1 20and the constraint isShapes of Budget Constraints with a Quantity Discountm = $1005010020Slope = - 2 / 1 = - 2
17、 (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 with a Quantity Discountm = $100501002080 x2x1Budget SetBudget ConstraintSha
18、pes 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 than from accepting commodity 1, is m = $10.uThen the constra
19、int 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 andx2 2x1 + 10.More General Choice SetsuC
20、hoices 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 Choice SetsFoodOther Stuff10Budg
21、et 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 theintersection of all ofthe constrain
22、t sets.SummaryChapter ThreePreferences 消费者偏好消费者偏好Where Are We in the Course?u We are studying the 1st of the three blocks of microeconomics: Consumer behavior, production theory, and market equilibriumuWithin the 1st block, we are working on the 2nd of the three components: choice set, preference, a
23、nd consumer demandWhat Do We Mean by Preference? (偏好)u It refers to the ordered relationship among alternative choices given by an economic agent.u In most economic literature, consumer preference is treated as the ultimate exogenous element.Preference RelationsuComparing two different consumption b
24、undles, 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.Notationsu denotes strict preference; u denotes indifference; u denotes weak preference;p pf fPreference Relationsux y and y x impl
25、y 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 that either x y or y x.f ff fAssumptions about Preference RelationsuReflexivity: Any bundle x is always at least as preferred
26、 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 z; i.e. x y and y z x z.f ff ff fIndifference Curves无差异曲线无差异曲线 (或或,无差异集无差异集)uTake a reference bundle x. The set of all
27、 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 CurvesxIndifference Curves p pp pxyzIndifference Curvesx2x1xAll bundles in I1 arestrictly
28、preferred to all in I2.yzAll bundles in I2 are strictly preferred to all in I3.I1I2I3Indifference Curvesx2x1WP(x), the set of bundles weakly 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 Curv
29、es Cannot Intersect ! (不相交!)I2Indifference Curves Cannot IntersectI2p pSlopes of Indifference CurvesuWhen more of a commodity is always preferred, the commodity is a good.uIf every commodity is a good then indifference curves are negatively sloped.Slopes of Indifference CurvesSlopes of Indifference
30、CurvesuIf less of a commodity is always preferred then the commodity is a bad.Slopes of Indifference CurvesExtreme Cases of Indifference Curves; Perfect SubstitutesuIf a consumer always regards units of commodities 1 and 2 as equivalent, then the commodities are perfect substitutes and only the sum
31、of the two commodities in bundles determines their preference rank-order. Extreme Cases of Indifference Curves; Perfect SubstitutesI2I1Extreme Cases of Indifference Curves; Perfect ComplementsuIf a consumer always consumes commodities 1 and 2 in fixed proportion (e.g. one-to-one), then the commoditi
32、es are perfect complements and only the number of pairs of units of the two commodities determines the preference rank-order of bundles. 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) wh
33、ich contains 9 pairs. Preferences 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 for Discrete CommoditiesuA com
34、modity 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 Commodities (study this yourself)uSuppose commodity 2 is an inf
35、initely divisible good (gasoline) while commodity 1 is a discrete good (aircraft). What do indifference “curves” look like?Indifference Curves With a Discrete Good (study this yourself)3Well-Behaved PreferencesuA preference relation is “well-behaved” if it ismonotonic and convex.uMonotonicity: More
36、of any commodity is always preferred (i.e. no satiation and every commodity is a good).Well-Behaved PreferencesuConvexity (凸性凸性): 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 pref
37、erred as x or y. Well-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) 0 and b 0 is called a Cobb-Douglas utility function.uE.g. U(x1,x2) = x11/2 x21/2 (a = b = 1/2) V(x1,x2) = x1 x23 (a = 1, b = 3)Cobb-Douglas Indifference Curvesx2x1
38、All curves are hyperbolic,asymptoting to, but nevertouching any axis.Marginal UtilitiesuMarginal means “incremental”.uThe marginal utility of commodity i is the rate-of-change of total utility as the quantity of commodity i consumed changes; i.e. MUUxii Marginal Utilities and Marginal Rates-of-Subst
39、itutionuThe general equation for an indifference curve is U(x1,x2) k, a constant.Totally differentiating this identity gives UxdxUxdx11220 Marginal Utilities and Marginal Rates-of-Substitution UxdxUxdx11220 UxdxUxdx2211 rearranged isMarginal Utilities and Marginal Rates-of-Substitution UxdxUxdx2211
40、rearranged isAnddxdxUxUx2112 /.This is the MRS.Marg. Rates-of-Substitution for Quasi-linear Utility FunctionsuA quasi-linear utility function is of the form U(x1,x2) = f(x1) + x2.so Uxfx11 () Ux21 MRSdxdxUxUxfx 21121 /().Marg. Rates-of-Substitution for Quasi-linear Utility FunctionsuMRS = - f (x1) d
41、oes not depend upon x2 so the slope of indifference curves for a quasi-linear utility function is constant along any line for which x1 is constant. What does that make the indifference map for a quasi-linear utility function look like? Marg. Rates-of-Substitution for Quasi-linear Utility Functionsx2
42、x1Each curve is a vertically shifted copy of the others.MRS is a constantalong any line for which x1 isconstant. MRS =- f(x1)MRS = -f(x1”)x1x1”Monotonic Transformations & Marginal Rates-of-SubstitutionuMore generally, if V = f(U) where f is a strictly increasing function, thenMRSVxVxfUUxfUUx /()/()/
43、1212 UxUx/.12So MRS is unchanged by a positivemonotonic transformation.The Key to this Chapteru The indifference curve of a consumer preference can be represented by a utility function based equation:U(x1, x2) = k, a constant.Chapter FiveChoice消费者最优选择消费者最优选择Where Are We Doing in This Chapter?uAfter
44、modeling a consumers choice set and his preference (represented by utility functions), we now put them together and model how he/she makes optimal choice.uIn mathematical terms, this is a constrained maximization problem;uIn economics, this is a rational choice problem.Rational Constrained ChoiceAff
45、ordablebundlesx1x2More preferredbundlesRational Constrained ChoiceuThe most preferred affordable bundle is called the consumers ORDINARY DEMAND at the given prices and budget.uOrdinary demands will be denoted byx1*(p1,p2,m) and x2*(p1,p2,m).Rational Constrained ChoiceuWhen x1* 0 and x2* 0 the demand
46、ed bundle is INTERIOR.uIf buying (x1*,x2*) costs $m then the budget is exhausted. Rational Constrained Choicex1x2x1*x2*(x1*,x2*) is interior.(a) (x1*,x2*) exhausts thebudget; p1x1* + p2x2* = m.Rational Constrained Choicex1x2x1*x2*(x1*,x2*) is interior .(b) The slope of the indiff.curve at (x1*,x2*)
47、equals the slope of the budget constraint.Rational Constrained Choiceu(x1*,x2*) satisfies two conditions:u (a) the budget is exhausted; p1x1* + p2x2* = mu (b) the slope of the budget constraint, -p1/p2, and the slope of the indifference curve containing (x1*,x2*) are equal at (x1*,x2*).Computing Ord
48、inary Demands - a Cobb-Douglas Example.uSuppose that the consumer has Cobb-Douglas preferences.U xxx xa b(,)1212 Computing Ordinary Demands - a Cobb-Douglas Example.uSuppose that the consumer has Cobb-Douglas preferences.uThenU xxx xa b(,)1212 MUUxaxxab11112 MUUxbx xa b22121 Computing Ordinary Deman
49、ds - a Cobb-Douglas Example.uSo the MRS isMRSdxdxUxUxaxxbx xaxbxaba b 211211212121 /.Computing Ordinary Demands - a Cobb-Douglas Example.uSo the MRS isuAt (x1*,x2*), MRS = -p1/p2 soMRSdxdxUxUxaxxbx xaxbxaba b 211211212121 /.*22*11xpxpba(A)Computing Ordinary Demands - a Cobb-Douglas Example.u(x1*,x2*
50、) also exhausts the budget sop xp xm1 12 2*. (B)Computing Ordinary Demands - a Cobb-Douglas Example.So we have discovered that the mostpreferred affordable bundle for a consumerwith Cobb-Douglas preferencesU xxx xa b(,)1212 is(,)(),().*()xxamab pbmab p1212 Computing Ordinary Demands - a Cobb-Douglas
