1. CDAE 254 - Class 3 Sept. 4 Last class: 1. Introduction Today: 1. Introduction 2. Preferences and choice Next class: 2. Preferences and choice Important date: Problem set 1 due Thursday, Sept. 6

2. 1. Introduction 1.1. Overview of an economy 1.2. Economics and microeconomics 1.3. Economic models & applied economic analysis 1.4. Development of economic models 1.5. Verification of economic models 1.6. Ten principles of economics 1.7. Functions and graphs used in economics

3. 1.7. Functions & graphs used in economics 1.7.1. How to express economic relations? 1.7.2. Functions of one variable 1.7.3. Graphing functions of one variable 1.7.4. Functions of more than one variable 1.7.5. Graphing functions of two variables 1.7.6. Simultaneous equations 1.7.7. Derivatives

4. 1.7.6. Simultaneous equations -- Definition: A set of equations with two or more variables that must be solved together for a particular solution. -- Example: Supply and demand -- General procedures for a set of two equations: (1) Substitution method (2) Other methods

5. 1.7.6. Simultaneous equations -- Example: 3X + 2Y = 19 2X – Y = 8

6. More examples Y = 20 – 2X 4X – Y = 10 Qd = 10 – P Qs = – 5 + 2P

7. 1.7.7. Derivatives and optimization (a) How to calculate derivatives? a) Interpretation and notation b) Rules of finding derivatives c) Examples (b) How to derive the maximum or minimum value of a nonlinear function? 1) Derive the first derivative 2) Set the first derivative to be equal to zero 3) Solve for the independent variable 4) Substitute the solution back to the function to get the maximum or minimum value of the function

8. 1.7.7. Derivatives and optimization (c) Applications – why do we need to learn derivatives in economics? 1) Profit maximization: profit = – 50 + 2 q – 0.01 q 2 2) Average cost (AC) minimization AC = 120 – 0.8 q + 0.002 q2

9. Class exercise 1 (Tuesday, Sept. 4) 1. Derive the derivatives: (a) Y = 10(b) Y = 100 + 2X + 0.1X 2 2. If a company’s profit function is profit = – 50 + 4 q – 0.01 q 2 (a) What should be the profit-maximizing production level (q*)? (b) What is the maximum profit?

10. 3. Utility and choice 3.1. Basic concepts 3.2. Assumptions about rational choice 3.3. Utility 3.4. Indifference curve and substitution 3.5. Marginal utility and MRS 3.6. Special utility functions 3.7. Budget constraints 3.8. Utility maximization 3.9. Applications

11. 3.1. Basic concepts (1) Factors that determine choice (demand) -- Preferences -- Constraints (e.g., income, time, etc.) (2) Consumer behavior: allocating limited resources to maximize her or his utility (satisfaction)

13. Preferences (tastes) individual tastes (preferences) determine pleasure people derive from goods economists usually – take tastes as given – do not judge tastes – consider that tastes can change

15. Individual decision making consumers face constraints on their choices consumers maximize their pleasure from consumption and subject to constraints we generally want to predict behavior--not judge it