CDAE 254 - Class 2 Aug. 31

Last class:Syllabus -- class requirements and policiesStudent information sheet with “quiz” questions1. Introduction

Today: 1. Introduction

Next class:1. Introduction2. Preferences and choice

Important date:Problem set 1 due Thursday, Sept. 7

Problem set 11. Draw each of the following equations on graphical paper (make sure

to label your graphs):(a) Y = 2 + 0.5 X (b) Q = 20 – 2 P(c) 2X + 3 Y = 18 (d) Y = – 2

2. Solve each of the following systems of two equations:(a) Q = 20 – 2P (b) X = 4Y Q = 2P – 4 2 – Y – 0.5 X = 0

3. Derive the derivative for each of the following functions:(a) Y = 20 + 2X – 0.4 X2 (b) Y = 20X – 2 X3

4. If a company’s profit = -100 + 20 Q – 0.4 Q2, what is the value of Q that will maximize the company’s profit?

1. Introduction1.1. Overview of an economy1.2. Economics and microeconomics1.3. Economic models and applied economic analysis1.4. Development of economic models1.5. Verification of economic models1.6. Ten principles of economics1.7. Functions and graphs used in economics

1.4. Supply-demand: the development of an economic model

1.4.1. Supply-demand model: A model that describes how a good’s price is determined by the behavior of the individuals who buy the good and the firms that sell the good.

1.4.2. Development of the supply-demand model -- Barter transaction

-- Adam Smith (1723-90) & the invisible hand -- David Ricardo & diminishing returns

-- Mashall’s supply & demand ……

David Ricardo (1772-1823):-- A businessman, economist, policymaker, and one of the

fathers of modern economics-- Major publication: Principles of Political Economy and Taxation,

1817-- Major contributions: theory of comparative advantage and

diminishing marginal return-- History:

-- In the early 19th century, British Parliament was controlled by landlords “Corn Laws” limit grain imports and

help exports high food price -- Industrial revolution increase in urban population

needs to reduce grain prices -- Corn Laws were replaced in 1848 (25 yrs after

Ricardo’s death)

1.5. Verification of economic models -- Test assumptions

-- Test predictions -- Positive vs. normative analyses

1.6. Ten principles of economics How people make decisions:

(1) People face tradeoffs

(2) The cost of something is what you give up to get it

(3) Rational people think at the margin

(4) People respond to incentives

How people interact: (5) Trade can benefit both sides

(6) Markets are usually a good way to organize ….

(7) Government can sometimes improve market …

1.6. Ten principles of economics How the economy as a whole works: (8) A country’s standard of living depends on …

(9) Prices rise when the government prints too much $

(10) Short-run tradeoff between inflation and unemployment

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

1.7.1. How to express economic relations? (1) Three ways to express economic relations:

-- Functions (equations) -- Graphs -- Tables (2) Advantages and disadvantages:

1.7.2. Functions of one variable (1) General notation: Y = f (X) Y is a function of X Y is the dependent variable X is the independent variable (2) Linear function: Y = a + b X Y is a linear function of X a is the intercept (constant) b is the slope(constant)

1.7.2. Functions of one variable (3) Nonlinear function: e.g., Y = 20 + 0.5 X - 0.02 X2 Y is a nonlinear function of X

1.7.3. Graphing functions of one variable (1) Linear functions(a) How to graph?(b) Interpretation of intercept and slope(c) Changes in intercept(d) Changes in slope(e) Change in both intercept and slope (2) Nonlinear functions

1.7.4. Functions of more than one variable (1) General notation: Y = f (X, Z) Y is a function of X and Z Y is the dependent variable X and Z are the independent variables (2) Example: Y = 20 + 0.5 X + 0.2 Z

1.7.5. Graphing functions of two variables -- Three dimension graphs -- Examples: indifference curve and

isoquant

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) Get ride of one variable (2) Get the solution for one variable (3) Substitute the solution back into any of

the two equations to get the solution for the other variable.

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 function?

Class exercise 1(Thursday, August 31)

1. Derive the derivatives:(a) Y = -20 (b) Y = 10 + 2X – 0.2X2

2. Solve the following system of equations:X = 2Y2X + Y = 20