Economics 214 Lecture 13 Systems of Equations. Examples of System of Equations Demand and Supply IS-LM Aggregate Demand and Supply.

Slides:

Advertisements

Similar presentations

Solve a System Algebraically

Advertisements

Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

Lecture 3: Basic Aggregate Demand Model Goal: Determine equilibrium output Short-run A bit more complex than standard micro demand and supply – Feedback.

Equations and Their Solutions

The labour market In this lecture, we will introduce the labour market into our IS-LM framework. The variables we will want to talk about are wages, prices,

The Demand for Goods Total Demand. The Demand for Goods –C = C 0 + C 1 Y D –C 1 = propensity to consume Change in C from a dollar change in income –0.

Economics 214 Lecture 14 Solving Simultaneous Equations.

The Demand for Goods Total Demand. The Demand for Goods C = C 0 + C 1 Y D Consumption (C)

Economics 214 Lecture 2 Mathematical Framework of Economic Analysis Continued.

Lecture 1 Mathematical Framework of Economic Analysis

Algebra II March 2 nd Students should complete warm-up problems. Given a graph of a system of equations students will be able to determine how many solutions.

Thinking Mathematically Algebra: Graphs, Functions and Linear Systems 7.3 Systems of Linear Equations In Two Variables.

7.1 SOLVING SYSTEMS BY GRAPHING The students will be able to: Identify solutions of linear equations in two variables. Solve systems of linear equations.

Math 71A 3.1 – Systems of Linear Equations in Two Variables 1.

TODAY IN ALGEBRA…  Learning Goal: 7.2 You will solve systems of linear equations by Substitution  Independent Practice.

Math 201 for Management Students

3x – 5y = 11 x = 3y + 1 Do Now. Homework Solutions 2)2x – 2y = – 6 y = – 2x 2x – 2(– 2x) = – 6 2x + 4x = – 6 6x = – 6 x = – 1y = – 2x y = – 2(– 1) y =

Inverse Matrices and Systems

Section 4-1: Introduction to Linear Systems. To understand and solve linear systems.

3-2 Solving Equations by Using Addition and Subtraction Objective: Students will be able to solve equations by using addition and subtraction.

SOLVING SYSTEMS ALGEBRAICALLY SECTION 3-2. SOLVING BY SUBSTITUTION 1) 3x + 4y = 12 STEP 1 : SOLVE ONE EQUATION FOR ONE OF THE VARIABLES 2) 2x + y = 10.

Martin-Gay, Beginning Algebra, 5ed Using Both Properties Divide both sides by 3. Example: 3z – 1 = 26 3z = 27 Simplify both sides. z = 9 Simplify.

Elimination Method: Solve the linear system. -8x + 3y=12 8x - 9y=12.

7.4. 5x + 2y = 16 5x + 2y = 16 3x – 4y = 20 3x – 4y = 20 In this linear system neither variable can be eliminated by adding the equations. In this linear.

Systems of Linear Equations in Two Variables. 1. Determine whether the given ordered pair is a solution of the system.

Solving Linear Systems by Substitution

Simultaneous Equations Models A simultaneous equations model is one in which there are endogenous variables which are determined jointly. e.g. the demand-supply.

Differential Equations Linear Equations with Variable Coefficients.

Lecture by: Jacinto Fabiosa Fall 2005 Methodology in Economics.

Section 3.5 Solving Systems of Linear Equations in Two Variables by the Addition Method.

Chapter 8 Systems of Linear Equations in Two Variables Section 8.3.

Topic 6.5. Solve Systems by Substitution Objectives: Solve Systems of Equations using Substitution Standards: Functions, Algebra, Patterns. Connections.

1 Mathematics for Economics and Business Jean Soper chapter three Macroeconomic Models.

Algebra Review. Systems of Equations Review: Substitution Linear Combination 2 Methods to Solve:

TODAY IN ALGEBRA 2.0…  Review: Solving Linear Systems by Graphing  Learning Goal 1: 3.2 Solving Linear Systems by Substitution with one equation solved.

Warm Up 116 Solve. 6n + 4 = n – 11 Determine whether each linear relationship is proportional. If so, state the constant of proportionality. Write an equation.

Use Inverse Matrices to Solve Linear Systems

6) x + 2y = 2 x – 4y = 14.

Warm UP: Solve the following systems of equations:

10.1 SYSTEMS OF LINEAR EQUATIONS: SUBTRACTION, ELIMINATION.

Equations Quadratic in form factorable equations

Example: Solve the equation. Multiply both sides by 5. Simplify both sides. Add –3y to both sides. Simplify both sides. Add –30 to both sides. Simplify.

Solve Linear Systems by Graphing

Solving Systems of Equations

6-2 Solving Systems using Substitution

Simple linear equation

Solving Linear Systems Algebraically

Solve a system of linear equation in two variables

Solving Equations with variables on each side

Solving Systems of Equations using Substitution

Systems of Linear Equations in Two Variables

Simultaneous Equations

Graphing systems of linear equations and inequalities

Matrix Solutions to Linear Systems

Solve Linear Equations by Elimination

Linear Algebra Lecture 3.

Chapter 3 Section 1 Systems of Linear Equations in Two Variables All graphs need to be done on graph paper. Four, five squares to the inch is the best.

Algebra 2 Ch.3 Notes Page 15 P Solving Systems Algebraically.

SECTION 2-4 : SOLVING EQUATIONS WITH THE VARIABLE ON BOTH SIDES

Systems of Equations Solve by Graphing.

Solving Systems of Equations By Substitution

Solve the linear system.

Equations Quadratic in form factorable equations

Chapter 8 Systems of Equations

Multivariable Linear Systems

2 Chapter Chapter 2 Equations, Inequalities and Problem Solving.

1. How do I Solve Linear Equations

Warm- Up: Solve by Substitution

Presentation transcript:

Economics 214 Lecture 13 Systems of Equations

Examples of System of Equations Demand and Supply IS-LM Aggregate Demand and Supply

Demand and Supply

IS-LM

Solving System of Equations Repeated Substitution Matrix Algebra or linear Algebra

Solving System of Equations Economic Models typically consist of a number of equations that represent identities, behavioral relationships, and conditions that constitute an equilibrium. These equations include both variables, which are economic quantities and parameters, which are unvarying constants.

Solving Systems of Equations Variables in a system are exogenous if determined outside the system or endogenous if the are determined within the system. A solution to the model is a representation of the endogenous variables as functions of only the parameters of the model and the exogenous variables.

Solving our Demand and Supply model

Solving our Demand & Supply Model

Solving our IS-LM Model