5. Aggregating Consumers Consumer Heterogeneity and a Discrete good b. The Properties of Aggregate Demand The Existence of a representative Consumer d. Externalities e. The Social Multiplier

4. Welfare Analysis and Other Issues a. Measuring Welfare b. First Order and Second Order Losses C. Taxes and Welfare d. Household Production (did last class) e. The Hedonic Approach

3. Comparative Statics a. Indirect Utility Functions b. Expenditure Functions and duality C. Expenditure Function and Price Indices d. Slutsky via Utility Functions e. Slutsky via Preferences

2. Choice and Utility Functions a. Choice in Consumer Demand Theory and Walrasian Demand b. Properties of demand from continuity and properties from WARP . Representing Preferences with a Utility Function d. Demand as Derived from Utility Maximization e. Application: Fertility

11. Competition and Monopoly, some preliminary discussions a. Monopoly Pricing b. Cournot and Bertrand Oligopoly C. Two Part Pricing d. Price Discrimination e. Regulation

10. More on Production a. Derived Demand-Marshall's Laws b. Long Run/Short Run, LeChatelier, Dynamics C. Aggregating Supply d. Theory of the Firm, the Holdup Problem e. Agency Issues f. Application: The Coase Theorem

Chapter 5: Tunneling and Application Gateway Chapter goal: Multiprotocol environment a Multiprotocol environment Mixing network technologies Mixing network technologies Encapsulation and tunneling Encapsulation and tunneling

Lecture D34 Coupled Oscillators Spring-Mass System(Undamped/Unforced)

Solution General solution x(t)= A cos wnt +B sin wnt or, x(t)=Csin(wnt+φ) Initial conditions

In lecture D28, we derived three basic relationships embodying Kepler's laws: Equation for the orbit trajectory