1、Chapter One The Market The Theory of Economics does not furnish a body of settled conclusions immediately applicable to policy. It is a method rather than a doctrine, an apparatus of the mind, a technique of thinking which helps its possessor to draw correct conclusions - John Maynard Keynes Economi
2、c Modeling uWhat 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 Market uHow are apartment rents determined?
3、 uSuppose apartments are close or distant, but otherwise identical distant apartments rents are exogenous and known many potential renters and landlords Modeling the Apartment Market uWho will rent close apartments? uAt what price? uWill the allocation of apartments be desirable in any sense? uHow c
4、an we construct an insightful model to answer these questions? Economic Modeling Assumptions uTwo 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
5、Apartment Demand uDemand: Suppose the most 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 Demand uThe lower is the rental rate p, the larger
6、is the quantity of close apartments demanded p QD . uThe quantity demanded vs. price graph is the market demand curve for close apartments. Market Demand Curve for Apartments p QD Modeling Apartment Supply uSupply: It takes time to build more close apartments so in this short-run the quantity availa
7、ble is fixed (at say 100). Market Supply Curve for Apartments p QS100 Competitive Market Equilibrium u“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
8、Market Equilibrium uQuantity demanded = quantity available price will neither rise nor fall uso the market is at a competitive equilibrium. Competitive Market Equilibrium p QD,QS100 Competitive Market Equilibrium p QD,QS pe 100 Competitive Market Equilibrium p QD,QS pe 100 People willing to pay pe f
9、or close apartments get close apartments. Competitive Market Equilibrium p QD,QS pe 100 People willing to pay pe for close apartments get close apartments. People not willing to pay pe for close apartments get distant apartments. Competitive Market Equilibrium uQ: Who rents the close apartments? uA:
10、 Those most willing to pay. uQ: Who rents the distant apartments? uA: Those least willing to pay. uSo the competitive market allocation is by “willingness-to-pay”. Comparative Statics uWhat is exogenous in the model? price of distant apartments quantity of close apartments incomes of potential rente
11、rs. uWhat happens if these exogenous variables change? Comparative Statics uSuppose the price of distant apartment rises. uDemand for close apartments increases (rightward shift), causing ua higher price for close apartments. Market Equilibrium p QD,QS pe 100 Market Equilibrium p QD,QS pe 100 Higher
12、 demand Market Equilibrium p QD,QS pe 100 Higher demand causes higher market price; same quantity traded. Comparative Statics uSuppose there were more close apartments. uSupply is greater, so uthe price for close apartments falls. Market Equilibrium p QD,QS pe 100 Market Equilibrium p QD,QS100 Highe
13、r supply pe Market Equilibrium p QD,QS pe 100 Higher supply causes a lower market price and a larger quantity traded. Comparative Statics uSuppose potential renters incomes rise, increasing their willingness-to- pay for close apartments. uDemand rises (upward shift), causing uhigher price for close
14、apartments. Market Equilibrium p QD,QS pe 100 Market Equilibrium p QD,QS pe 100 Higher incomes cause higher willingness-to-pay Market Equilibrium p QD,QS pe 100 Higher incomes cause higher willingness-to-pay, higher market price, and the same quantity traded. Taxation Policy Analysis uLocal governme
15、nt taxes apartment owners. uWhat happens to price quantity of close apartments rented? uIs any of the tax “passed” to renters? Taxation Policy Analysis uMarket supply is unaffected. uMarket demand is unaffected. uSo the competitive market equilibrium is unaffected by the tax. uPrice and the quantity
16、 of close apartments rented are not changed. uLandlords pay all of the tax. Imperfectly Competitive Markets uAmongst many possibilities are: a monopolistic landlord a perfectly discriminatory monopolistic landlord a competitive market subject to rent control. A Monopolistic Landlord uWhen the landlo
17、rd sets a rental price p he rents D(p) apartments. uRevenue = pD(p). uRevenue is low if p 0 uRevenue is low if p is so high that D(p) 0. uAn intermediate value for p maximizes revenue. Monopolistic Market Equilibrium p QD Low price Low price, high quantity demanded, low revenue. Monopolistic Market
18、Equilibrium p QD High price High price, low quantity demanded, low revenue. Monopolistic Market Equilibrium p QD Middle price Middle price, medium quantity demanded, larger revenue. Monopolistic Market Equilibrium p QD,QS Middle price Middle price, medium quantity demanded, larger revenue. Monopolis
19、t does not rent all the close apartments. 100 Monopolistic Market Equilibrium p QD,QS Middle price Middle price, medium quantity demanded, larger revenue. Monopolist does not rent all the close apartments. 100 Vacant close apartments. Perfectly Discriminatory Monopolistic Landlord uImagine the monop
20、olist 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 Equilibrium p QD,QS100 p1 =$500 1 Discriminatory Monopolistic Market Equilibrium p QD,QS100 p1 =$500 p2 =$490 12 Discriminatory Mon
21、opolistic Market Equilibrium p QD,QS100 p1 =$500 p2 =$490 12 p3 =$475 3 Discriminatory Monopolistic Market Equilibrium p QD,QS100 p1 =$500 p2 =$490 12 p3 =$475 3 Discriminatory Monopolistic Market Equilibrium p QD,QS100 p1 =$500 p2 =$490 12 p3 =$475 3 pe Discriminatory monopolist charges the competi
22、tive market price to the last renter, and rents the competitive quantity of close apartments. Rent Control uLocal government imposes a maximum legal price, pmax 20. Shapes of Budget Constraints - Quantity Discounts uSuppose p2 is constant at $1 but that p1=$2 for 0 x1 20 and p1=$1 for x120. Then the
23、 constraints slope is - 2, for 0 x1 20 -p1/p2 = - 1, for x1 20 and the constraint is 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 Shapes of Budget Constraints with a Quantity Discount m = $100 5
24、0 100 20 Slope = - 2 / 1 = - 2 (p1=2, p2=1) Slope = - 1/ 1 = - 1 (p1=1, p2=1) 80 x2 x1 Shapes of Budget Constraints with a Quantity Discount m = $100 50 100 20 80 x2 x1 Budget Set Budget Constraint Shapes of Budget Constraints with a Quantity Penalty x2 x1 Budget Set Budget Constraint Shapes of Budg
25、et Constraints - One Price Negative uCommodity 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 constraint is - 2x1 + x2 = 10 or x2 = 2x1 + 10. Shapes of Budget Constraints - One Price Negative 1
26、0 Budget constraints slope is -p1/p2 = -(-2)/1 = +2 x2 x1 x2 = 2x1 + 10 Shapes of Budget Constraints - One Price Negative 10 x2 x1 Budget set is all bundles for which x1 0, x2 0 and x2 2x1 + 10. More General Choice Sets uChoices are usually constrained by more than a budget; e.g. time constraints an
27、d other resources constraints. uA bundle is available only if it meets every constraint. More General Choice Sets Food Other Stuff 10 At least 10 units of food must be eaten to survive More General Choice Sets Food Other Stuff 10 Budget Set More General Choice Sets Food Other Stuff 10 Choice is furt
28、her restricted by a time constraint. More General Choice Sets More General Choice Sets Food Other Stuff 10 More General Choice Sets Food Other Stuff 10 More General Choice Sets Food Other Stuff 10 The choice set is the intersection of all of the constraint sets. Chapter Three Preferences Rationality
29、 in Economics u 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 Relations uComparing two different consumption bundles, x and y: strict preference: x i
30、s 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 Relations uStrict preference, weak preference and indifference are all preference relations. uParticularly, they are ordinal relations; i.e. they state only
31、 the order in which bundles are preferred. Preference Relations u denotes strict preference; x y means that bundle x is preferred strictly to bundle y. p p p p Preference Relations u denotes strict preference; x y means bundle x is preferred strictly to bundle y. u denotes indifference; x y means x
32、and y are equally preferred. p p p p Preference Relations u 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 preferred at least as much as is y. f f f f p
33、 p p p Preference Relations ux y and y x imply x y. f f f f Preference Relations ux y and y x imply x y. ux y and (not y x) imply x y. f f f f f f f f p p Assumptions about Preference Relations uCompleteness: For any two bundles x and y it is always possible to make the statement that either x y or
34、y x. f f f f Assumptions about Preference Relations uReflexivity: Any bundle x is always at least as preferred as itself; i.e. x x. f f Assumptions about Preference Relations uTransitivity: If x is at least as preferred as y, and y is at least as preferred as z, then x is at least as preferred as z;
35、 i.e. x y and y z x z. f f f f f f Indifference Curves uTake 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”. Indi
36、fference Curves x Indifference Curves p pp p x y z Indifference Curves x2 x1 x All bundles in I1 are strictly preferred to all in I2. y z All bundles in I2 are strictly preferred to all in I3. I1 I2 I3 Indifference Curves x2 x1 I(x) x I(x) WP(x), the set of bundles weakly preferred to x. Indifferenc
37、e Curves x2 x1 WP(x), the set of bundles weakly preferred to x. WP(x) includes I(x). x I(x) Indifference Curves x2 x1 SP(x), the set of bundles strictly preferred to x, does not include I(x). x I(x) Indifference Curves Cannot Intersect I2 Indifference Curves Cannot Intersect I2 p p Slopes of Indiffe
38、rence Curves uWhen 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 Curves Slopes of Indifference Curves uIf less of a commodity is always preferred then the commodity is a bad. Slop
39、es of Indifference Curves Extreme Cases of Indifference Curves; Perfect Substitutes uIf 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-orde
40、r. Extreme Cases of Indifference Curves; Perfect Substitutes I2 I1 Extreme Cases of Indifference Curves; Perfect Complements uIf 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
41、 the two commodities determines the preference rank-order of bundles. Extreme Cases of Indifference Curves; Perfect Complements I1 Each of (5,5), (5,9) and (9,5) contains 5 pairs so each is equally preferred. Extreme Cases of Indifference Curves; Perfect Complements I2 I1 Since each of (5,5), (5,9)
42、and (9,5) contains 5 pairs, each is less preferred than the bundle (9,9) which contains 9 pairs. Preferences Exhibiting Satiation uA 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
43、 Curves Exhibiting Satiation Indifference Curves Exhibiting Satiation Indifference Curves Exhibiting Satiation Indifference Curves for Discrete Commodities uA 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 l
44、umps of 1, 2, 3, and so on; e.g. aircraft, ships and refrigerators. Indifference Curves for Discrete Commodities uSuppose commodity 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 Discre
45、te Good 3 Well-Behaved Preferences uA preference relation is “well- behaved” if it is monotonic and convex. uMonotonicity: More of any commodity is always preferred (i.e. no satiation and every commodity is a good). Well-Behaved Preferences uConvexity: Mixtures of bundles are (at least weakly) prefe
46、rred 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 Preferences - Convexity. x y z = x+ y2 Well-Behaved Preferences - Convexity. x y z =(tx1+(1-t)y1, tx2+(1-t)y2) is preferred to x and y for all 0 t
47、 U(x”) x x” U(x) U(4,1) = U(2,2) = 4. uCall these numbers utility levels. p p Utility Functions each is the other. Utility Functions uThere is no unique utility function representation of a preference relation. uSuppose U(x1,x2) = x1x2 represents a preference relation. uAgain consider the bundles (4
48、,1), (2,3) and (2,2). Utility Functions uU(x1,x2) = x1x2, so U(2,3) = 6 U(4,1) = U(2,2) = 4; that is, (2,3) (4,1) (2,2). p p Utility Functions uU(x1,x2) = x1x2 (2,3) (4,1) (2,2). uDefine V = U2. p p Utility Functions uU(x1,x2) = x1x2 (2,3) (4,1) (2,2). uDefine V = U2. uThen V(x1,x2) = x12x22 and V(2
49、,3) = 36 V(4,1) = V(2,2) = 16 so again (2,3) (4,1) (2,2). uV preserves the same order as U and so represents the same preferences. p p p p Utility Functions uU(x1,x2) = x1x2 (2,3) (4,1) (2,2). uDefine W = 2U + 10. p p Utility Functions uU(x1,x2) = x1x2 (2,3) (4,1) (2,2). uDefine W = 2U + 10. uThen W
50、(x1,x2) = 2x1x2+10 so W(2,3) = 22 W(4,1) = W(2,2) = 18. Again, (2,3) (4,1) (2,2). uW preserves the same order as U and V and so represents the same preferences. p p p p Utility Functions uIf U is a utility function that represents a preference relation and f is a strictly increasing function, u then
