Introduktion. Unifying Framework

Transcription

1 Introduktion Velkommen til 2. del af kurset Introduktion til Matematiske Metoder i Økonomi, efterår del var fælles for MAT og MAT-ØK studerende. Nærværende 2. del er kun for MAT-ØK studerende, og den vil omhandle det basale matematiske grundlag for adfærdsøkonomi, dvs. grundlæggende mikroøkonomisk teori. Litteraturgrundlag Nærværende lancher tager udgangsunkt i bogen: Hal Varian: Intermediate Microeconomics, 7 th edition, W.W.Norton New York. Pensum er disse og de følgende lancher Ansvarlig for denne del Esben Høg, Institut for Matematiske Fag, Aalborg Universitet, esben@math.aau.dk 1 Unifying Framework Economic agents (individuals, firms etc.) don't change their references of goods or services (allocations) within the eriod of study There are constraints (hysical and financial) laced on the feasible allocation (e.g. I can't afford flying to the moon) However, given the constraints eole choose the best (we say they otimize). Changes in behavior is thus due to changes in constraints (e.g. rices go down on a moon tri, so I buy it) Equilibrium. u Agents adjust their behavior until they are satisfied, s where e the economy are at equilibrium Economist use this framework to build models of reality. 2 1

2 Economists Use Models Models are simlified and analytical deictions of reality (Models can't be reality, neither can a theory since that is a contradiction) Hel us understand comlex realities by focusing on what we think is imortant Analytical in the sense of breaking down a whole into small ieces, examining them and then utting some ieces together Goal: Sharen intuition - learn "what is imortant and why Give us testable redictions which can be rejected, if so go back to the assumtions and start over again. (Comare with Poer's criterion of science as falsifiable). Now it is hoefully clear why alied math is imortant in economics. 3 Chater One The Market 4 2

3 Economic Modeling What causes what in economic systems? At what level of detail shall we model an economic henomenon? Which variables are determined outside the model (exogenous) and which are to be determined by the model (endogenous)? 5 Modeling the Aartment Market How are aartment rents determined? Suose aartments are close or distant, but otherwise identical distant aartments rents are exogenous and known many otential renters and landlords 6 3

4 Modeling the Aartment Market Who will rent close aartments? At what rice? Will the allocation of aartments be desirable in any sense? How can we construct an insightful model to answer these questions? 7 Modeling Aartment Demand Demand: Suose the most any one erson is willing to ay to rent a close aartment is $500/month. Then = $500 Q D = 1. Suose the rice has to dro to $490 before a 2nd erson would rent. Then = $490 Q D =

5 Modeling Aartment Demand The lower is the rental rate, the larger is the quantity of close aartments demanded Q D. The quantity demanded vs. rice grah is the market demand curve for close aartments. 9 Market Demand Curve for Aartments Q D 10 5

6 Modeling Aartment Suly Suly: It takes time to build more close aartments t so in this short-run the quantity available is fixed (at say ). Is this reasonable in the long run? 11 Market Suly Curve for Aartments Q S 12 6

7 Cometitive Market Equilibrium low rental rice quantity demanded of close aartments t exceeds quantity available rice will rise. high rental rice quantity demanded less than quantity available rice will fall. 13 Cometitive Market Equilibrium Quantity demanded = quantity available rice will neither rise nor fall so the market is at a cometitive equilibrium. 14 7

8 Cometitive Market Equilibrium Suly Demand 15 Cometitive Market Equilibrium Suly e Demand 16 8

9 Cometitive Market Equilibrium Peole willing to ay e for close aartments get close aartments. e 17 Cometitive Market Equilibrium e Peole willing to ay e for close aartments get close aartments. Peole not willing to ay e for close aartments get distant aartments. 18 9

10 Cometitive Market Equilibrium Q: Who rents the close aartments? A: Those most willing to ay. Q: Who rents the distant aartments? A: Those least willing to ay. So the cometitive market allocation is by willingness-to-ay. 19 Comarative Statics What is exogenous in the model? rice of distant aartments quantity of close aartments incomes of otential renters. What haens if these exogenous variables change? Hint are these variables deicted on the axis? No, thus always a shift! 20 10

11 Comarative Statics Suose the rice of distant aartment rises. Demand for close aartments increases (rightward shift), causing a higher rice for close aartments. 21 Market Equilibrium e 22 11

12 Market Equilibrium Higher demand e 23 Market Equilibrium Higher demand causes higher market rice; same quantity traded. e 24 12

13 Comarative Statics Suose there were more close aartments. t Suly is greater, so the rice for close aartments falls. 25 Market Equilibrium e 26 13

14 Market Equilibrium Higher suly e 27 Market Equilibrium Higher suly causes a lower market rice and a larger quantity traded. e 28 14

15 Taxation Policy Analysis Local government taxes aartment owners. What haens to rice quantity of close aartments rented? Is any of the tax assed to renters? 29 Taxation Policy Analysis Market suly is unaffected. Market demand is unaffected. So the cometitive market equilibrium is unaffected by the tax. Price and the quantity of close aartments rented are not changed. Landlords ay all of the tax. Why is that? (Hint the suly curve) This is a very secial case! 30 15

16 Imerfectly Cometitive Markets Amongst many ossibilities are: a monoolistic landlord a erfectly discriminatory monoolistic landlord a cometitive market subject to rent control. 31 A Monoolistic Landlord When the landlord sets a rental rice he rents D() aartments. What is D()? Revenue = D(). Revenue is low if 0 Revenue is low if is so high that D() 0. An intermediate value for maximizes revenue

17 Monoolistic Market Equilibrium Low rice, high quantity demanded, low revenue. Low rice Q D 33 Monoolistic Market Equilibrium High rice High rice, low quantity demanded, low revenue. Q D 34 17

18 Monoolistic Market Equilibrium Middle rice, medium quantity demanded, d d larger revenue. Middle rice Q D 35 Monoolistic Market Equilibrium Middle rice, medium quantity demanded, d d larger revenue. Monoolist does not rent all the close aartments. Middle rice 36 18

19 Monoolistic Market Equilibrium Middle rice Middle rice, medium quantity demanded, d d larger revenue. Monoolist does not rent all the close aartments. Vacant close aartments. 37 Perfectly Discriminatory Monoolistic Landlord Imagine the monoolist knew everyone s willingness-to-ay. Charge $500 to the most willing-to-ay, Charge $490 to the 2nd most willing-toay, etc

20 Discriminatory Monoolistic Market Equilibrium 1 =$ Discriminatory Monoolistic Market Equilibrium 1 =$500 2 =$

21 Discriminatory Monoolistic Market Equilibrium 1 =$500 2 =$490 3 =$ Discriminatory Monoolistic Market Equilibrium 1 =$500 2 =$490 3 =$

22 Discriminatory Monoolistic Market Equilibrium 1 =$500 2 =$490 3 =$475 Discriminatory monoolist charges the cometitive market rice to the last renter, and rents the cometitive quantity of close aartments. e Which Market Outcomes Are Desirable? Which is better? Perfect cometition Monooly Discriminatory monooly 44 22

23 Pareto Efficiency Vilfredo Pareto; A Pareto outcome allows no wasted welfare ; i.e. the only way one erson s welfare can be imroved is to lower another erson s welfare. A areto efficient outcome is such that no one can get it better without someone else getting it worse 45 Pareto Efficiency Jill has an aartment; Jack does not. Jill values the aartment at $200; Jack would ay $400 for it. Jill could sublet the aartment to Jack for $300. Both gain, so it was Pareto inefficient for Jill to have the aartment

24 Pareto Efficiency A Pareto inefficient outcome means there remain unrealized mutual gains-to-trade. Any market outcome that achieves all ossible gains-to-trade trade must be Pareto efficient. 47 Pareto Efficiency Cometitive equilibrium: all close aartment renters value them at the market rice e or more all others value close aartments at less than e so no mutually beneficial trades remain so the outcome is Pareto efficient

25 Pareto Efficiency Discriminatory Monooly: assignment of aartments is the same as with the erfectly cometitive market so the discriminatory monooly outcome is also Pareto efficient. 49 Monooly: Pareto Efficiency not all aartments are occuied so a distant aartment renter could be assigned a close aartment and have higher welfare without lowering anybody else s welfare. so the monooly outcome is Pareto inefficient

26 Harder Questions So far we have made the analysis by looking at the short run where the suly curve was fixed. What will haen in the long run? Usually a more comlicated question since interactions within and between markets? Next time we start by more exlicitly building our model 51 26