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Economic Modeling

Explore the factors that determine apartment rents in the student housing market and construct a simple economic model to analyze the allocation of apartments and the equilibrium price.

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Economic Modeling

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  1. Economic Modeling • What causes what (causality, 因果關係) in economic systems? • At what level of detail shall we model an economic phenomenon? • Which variables are determined outside the model (exogenous, 外生), and which are to be determined by the model (endogenous, 內生)?

  2. The Student Apartment Market • How are apartment rents determined? • Suppose: • 2 types of identical apartments: close (inner ring) v. distant (outer ring) • distant apartments: abundant, rents P fixed and known • many potential renters and landlords

  3. Modeling the Apartment Market • Who will rent close apartments? • At what price? • Will the apartment allocation be desirable in any sense? • How can we construct a simple model to answer these questions?

  4. Economic Modeling Assumptions • Two basic postulates/principles: • Rational Consumer: Each person tries to choose the best alternative available to him/her (optimize). • Equilibrium: Market price adjusts until quantity demanded equals quantity supplied.

  5. Modeling Apartment Demand • Demand: Suppose the most any one is willing to pay to rent a close apartment is $500/month (reservationprice). Then: p = $500  QD = 1. • Suppose the price drops $490, then 2nd person will also rent: p = $490  QD = 2.

  6. Modeling Apartment Demand • The lower is the rental rate p, the larger is the quantity of close apts demanded: p   QD. • The quantity demanded vs. price graph is the market demand curve for close apts. • Quantity demanded at P is #people with reservation prices > P

  7. Market Demand Curve with Many Consumers p QD

  8. Modeling Apartment Supply • Supply: It takes time to build more close apts, so in the short-run, the quantity available is fixed, at say Q=100.

  9. Market Supply Curve in the Short Run p QS 100

  10. Competitive Market Equilibrium • “low” rental price  quantity demanded of close apartments exceeds quantity available  price will rise. • “high” rental price  quantity demanded less than quantity available  price will fall.

  11. Competitive Market Equilibrium • When quantity demanded = supplied  price will stabilize (neither rise nor fall) • The market is at a competitive equilibrium.

  12. Competitive Market Equilibrium p 100 QD,QS

  13. Competitive Market Equilibrium p pe 100 QD,QS

  14. Competitive Market Equilibrium p People willing to pay pe for close apartments get close apartments. pe 100 QD,QS

  15. Competitive Market Equilibrium p People not willing to pay pe for close apartments rent distant apartments. pe 100 QD,QS

  16. Competitive Market Equilibrium • Q: Who rents the close apts? • A: Those most willing to pay. • Q: Who rents the distant apts? • A: Those least willing to pay. • Competitive market allocation is by “willingness-to-pay(WTP)”.

  17. Comparative Statics(比較靜態分析) • What is exogenous in the model? • P, price of distant apartments • Q, quantity of close apartments • WTP of potential renters. • What happens if these exogenous variables change? • Comparing 2 static equilibria

  18. Comparative Statics #1 • Suppose the price of distant apartment, P, rises. • Demand for close apartments increases (rightward shift), causing a higher price for close apartments.

  19. Market Equilibrium p pe 100 QD,QS

  20. Market Equilibrium p Higher demand pe 100 QD,QS

  21. Market Equilibrium p Higher demand causes highermarket price; same quantitytraded. pe 100 QD,QS

  22. Comparative Statics #2 • Suppose there were more close apartments: higher Q • Supply is greater, so the price for close apartments falls to induce more demand for equilibrium

  23. Market Equilibrium p pe 100 QD,QS

  24. Market Equilibrium p Higher supply Q pe 100 QD,QS

  25. Market Equilibrium p Higher supply causes alower market price and alarger quantity traded. pe 100 QD,QS

  26. Comparative Statics #3 • Suppose potential renters’ incomes rise, increasing their WTP for close apartments. • Demand rises (upward shift), causing • higher price for close apartments.

  27. Market Equilibrium p pe 100 QD,QS

  28. Market Equilibrium p Higher incomes causehigher WTP pe 100 QD,QS

  29. Market Equilibrium p Higher incomes causehigher WTP,higher market price, andthe same quantity Q traded. pe 100 QD,QS

  30. Taxation Policy Analysis • Local government taxes apartment owners. • What happens to • price • quantity of close apartments rented? • Is any of the tax “passed” to renters?

  31. Tax Incidence (稅負歸宿) • Market supply: unaffected • Market demand: unaffected • Market equilibrium: unaffected • Price/quantity of close apartments: not changed. • So, landlords bear all of the tax, no tax transfer.

  32. Imperfectly Competitive Markets • Many possibilities: • a monopolistic landlord • a perfectly discriminatory monopolistic landlord • a competitive market subject to rent control.

  33. Ordinary Monopolistic Landlord • When the landlord sets a rental price p, he can rent D(p) apartments. • Landlord revenue: pD(p). • Revenue is low If P is too low: p 0 • Revenue is low if p is so high that D(p)  0. • An intermediate value for p maximizes revenue.

  34. Monopolistic Market Equilibrium p Low price, high quantitydemanded, low revenue. Lowprice QD

  35. Monopolistic Market Equilibrium p High price, low quantitydemanded, low revenue. Highprice QD

  36. Monopolistic Market Equilibrium p Middle price, medium quantitydemanded, larger revenue. Middleprice QD

  37. Monopolistic Market Equilibrium p Middle price, medium quantitydemanded, larger revenue.Monopolist does not rent all theclose apartments. Middleprice 100 QD,QS

  38. Monopolistic Market Equilibrium p Middle price, medium quantitydemanded, larger revenue.Monopolist does not rent all theclose apartments. Vacant close apartments. Middleprice 100 QD,QS

  39. Perfectly Discriminatory Monopolistic Landlord • Suppose the monopolist knows everyone’s WTP. • Charge $500 to the most WTP • Charge $490 to the 2nd most WTP, etc. • Individualized prices

  40. Discriminatory Monopolistic Market Equilibrium p p1 =$500 1 100 QD,QS

  41. Discriminatory Monopolistic Market Equilibrium p p1 =$500 p2 =$490 1 2 100 QD,QS

  42. Discriminatory Monopolistic Market Equilibrium p p1 =$500 p2 =$490 p3 =$475 1 2 3 100 QD,QS

  43. Discriminatory Monopolistic Market Equilibrium p p1 =$500 p2 =$490 p3 =$475 1 2 3 100 QD,QS

  44. Discriminatory Monopolistic Market Equilibrium p Discriminatory monopolistcharges the competitive marketprice to the last renter, andrents the competitive quantityof close apartments. p1 =$500 p2 =$490 p3 =$475 pe 1 2 3 100 QD,QS

  45. Rent Control • Local government imposes a maximum legal price, pmax < pe, the competitive price.

  46. Market Equilibrium p pe 100 QD,QS

  47. Market Equilibrium p pe Excess demand, 超額需求 pmax 100 QD,QS

  48. Market Equilibrium p The 100 close apartments are no longer allocated bywillingness-to-pay (lottery, lines,large families first?). Excess demand pe pmax 100 QD,QS

  49. Which Market Outcomes Are Desirable? • Which is better? • Perfect competition • Monopoly • Discriminatory monopoly • Rent control

  50. Pareto Efficiency • Vilfredo Pareto: 1848-1923 • Pareto outcomes: no wasted welfare • The only way one person can be better off is to sacrifice welfare of other people. • Pareto Improvement: none hurt, some better off

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