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Economic Modeling

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. Economic Modeling.

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Economic Modeling

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  1. The Theory of Economics does notfurnish a body of settled conclusionsimmediately applicable to policy. It isa method rather than a doctrine, anapparatus of the mind, a technique ofthinking which helps its possessor todraw correct conclusions --- John Maynard Keynes

  2. Economic Modeling • What causes what in economic systems? • At what level of detail shall we model an economic phenomenon? • Which variables are determined outside the model (exogenous) and which are to be determined by the model (endogenous)?

  3. Modeling the Flat Rental Market • How are flats/apartments rent determined? • Suppose • flats are close or distant, but otherwise identical • distant flats rents are exogenous and known • many potential renters and landlords • Price of close flats is endogenous.

  4. An Economist’s concerns: Modeling the Apartment Market • Who will rent close apartments? • At what price? • Will the allocation of apartments be desirable in any sense? • How can we construct an insightful model to answer these questions?

  5. Economic Modeling Assumptions • Two basic postulates: • Rational Choice: Each person tries to choose the best alternative available to him or her. • Competitive Equilibrium: Market price adjusts until quantity demanded equals quantity supplied.

  6. Solving: • What does the demand curve look like? • Supply curve. • Equilibrium. • What if there isn’t a competitive equilibrium? • (If there is Monopolist or Rent Control)

  7. If Jack has a willingness to pay of £300, what does that mean. Can get far flat at £200. With £100, travel and inconvenience costs. If p>300, he won’t buy. If p<300, he would buy and get surplus of: Sample Demand Bill 200 Sam 100 George 300 Pete 400 Ted 200 Discrete Demand

  8. Pareto Efficiency/Optimality • Vilfredo Pareto; 1848-1923. • A Pareto outcome allows no “wasted welfare”; • i.e. the only way one person’s welfare can be improved is to lower another person’s welfare. • You can’t make someone better off without making someone else worse off.

  9. Pareto Optimality/Efficiency • An allocation is a possible distribution of goods in the economy. • An allocation is Pareto optimal if there does not exist another allocation where no one is worse off and at least one person is strictly better off. • Bill & Ted have £10 between them. What are the P.O. allocations?

  10. Pareto Efficiency • Jill has an apartment; Jack does not. • Jill values the apartment at $200; Jack would pay $400 for it. • Jill could sublet the apartment to Jack for $300. • Both gain, so it was Pareto inefficient for Jill to have the apartment.

  11. Pareto Efficiency • Competitive equilibrium: • all close flat renters value them at the market price p* or more • all others value close apartments at less than p* • so no mutually beneficial trades remain • so the outcome is Pareto efficient.

  12. Pareto Efficiency • Discriminatory Monopoly: • assignment of flats is the same as with the perfectly competitive market • so the discriminatory monopoly outcome is also Pareto efficient.

  13. Pareto Efficiency • Monopoly: • not all flats are occupied • so a distant flat renter could be assigned a close flat and have higher welfare without lowering anybody else’s welfare. • so the monopoly outcome is Pareto inefficient.

  14. Pareto Efficiency • Rent Control: • some close flats are assigned to renters valuing them at below the competitive price p* • some renters valuing a close flat above p* don’t get close flats • Pareto inefficient outcome.

  15. Housemates problem • Bill and Ted rent an apartment together for £400. • There is a large room and a small room. • Bill values the large room £100 more than the small room and Ted values the large room £20 more. • Which allocations are Pareto Optimal? • How will they divide up the rent?

  16. Envy-Free Allocations • An allocation is envy free if neither party is willing to swap situations. • For instance, Todd and Will Young are in envy-free allocations. • What are the Envy-Free allocations of the previous example?

  17. Envy Free Example • If Bill gets the large room, • Rent is B & T. • Rent must be paid: B+T=400 • Bill must not envy Ted 100-B>-T • Ted must not envy Bill –T>20-B • Show that B must be between £210 and £250 with T=400-B. • If Ted gets the large room, • ??? • Are the Envy-Free allocations Pareto optimal?

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