Chapter One. Economic Modeling. Modeling the Apartment Market. Economic Modeling Assumptions. Modeling the Apartment Market.

Transcription

1 Chater One The Market The Theory of Economics does not furnish a body of settled conclusions immediately alicable to olicy. It is a method rather than a doctrine, an aaratus of the mind, a technique of thinking which hels its ossessor to draw correct conclusions --- John Maynard Keynes 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)? 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 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? Economic Modeling Assumtions Two basic ostulates: Rational Choice: Each erson tries to choose the best alternative available to him or her. Equilibrium: Market rice adjusts until quantity demanded equals quantity sulied. 1

2 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 = 2. 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. Market Demand Curve for Aartments Modeling Aartment Suly Suly: It takes time to build more close aartments so in this short-run the quantity available is fixed (at say ). Q D Market Suly Curve for Aartments Cometitive low rental rice quantity demanded of close aartments exceeds quantity available rice will rise. high rental rice quantity demanded less than quantity available rice will fall. Q S 2

3 Cometitive Quantity demanded = quantity available rice will neither rise nor fall so the market is at a cometitive equilibrium. Cometitive Cometitive Cometitive Peole willing to ay e for close aartments get close aartments. e e Cometitive Cometitive e Peole willing to ay e for close aartments get close aartments. Peole not willing to ay e for close aartments get distant aartments. 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. 3

4 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? Comarative Statics Suose the rice of distant aartment rises. Demand for close aartments increases (rightward shift), causing a higher rice for close aartments. Higher demand e e e Higher demand causes higher market rice; same quantity traded. Comarative Statics Suose there were more close aartments. Suly is greater, so the rice for close aartments falls. 4

5 Higher suly e e Higher suly causes a lower market rice and a larger quantity traded. Comarative Statics Suose otential renters incomes rise, increasing their willingness-toay for close aartments. Demand rises (uward shift), causing higher rice for close aartments. e Higher incomes cause higher willingness-to-ay e e 5

6 Taxation Policy Analysis e Higher incomes cause higher willingness-to-ay, higher market rice, and the same quantity traded. Local government taxes aartment owners. What haens to rice quantity of close aartments rented? Is any of the tax assed to renters? 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. Imerfectly Cometitive Markets Amongst many ossibilities are: a monoolistic landlord a erfectly discriminatory monoolistic landlord a cometitive market subject to rent control. A Monoolistic Landlord Monoolistic When the landlord sets a rental rice he rents D() aartments. Revenue = D(). Revenue is low if 0 Revenue is low if is so high that D() 0. An intermediate value for maximizes revenue. Low rice Low rice, high quantity demanded, low revenue. Q D 6

7 Monoolistic Monoolistic High rice High rice, low quantity demanded, low revenue. Middle rice, medium quantity demanded, larger revenue. Middle rice Q D Q D Monoolistic Monoolistic Middle rice, medium quantity demanded, larger revenue. Monoolist does not rent all the close aartments. Middle rice, medium quantity demanded, larger revenue. Monoolist does not rent all the close aartments. Middle rice Middle rice Vacant close aartments. Perfectly Discriminatory Monoolistic Landlord Imagine the monoolist knew everyone s willingness-to-ay. Charge $500 to the most willing-toay, charge $490 to the 2nd most willingto-ay, etc. 1 =$500 Discriminatory Monoolistic 1 7

8 1 =$500 2 =$490 Discriminatory Monoolistic 1 =$500 2 =$490 3 =$475 Discriminatory Monoolistic =$500 2 =$490 3 =$475 Discriminatory Monoolistic 1 =$500 2 =$490 3 =$475 Discriminatory Monoolistic Discriminatory monoolist charges the cometitive market rice to the last renter, and rents the cometitive quantity of close aartments. e Rent Control Local government imoses a maximum legal rice, max < e, the cometitive rice. e 8

9 e max e max Excess demand e max The close aartments are no longer allocated by willingness-to-ay (lottery, lines, large families first?). Excess demand Which Market Outcomes Are Desirable? Which is better? Rent control Perfect cometition Monooly Discriminatory monooly 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. 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. 9

10 A Pareto inefficient outcome means there remain unrealized mutual gains-to-trade. Any market outcome that achieves all ossible gains-to-trade must be Pareto efficient. 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. Discriminatory Monooly: assignment of aartments is the same as with the erfectly cometitive market so the discriminatory monooly outcome is also Pareto efficient. Monooly: 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. Rent Control: some close aartments are assigned to renters valuing them at below the cometitive rice e some renters valuing a close aartment above e don t get close aartments Pareto inefficient outcome. Harder Questions Over time, will the suly of close aartments increase? rent control decrease the suly of aartments? a monoolist suly more aartments than a cometitive rental market? 10