RL3Review

Exam Date: Room:

Cumulative 2 hours (120 min) Closed book (calculators not needed) Format: Problems as in PS (no true false q) Course Grade: 25-20-20-35, Curve!

Preparation1. Master all PS and past exams2. Read slides3. Read book

Consumer’s TheoryFix (parameter) Budget set (plot, interpret slope) 4 types of preferences (plot, find interpret MRS, MT)

Optimal choice (SoH, find analytically and geometrically) Magic formula for Cobb-Douglass! (derive it)

Changes in p and m Substitution and Income effect Ordinary and Giffen, Inferior and Normal goods

Real endowments (choice) Geometric representation Choice – buying and selling

1 21, 1, 10p p m 1 2( , )U x x

3 applications Labor market - labor supply: w given

Budget set, Choice, Labor Supply, Elasticity

Intertemporal Choice: r given1) 2 periods: Budget set, Choice, PV, FV, CS

Consumption smoothing2) T periods: Annuity and perpetuity: PV formula Lease or buy, loan, pension plan, value of the bond

Uncertainty: gamma given1) Lottery, Bernoulli and VNM utility2) Risk aversion and certainty equivalent 3) Insurance (fair insurance)

Markets and Equilibrium

Many (2) agents Edgeworth Box

Markets: Competitive Equilibrium Competitive Equilibrium

1) Choices optimal given prices 2) Markets clear (supply=demand)

Find CE analytically and geometrically. Tricks: 1) one price =1, 2) market clearing for only one good 3) magic formula!

FWT: Competitive equilibrium is Pareto efficient!

1 2 1 2( , ), ( , )A A B Bx x x x1 2( , )p p

Competitive Equilibrium 2121 lnln),( xxxxu

Competitive Equilibrium (Geometry)2121 lnln),( xxxxu

Are Markets Efficient?2121 lnln),( xxxxu

Pareto Efficiency2121 lnln),( xxxxu

Are Markets Efficient?2121 lnln),( xxxxu

Competitive Producers Producers have technology and maximize profit Properties of F( , ): RS, MPK, MPL Geometric representation: Isoquants SoH for Profit Maximization, Cost Minimization Profit maximization= cost minimization + choice of y

Derive cost functions, shapes for IRS, CRS and DRS

Supply function (also with fixed costs)

Equilibrium with N producers Equilibrium with free entry (determine N)

( , )F K L

Market failure 1. Market Power One producer (Monopoly) = it has market power Demand Cost function Optimal choice, elasticity and markup (uniform price)

TS, CS, PS, DWL Price discrimination (three types)

( ) 10p y y ( ) 2TC y y

Market failure 1. Market Power N firms Demand Cost function( ) 10p y y ( ) 2TC y y

DWL

Market failure 2. Externality Our utility/profit depends on action of others Positive and negative externality Problem strategic interdependence = Nash equilibrium Equilibrium : mutual best responses Special case of positive externality: Public good

Pareto efficiency: Too little or too much? Free riding

(, ) ln( ) , (, ) 2 ln( )A A B A B A B BU x x x U x x x

* *,A Bx x

Market failure 3. Asymmetric Information Adverse selection (hidden information) Example: Buyers of cars know less then sellers

1) Separating equilibrium: good cars not traded 2) Pooling equilibrium: both cars traded

Incentives for good types to send credible signals Credibility: for bad types too costly to pretend good ones

Moral hazard (hidden action)Insurance contracts change incentives!Insurers should take it into account