Welcome! Econ A494 Math Econ & Advanced Micro Theory Spring 2013 Prof. Jim Murphy

Course Overview Introduce you to the mathematical tools behind microeconomic theory This is not a pure math econ course Rather, my goal is to show you how to use and apply the tools of math econ to microeconomics. Success in the class requires you to apply the math and interpret the results It is not sufficient to just be able to do the math, you also need to interpret it. Purpose of the course Prepare you for grad school Provide an intellectual challenge Understand the theoretical underpinnings of microeconomics 2

Stuff I assume you already know Intermediate Microeconomics College algebra including how to solve systems of equations Calculus Differentiation with single and multiple variables Make sure you are comfortable with the rules for finding derivatives! Unconstrained and constrained optimization The pre-requisites require at least a B in Intermediate Micro and in Calculus. Success in this class requires that you are already confident in your understanding of that material. 3

Expectations This course is designed to be rigorous and challenging. For those of you thinking about grad school, my goal is to give you a taste of what to expect. Problem sets are important! OK to work in groups. Must be neat, clearly shows your work, proper notation. Office hours Drop by if you have questions—except right before class At least try to solve the problem before coming by. My first question will always be “what have you tried?” Do not wait until the last minute! Do not “punt” by turning in an assignment with notes like “I wasn’t sure how to do this one…” 4

Agenda Own your own… Review Chiang Ch 2 and Hoy Ch 2 In Hoy, pay particular attention to the notation Readings Silb Ch 1. Handout #1 – Paradigm of Economics Calculus Practice Quiz Overview – structure of economic theory Problem set #1 is due Mon Jan 28 or Wed Jan 30 Calculus review – can start now Due date depends upon how much review we will need Will announce due date next class 5

The Paradigm of Economics Silb ch 1 Handout 1

Introduction How would you define microeconomic theory? Microeconomics addresses the allocation of scarce resources among competing uses. Theory of choice Decisions, or choices, are the consequence of scarce resources Neoclassical economics: Changes in behavior due to changes in constraints faced by rational, self- interested economic actors Firms Individuals 7

Theories and Models Microeconomic Analysis Theories are used to explain observed phenomena in terms of a set of basic rules and assumptions. For example The Theory of the Firm The Theory of Consumer Behavior 8

Theories and Models Microeconomic Analysis Models a mathematical representation of a theory used to make a prediction. Validating a Theory The validity of a theory is determined by the quality of its prediction, given the assumptions. Evolving the Theory Testing and refining theories is central to the development of the science of economics. 9

What is a theory? A theory is a set of explanations or predictions about various objects in the real world Theories consist of 3 parts: 1. Assertions, or postulates 2. Assumptions, or test conditions 3. Events, or predictions 10

Structure of economic theories 1-2.Assertions (postulates) & assumptions Webster’s definition of postulate: “to assume without proof to be true, real, or necessary, especially as a basis for argument.” These give structure to the model Silb. distinguishes between assertions and assumptions. Assertions: not observable, but can use to observe implications e.g., “Firms maximize profits” Do not have to be realistic as long as they predict well Assumptions: observable. Must be realistic “a relative price declined”; “consumer income increased” 11

Structure of economic theories 2 types of initial postulates or assertions Behavioral postulates Suppositions about how agents behave “Firms maximize profits” “Consumers maximize utility” Market postulates or assertions Institutional setting for economic agents to perform “Firm operates in a perfectly competitive market” 12

Structure of economic theories 3.Events or predictions Theory says that the behavioral assertions imply that if the assumptions are valid, then certain events will occur. Events are logical implications of postulates and assumptions Both the test conditions and events must be observable Meaningful theory yields refutable predictions (which can be tested) Example ASSERTION: consumers maximize utility subject to budget constraint ASSUMPTION: Consumer income increased EVENT: Consumption of good increased 13

Economics: A theory of choice 14

Types of variables 15

Example 16

Paradigm of economics 17

Example 18

Profit maximization Goals: Build a model that describes the decision-making process by which the firm will choose the level of output to produce. Set up the objective function Use this model to formulate refutable hypotheses about the firm’s behavior when exogenous parameters (constraints) change. How does the firm react to things they can not control?  comparative statics 19

Refutable hypotheses A refutable hypothesis has the possibility that it will be wrong. “It will rain tomorrow” is refutable because it might not rain tomorrow. “It may or may not rain tomorrow” is NOT refutable because this statement is consistent with all possible weather outcomes. 20

Refutable hypotheses Postulates are refutable only through: making logically valid predictions about real observable events based on the postulates, then discovering that the predictions are false. Example: Assertion of profit maximization Certain behavior should be observed under certain assumptions Firms will increase output when the price increases. If this is what we observe, the theory will be confirmed, but not proven. 21

Mathematical formulation 22 Typo corrected

Implications of model 23 Typo corrected