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 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)?

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.

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?

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.

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)

Discrete Demand 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

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.

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?

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.

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.

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.

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.

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.

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?

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?

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?