L18 Review

Three parts Applications of buying and selling Labor Supply Intertemporal Choice (T=2,T>2) Uncertainty Markets and Exchange Pareto (In) efficiency Competitive equilibrium Producers Production function Profit Maximization (labor demand) Cost Minimization Supply of the firm

Budget set Buying and selling BS LM IC U

Intertemporal Choice T=2 BS derivation, the slope PV and FV: relation to BS Find optimal choice of C1 and C2 (with 1+r as a parameter!) Cobb-Douglass magic formula Borrowing and lending (saving) Consumption Smoothing

Intertemporal Choice T>2 Constant payments: annuity (perpetuity) PV formulas Applications: leasing, loans, bonds, Life cycle models

Pension plan How much to save to get $100 annually? Cashflow How much you get if you save $100 annually?

Uncertainty: Theory States of the world (two) Risky and Safe Lottery Expected value Bernoulli and von Neumann Morgernstern f. Risk Aversion and Bernouli U. Certainty Equivalent

Uncertainty: Insurance Insurance contract BS derivation, the slope Choice with fair insurance Choice with no fair insurance

Markets and Exchange Edgeworth Box (apple-orange, IC, U) Pareto Efficiency Give a definition Find all Pareto efficient allocations Competitive Equilibrium Definition Find it (p2=1, 1 market) Competitive Equilibrium Pareto efficient? Application: apple-orange, IC, U

Markets and Exchange: Example

Producers Producers: have a technology Technology given by production function Two inputs: Capital and Labor 3 examples MPL and MPK (decreasing) Short and Long run (fixed K or not) Constant Returns to Scale

Goal Profit Maximization (Short and Long Run) Find optimal L,K Secrets of happiness (derive, interpret) Solve! Long Run Optimization and Returns to Scale

Labor Market Labor demand (short run) and real wage rate Given labor supply find “equilibrium” How equilibrium (real) wage rate is affected by Increased capital Increased willingness to work Implications of minimal wage rate

Cost Minimization How to efficiently produce Find cost minimizing L,K Secrets of happiness (derive, interpret) Solve! Shapes of C(y) and AC, profit!

Cost Minimization Returns to Scale and Cost functions