Marginal Functions in Economics

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Marginal Functions in Economics"

Transcription

1 Marginal Functions in Economics One of the applications of derivatives in a real world situation is in the area of marginal analysis. Marginal analysis uses the derivative (or rate of change) to determine the rate at which a particular quantity is increasing or decreasing. In this section, the marginal functions that we will cover are those for the cost, average cost, revenue, and profit functions. The last topic that will be covered is the elasticity of demand. No matter which function we are dealing with, the word marginal indicates to us that we need to find the derivative of the function. For eample, if we are asked to find the marginal cost function then we need to find the derivative of the cost function. When the marginal function is evaluated it will give the approimate change for the net unit. For eample, if we evaluated a marginal cost function when = 100 then the value of C (100) would be the approimate cost of producing the net unit (or the 101 st unit). Eample 1: If a company s total cost function is defined as C() = , find the marginal cost function and evaluate it when = 200. Solution: Find the first derivative of the cost function C() = C () = Substitute the given value for into the marginal cost function C () = C (200) = (200) (200) C (200) = (40000) 0.04(200) C (200) = C (200) = The approimate cost of producing the 201 st unit will be $ The net function that you may be asked to find is the average cost function. The average cost function is determined in the same manner that you would find an average. We want to divide the total production cost, C(), by the total number of units,. The average cost function is distinguished from the cost function with a bar above the function notation, C. ( ) Average cost C ( ) = C ( ) The marginal average cost function would then be obtained by taking the first derivative of the average cost function. Gerald Manahan SLAC, San Antonio College,

2 Eample 2: Using the same cost function from Eercise 1, C() = , find the marginal average cost when = 200. Solution: First, we need to find the average cost function C ( ) = C ( ) C ( ) = C ( ) = Net, find the marginal average cost function by taking the 1 st derivative of C ( ) C ( ) = C ( ) = C ( ) = C ( ) = Now, evaluate the marginal average cost function when = 200 C ( ) = C (200) = (200) (200) C (200) = C (200) = C (200) = The process of finding the marginal revenue and marginal profit function is the same as how we found the marginal cost function. The only difference that you may encounter is the need to first determine the revenue or profit functions. If the revenue function is not given, then it will be equal to the price per unit (p) times the number of items sold (). R() = p Gerald Manahan SLAC, San Antonio College,

3 The profit function is the difference between the revenue and cost functions. P() = R() C() Eample 3: Suppose the relationship between the unit price p in dollars and the quantity demanded is given by the equation p = where 0 25,000. Find and interpret R (3000). Solution First, find the revenue function R() = p R() = ( )() R() = Net, find the marginal revenue function R() = R () = Now, evaluate the marginal revenue function when = 3000 R () = R (3000) = 0.06(3000) R (3000) = R (3000) = 570 The sale of the 3001 st unit would produce revenue of approimately $570. Eample 4: Suppose a company s weekly demand for their product is p = where p is the unit price in dollars and is the quantity demanded which must be between 0 and The cost function is given by C() = Find P (2500) and interpret the results. Solution First, we need to find the revenue function R() = p R() = ( )() R() = Gerald Manahan SLAC, San Antonio College,

4 Eample 4 (Continued): Net, find the profit function P() = R() C() P() = ( ) ( ) P() = P() = Now, find the marginal profit function P() = P () = Last, evaluate the marginal profit function when = 2500 P () = P (2500) = (2500) (2500) P (2500) = ( ) 0.04(2500) P (2500) = P (2500) = 275 The sale of the 2501 st unit would result in a loss of approimately $275. The last topic for this section of notes is the elasticity of demand. The elasticity of demand represents a ratio of the percentage change in quantity demanded to the percentage change in the unit price. pf ( p) f ( p) There are three possible cases for the elasticity of demand: 1. Elastic when E(p) > 1 A small percentage change in unit price will result in a larger percentage change in quantity demanded. Revenue is decreasing on an interval where the demand is elastic. 2. Unitary when 1 A small percentage change in unit price will result in the same percentage change in quantity demanded. Revenue is constant at the point where the demand is unitary. Gerald Manahan SLAC, San Antonio College,

5 3. Inelastic when E(p) < 1 A small percentage change in unit price will result in a smaller percentage change in quantity demanded. Revenue is increasing on an interval where the demand is inelastic. Eample 5: Compute the elasticity of demand for the demand equation, 4 + 5p = 80, and determine whether the demand is elastic, unitary, or inelastic when the price is $10. Solution Solve the demand equation in terms of 4 + 5p = 80 4 = -5p + 80 = p + 20 let f(p) = f(p) = p + 20 Find the derivative of the demand function f(p) f(p) = p + 20 f (p) = Find the elasticity of demand pf ( p) f ( p) 5 p( 4) 5 p p( 4) * p p 5p + 80 Gerald Manahan SLAC, San Antonio College,

6 Eercise 5 (Continued): p p 16 Evaluate the elasticity of demand when p = 10 p p E(10) = E(10) = 10 6 E(10) = Since the elasticity of demand is < 1, the demand is inelastic when p = 10. Gerald Manahan SLAC, San Antonio College,

Solutions to Assignment 8

Solutions to Assignment 8 Solutions to Assignment 8 12.4, 2. The graph of a typical average cost function A(x) = C(x)/x, where C(x) is a total cost function associated with the manufacture of x units of a certain commodity is shown

More information

Business and Economic Applications

Business and Economic Applications Appendi F Business and Economic Applications F1 F Business and Economic Applications Understand basic business terms and formulas, determine marginal revenues, costs and profits, find demand functions,

More information

Sec 3.5 Business and Economics Applications. Solution step1 sketch the function. step 2 The primary equation is

Sec 3.5 Business and Economics Applications. Solution step1 sketch the function. step 2 The primary equation is Sec 3.5 Business and Economics Applications rev0216 Objectives: 1. Solve business and economics optimization problems 2. Find the price elasticity of demand for demand functions. 3. Recognize basic business

More information

Price. Elasticity. Demand

Price. Elasticity. Demand + Price Elasticity of Demand + n Elasticity = measure the responsiveness of one variable to changes in another variable. n Price elasticity of demand measures the responsiveness of demand to changes in

More information

Marginal Cost. Example 1: Suppose the total cost in dollars per week by ABC Corporation for 2

Marginal Cost. Example 1: Suppose the total cost in dollars per week by ABC Corporation for 2 Math 114 Marginal Functions in Economics Marginal Cost Suppose a business owner is operating a plant that manufactures a certain product at a known level. Sometimes the business owner will want to know

More information

1 Calculus of Several Variables

1 Calculus of Several Variables 1 Calculus of Several Variables Reading: [Simon], Chapter 14, p. 300-31. 1.1 Partial Derivatives Let f : R n R. Then for each x i at each point x 0 = (x 0 1,..., x 0 n) the ith partial derivative is defined

More information

Two aspects of an elasticity are important: (1) whether it positive or negative and (2) whether it is greater than 1 or less than 1 in absolute value

Two aspects of an elasticity are important: (1) whether it positive or negative and (2) whether it is greater than 1 or less than 1 in absolute value Overview I. The Elasticity Concept - Own Price Elasticity - Elasticity and Total Revenue - Cross-Price Elasticity - Income Elasticity II. Demand Functions - Linear - Log-Linear II. Regression Analysis

More information

Labor Demand. Labor Economics VSE Praha March 2009

Labor Demand. Labor Economics VSE Praha March 2009 Labor Demand Labor Economics VSE Praha March 2009 Labor Economics: Outline Labor Supply Labor Demand Equilibrium in Labor Market et cetera Labor Demand Model: Firms Firm s role in: Labor Market consumes

More information

Graphing Nonlinear Systems

Graphing Nonlinear Systems 10.4 Graphing Nonlinear Sstems 10.4 OBJECTIVES 1. Graph a sstem of nonlinear equations 2. Find ordered pairs associated with the solution set of a nonlinear sstem 3. Graph a sstem of nonlinear inequalities

More information

Appendix B. Making Smart Choices

Appendix B. Making Smart Choices Appendix B Making Smart Choices Making Smart Choices The Law of Demand LEARNING OBJECTIVES B.1 Describe what determines your willingness to pay for a product/service B.2 Choice depends on marginal benefit,

More information

Module 2 Lecture 5 Topics

Module 2 Lecture 5 Topics Module 2 Lecture 5 Topics 2.13 Recap of Relevant Concepts 2.13.1 Social Welfare 2.13.2 Demand Curves 2.14 Elasticity of Demand 2.14.1 Perfectly Inelastic 2.14.2 Perfectly Elastic 2.15 Production & Cost

More information

Price Elasticity of Demand

Price Elasticity of Demand rice Elasticity of Demand Demand A B The percentage change in the quantity demanded given...... a one percent change in the price. rinciples of Microeconomics & rinciples of Macroeconomics: Ch. 5 First

More information

Section 3-7. Marginal Analysis in Business and Economics. Marginal Cost, Revenue, and Profit. 202 Chapter 3 The Derivative

Section 3-7. Marginal Analysis in Business and Economics. Marginal Cost, Revenue, and Profit. 202 Chapter 3 The Derivative 202 Chapter 3 The Derivative Section 3-7 Marginal Analysis in Business and Economics Marginal Cost, Revenue, and Profit Application Marginal Average Cost, Revenue, and Profit Marginal Cost, Revenue, and

More information

Price Elasticity of Demand & Supply

Price Elasticity of Demand & Supply 13 10 Price Elasticity of Demand & Supply A. Price elasticity of demand Elastic demand (Ed > 1) % change in quantity demanded > % change in price Inelastic demand (Ed < 1) % change in quantity demanded

More information

Chapter 6. Elasticity: The Responsiveness of Demand and Supply

Chapter 6. Elasticity: The Responsiveness of Demand and Supply Chapter 6. Elasticity: The Responsiveness of Demand and Supply Instructor: JINKOOK LEE Department of Economics / Texas A&M University ECON 202 504 Principles of Microeconomics Elasticity Demand curve:

More information

AP Microeconomics Chapter 12 Outline

AP Microeconomics Chapter 12 Outline I. Learning Objectives In this chapter students will learn: A. The significance of resource pricing. B. How the marginal revenue productivity of a resource relates to a firm s demand for that resource.

More information

CBE Selected-Response Questions Sample items aligned to Economics and Accounting courses. Copyright 2015 Council for Aid to Education

CBE Selected-Response Questions Sample items aligned to Economics and Accounting courses. Copyright 2015 Council for Aid to Education CBE Selected-Response Questions Sample items aligned to Economics and Accounting courses Copyright 2015 Council for Aid to Education Economics Objective Evaluate supply and demand information and apply

More information

Chapter 5 Applications of Supply and Demand

Chapter 5 Applications of Supply and Demand 1. Elasticity of Demand (E d ) Chapter 5 Applications of Supply and Demand Measures the responsiveness of Q d to a change in price. How much does Q d change (%) when P changes (%)? We can use a formula

More information

Cost-Volume-Profit Analysis

Cost-Volume-Profit Analysis Cost-Volume-Profit Analysis Cost-volume-profit (CVP) analysis is used to determine how changes in costs and volume affect a company's operating income and net income. In performing this analysis, there

More information

LINEAR INEQUALITIES. less than, < 2x + 5 x 3 less than or equal to, greater than, > 3x 2 x 6 greater than or equal to,

LINEAR INEQUALITIES. less than, < 2x + 5 x 3 less than or equal to, greater than, > 3x 2 x 6 greater than or equal to, LINEAR INEQUALITIES When we use the equal sign in an equation we are stating that both sides of the equation are equal to each other. In an inequality, we are stating that both sides of the equation are

More information

Chapter 5 Elasticity of Demand and Supply. These slides supplement the textbook, but should not replace reading the textbook

Chapter 5 Elasticity of Demand and Supply. These slides supplement the textbook, but should not replace reading the textbook Chapter 5 Elasticity of Demand and Supply These slides supplement the textbook, but should not replace reading the textbook 1 What is total revenue? Price multiplied by the quantity sold at that price

More information

Chapter 3 Quantitative Demand Analysis

Chapter 3 Quantitative Demand Analysis Managerial Economics & Business Strategy Chapter 3 uantitative Demand Analysis McGraw-Hill/Irwin Copyright 2010 by the McGraw-Hill Companies, Inc. All rights reserved. Overview I. The Elasticity Concept

More information

Basic Microeconomics. P related = the price or prices of relevant related goods. The goods considered are compliments and substitutes of good X.

Basic Microeconomics. P related = the price or prices of relevant related goods. The goods considered are compliments and substitutes of good X. Basic Microeconomics Demand is a term that represents models that eplain how a set of variables influence buyer or consumer behavior. There are two ways to perceive demand: 1) Demand is a schedule of quantities

More information

Linear Equations and Inequalities

Linear Equations and Inequalities Linear Equations and Inequalities Section 1.1 Prof. Wodarz Math 109 - Fall 2008 Contents 1 Linear Equations 2 1.1 Standard Form of a Linear Equation................ 2 1.2 Solving Linear Equations......................

More information

SECTION 1-4 Absolute Value in Equations and Inequalities

SECTION 1-4 Absolute Value in Equations and Inequalities 1-4 Absolute Value in Equations and Inequalities 37 SECTION 1-4 Absolute Value in Equations and Inequalities Absolute Value and Distance Absolute Value in Equations and Inequalities Absolute Value and

More information

2 Price Elasticity of Demand

2 Price Elasticity of Demand 1 1.1 Goals of this class Goals of this class Expand on supply and demand: how much do quantities change in responses to: changes in price? changes in income? changes in price of related goods? Learn implications

More information

5. The supply curve of a monopolist is A) upward sloping. B) nonexistent. C) perfectly inelastic. D) horizontal.

5. The supply curve of a monopolist is A) upward sloping. B) nonexistent. C) perfectly inelastic. D) horizontal. Chapter 12 monopoly 1. A monopoly firm is different from a competitive firm in that A) there are many substitutes for a monopolist's product but there are no substitutes for a competitive firm's product.

More information

Microeconomics Instructor Miller Practice Problems Monopolistic Competition

Microeconomics Instructor Miller Practice Problems Monopolistic Competition Microeconomics Instructor Miller Practice Problems Monopolistic Competition 1. A monopolistically competitive market is described as one in which there are A) a few firms producing an identical product.

More information

Identify how changes in volume affect costs

Identify how changes in volume affect costs Chapter 18 Identify how changes in volume affect Total variable change in direct proportion to changes in the volume of activity Unit variable cost remains constant Units produced 3 5 Total direct materials

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. MBA 640 Survey of Microeconomics Fall 2006, Quiz 6 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A monopoly is best defined as a firm that

More information

10/1/2011 25% 25% 25% 25% Impact of lower price on total consumer expenditures or a firm s total revenue

10/1/2011 25% 25% 25% 25% Impact of lower price on total consumer expenditures or a firm s total revenue Micro Chapter 7 Consumer Choice and Elasticity This chapter is an extension of the first part of Chapter 3 on demand and consumer theory Refer back to your Chapter 3 notes and mentally combine them with

More information

2011 Pearson Education. Elasticities of Demand and Supply: Today add elasticity and slope, cross elasticities

2011 Pearson Education. Elasticities of Demand and Supply: Today add elasticity and slope, cross elasticities 2011 Pearson Education Elasticities of Demand and Supply: Today add elasticity and slope, cross elasticities What Determines Elasticity? Influences on the price elasticity of demand fall into two categories:

More information

Measuring Elasticity of Demand

Measuring Elasticity of Demand C H A P T E R E I G H T P r i c e e l a s t i c i t y o f d e m a n d Measuring Elasticity of Demand Demand curves can have many different shapes and so it is important to derive a way to convey their

More information

Elasticity of Demand and Supply

Elasticity of Demand and Supply Elasticity of Demand and Supply Price Elasticity of Demand (Ep) Calculating Percentage Change Significance of Price Elasticity of Demand (Ep) Determinants of Price Elasticity of Demand (Ep) For Next Time

More information

5.2 Percent: Converting Between Fractions, Decimals, and Percents

5.2 Percent: Converting Between Fractions, Decimals, and Percents 5.2 Percent: Converting Between Fractions, Decimals, and Percents The concept of percent permeates most common uses of mathematics in everyday life. We pay taes based on percents, many people earn income

More information

Microeconomics Instructor Miller Practice Problems Labor Market

Microeconomics Instructor Miller Practice Problems Labor Market Microeconomics Instructor Miller Practice Problems Labor Market 1. What is a factor market? A) It is a market where financial instruments are traded. B) It is a market where stocks and bonds are traded.

More information

5. Equations of Lines: slope intercept & point slope

5. Equations of Lines: slope intercept & point slope 5. Equations of Lines: slope intercept & point slope Slope of the line m rise run Slope-Intercept Form m + b m is slope; b is -intercept Point-Slope Form m( + or m( Slope of parallel lines m m (slopes

More information

Question 2: How are derivatives used to compute elasticity?

Question 2: How are derivatives used to compute elasticity? Question : How are derivatives used to compute elasticity? In economics, the term elasticity refers to the responsiveness of one economic variable to changes in another economic variable. The elasticity

More information

ECON 103, 2008-2 ANSWERS TO HOME WORK ASSIGNMENTS

ECON 103, 2008-2 ANSWERS TO HOME WORK ASSIGNMENTS ECON 103, 2008-2 ANSWERS TO HOME WORK ASSIGNMENTS Due the Week of June 23 Chapter 8 WRITE [4] Use the demand schedule that follows to calculate total revenue and marginal revenue at each quantity. Plot

More information

Quadratic Functions and Parabolas

Quadratic Functions and Parabolas MATH 11 Quadratic Functions and Parabolas A quadratic function has the form Dr. Neal, Fall 2008 f () = a 2 + b + c where a 0. The graph of the function is a parabola that opens upward if a > 0, and opens

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Chapter 11 Monopoly practice Davidson spring2007 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A monopoly industry is characterized by 1) A)

More information

A Detailed Price Discrimination Example

A Detailed Price Discrimination Example A Detailed Price Discrimination Example Suppose that there are two different types of customers for a monopolist s product. Customers of type 1 have demand curves as follows. These demand curves include

More information

volume-profit relationships

volume-profit relationships Slide 1.3.1 1. Accounting for decision making 1.3 Cost-volume volume-profit relationships Slide 1.3.2 Introduction This chapter examines one of the most basic planning tools available to managers: cost

More information

EconS 301 Review Session #8 Chapter 11: Monopoly and Monopsony

EconS 301 Review Session #8 Chapter 11: Monopoly and Monopsony EconS 301 Review Session #8 Chapter 11: Monopoly and Monopsony 1. Which of the following describes a correct relation between price elasticity of demand and a monopolist s marginal revenue when inverse

More information

a. Meaning: The amount (as a percentage of total) that quantity demanded changes as price changes. b. Factors that make demand more price elastic

a. Meaning: The amount (as a percentage of total) that quantity demanded changes as price changes. b. Factors that make demand more price elastic Things to know about elasticity. 1. Price elasticity of demand a. Meaning: The amount (as a percentage of total) that quantity demanded changes as price changes. b. Factors that make demand more price

More information

Fixed costs. Contribution margin ratio

Fixed costs. Contribution margin ratio SOLUTIONS TO EXERCISES EXERCISE 3-1 (20 minutes) 1. Fixed costs B E point in units = Contribution margin per unit $180,000 $180,000 = = = 7,500 units $40 - $16 $24 B E point in sales dollars = Fixed costs

More information

AP MICRO Week 4 Practice Quiz: M, 20

AP MICRO Week 4 Practice Quiz: M, 20 1 1. A marketing survey shows that gate receipts would increase if the price of tickets to a summer rock concert increased, even though the number of tickets sold would fall. What does this imply about

More information

Microeconomics and mathematics (with answers) 5 Cost, revenue and profit

Microeconomics and mathematics (with answers) 5 Cost, revenue and profit Microeconomics and mathematics (with answers) 5 Cost, revenue and profit Remarks: = uantity Costs TC = Total cost (= AC * ) AC = Average cost (= TC ) MC = Marginal cost [= (TC)'] FC = Fixed cost VC = (Total)

More information

Chapter 9: Perfect Competition

Chapter 9: Perfect Competition Chapter 9: Perfect Competition Perfect Competition Law of One Price Short-Run Equilibrium Long-Run Equilibrium Maximize Profit Market Equilibrium Constant- Cost Industry Increasing- Cost Industry Decreasing-

More information

9.3 OPERATIONS WITH RADICALS

9.3 OPERATIONS WITH RADICALS 9. Operations with Radicals (9 1) 87 9. OPERATIONS WITH RADICALS In this section Adding and Subtracting Radicals Multiplying Radicals Conjugates In this section we will use the ideas of Section 9.1 in

More information

Name Date. Break-Even Analysis

Name Date. Break-Even Analysis Name Date Break-Even Analsis In our business planning so far, have ou ever asked the questions: How much do I have to sell to reach m gross profit goal? What price should I charge to cover m costs and

More information

John Kennan University of Wisconsin-Madison October, 1998

John Kennan University of Wisconsin-Madison October, 1998 The Hicks-Marshall Rules of Derived Demand: An Expository Note John Kennan University of Wisconsin-Madison October, 1998 1. "The demand for anything is likely to be more elastic, the more readily substitutes

More information

OVERVIEW. 2. If demand is vertical, demand is perfectly inelastic. Every change in price brings no change in quantity.

OVERVIEW. 2. If demand is vertical, demand is perfectly inelastic. Every change in price brings no change in quantity. 7 PRICE ELASTICITY OVERVIEW 1. The elasticity of demand measures the responsiveness of 1 the buyer to a change in price. The coefficient of price elasticity is the percentage change in quantity divided

More information

NAME: INTERMEDIATE MICROECONOMIC THEORY SPRING 2008 ECONOMICS 300/010 & 011 Midterm II April 30, 2008

NAME: INTERMEDIATE MICROECONOMIC THEORY SPRING 2008 ECONOMICS 300/010 & 011 Midterm II April 30, 2008 NAME: INTERMEDIATE MICROECONOMIC THEORY SPRING 2008 ECONOMICS 300/010 & 011 Section I: Multiple Choice (4 points each) Identify the choice that best completes the statement or answers the question. 1.

More information

PROBLEM SET#3 PART I: MULTIPLE CHOICE

PROBLEM SET#3 PART I: MULTIPLE CHOICE 1 PROBLEM SET#3 PART I: MULTIPLE CHOICE 1. In general, elasticity is a measure of a. the extent to which advances in technology are adopted by producers. b. the extent to which a market is competitive.

More information

Solutions to Homework Problems for Basic Cost Behavior by David Albrecht

Solutions to Homework Problems for Basic Cost Behavior by David Albrecht Solutions to Homework Problems for Basic Cost Behavior by David Albrecht Solution to Problem #11 This problem focuses on being able to work with both total cost and average per unit cost. As a brief review,

More information

Applications of Linear Equations. Chapter 5

Applications of Linear Equations. Chapter 5 5-2 Applications of Linear Equations Chapter 5 5-3 After completing this chapter, you will be able to: > Solve two linear equations in two variables > Solve problems that require setting up two linear

More information

Simplification of Rational Expressions and Functions

Simplification of Rational Expressions and Functions 7.1 Simplification of Rational Epressions and Functions 7.1 OBJECTIVES 1. Simplif a rational epression 2. Identif a rational function 3. Simplif a rational function 4. Graph a rational function Our work

More information

(P 2 P 1 )/[(P 1 + P 2 )/2]. It shows how flexible sellers are to a change in price.

(P 2 P 1 )/[(P 1 + P 2 )/2]. It shows how flexible sellers are to a change in price. September 15, 2008 Elasticity of supply The price elasticity of supply measures how quantity offered of a good responds to a change in the good s price. It is defined the same as price elasticity of demand,

More information

Merchandise Accounts. Chapter 7 - Unit 14

Merchandise Accounts. Chapter 7 - Unit 14 Merchandise Accounts Chapter 7 - Unit 14 Merchandising... Merchandising... There are many types of companies out there Merchandising... There are many types of companies out there Service company - sells

More information

Objectives. By the time the student is finished with this section of the workbook, he/she should be able

Objectives. By the time the student is finished with this section of the workbook, he/she should be able QUADRATIC FUNCTIONS Completing the Square..95 The Quadratic Formula....99 The Discriminant... 0 Equations in Quadratic Form.. 04 The Standard Form of a Parabola...06 Working with the Standard Form of a

More information

Lecture 2. Marginal Functions, Average Functions, Elasticity, the Marginal Principle, and Constrained Optimization

Lecture 2. Marginal Functions, Average Functions, Elasticity, the Marginal Principle, and Constrained Optimization Lecture 2. Marginal Functions, Average Functions, Elasticity, the Marginal Principle, and Constrained Optimization 2.1. Introduction Suppose that an economic relationship can be described by a real-valued

More information

GRE MATH REVIEW #5. 1. Variable: A letter that represents an unknown number.

GRE MATH REVIEW #5. 1. Variable: A letter that represents an unknown number. GRE MATH REVIEW #5 Eponents and Radicals Many numbers can be epressed as the product of a number multiplied by itself a number of times. For eample, 16 can be epressed as. Another way to write this is

More information

Algebra Concept-Readiness Test, Form A

Algebra Concept-Readiness Test, Form A Algebra Concept-Readiness Test, Form A Concept : The Distributive Property Study the concept, and then answer the test questions on the net page. You can use the distributive property to simplify an epression

More information

Elasticities of Demand and Supply

Elasticities of Demand and Supply 1 CHAPTER CHECKLIST Elasticities of Demand and Supply Chapter 5 1. Define, explain the factors that influence, and calculate the price elasticity of demand. 2. Define, explain the factors that influence,

More information

UNIT 6 cont PRICING UNDER DIFFERENT MARKET STRUCTURES. Monopolistic Competition

UNIT 6 cont PRICING UNDER DIFFERENT MARKET STRUCTURES. Monopolistic Competition UNIT 6 cont PRICING UNDER DIFFERENT MARKET STRUCTURES Monopolistic Competition Market Structure Perfect Competition Pure Monopoly Monopolistic Competition Oligopoly Duopoly Monopoly The further right on

More information

Problems 1-21 could be on the no Derive part. Sections 1.2, 2.2, 2.3, 3.1, 3.3, 3.4, 4.1, 4.2

Problems 1-21 could be on the no Derive part. Sections 1.2, 2.2, 2.3, 3.1, 3.3, 3.4, 4.1, 4.2 MTH 120 Practice Test #1 Sections 1.2, 2.2, 2.3, 3.1, 3.3, 3.4, 4.1, 4.2 Use the properties of limits to help decide whether the limit eists. If the limit eists, find its value. 1) lim 5 2) lim 3 2-25

More information

Chapter 4. Elasticity

Chapter 4. Elasticity Chapter 4 Elasticity -comparative static exercises in the supply and demand model give us the direction of changes in equilibrium prices and quantities -sometimes we want to know more we want to know about

More information

COST-VOLUME-PROFIT RELATIONSHIPS

COST-VOLUME-PROFIT RELATIONSHIPS TM 5-1 COST-VOLUME-PROFIT RELATIONSHIPS Cost-volume-profit (CVP) analysis is concerned with the effects on net operating income of: Selling prices. Sales volume. Unit variable costs. Total fixed costs.

More information

Domain of a Composition

Domain of a Composition Domain of a Composition Definition Given the function f and g, the composition of f with g is a function defined as (f g)() f(g()). The domain of f g is the set of all real numbers in the domain of g such

More information

Math 130 Winter 2010 Quotient/Product/Chain Rule Practice January 28, 2010

Math 130 Winter 2010 Quotient/Product/Chain Rule Practice January 28, 2010 Math Winter 0 Quotient/Product/Chain Rule Practice January 8, 0 1. Find the derivative of the following functions: a) gx) = x + 4x) 5 + x x + 1. To do this problem we treat each part seperately. F the

More information

Tools for Project Evaluation. Nathaniel Osgood 1.040/1.401J 2/11/2004

Tools for Project Evaluation. Nathaniel Osgood 1.040/1.401J 2/11/2004 Tools for Project Evaluation Nathaniel Osgood 1.040/1.401J 2/11/2004 Basic Compounding Suppose we invest $x in a bank offering interest rate i If interest is compounded annually, asset will be worth $x(1+i)

More information

Math 1314 Lesson 8: Business Applications: Break Even Analysis, Equilibrium Quantity/Price

Math 1314 Lesson 8: Business Applications: Break Even Analysis, Equilibrium Quantity/Price Math 1314 Lesson 8: Business Applications: Break Even Analysis, Equilibrium Quantity/Price Cost functions model the cost of producing goods or providing services. Examples: rent, utilities, insurance,

More information

Online Review Copy. AP Micro Chapter 8 Test. Multiple Choice Identify the choice that best completes the statement or answers the question.

Online Review Copy. AP Micro Chapter 8 Test. Multiple Choice Identify the choice that best completes the statement or answers the question. AP Micro Chapter 8 Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. There would be some control over price within rather narrow limits in which market

More information

MFP SET. Lecture 3 Surplus: Consumer & producer Elasticity & its applications MFP SET 2000 1

MFP SET. Lecture 3 Surplus: Consumer & producer Elasticity & its applications MFP SET 2000 1 MFP SET Lecture 3 Surplus: Consumer & producer Elasticity & its applications MFP SET 1 Consumer surplus! Willingness to pay: the maximum amount that a consumer will pay for a good! Consumer surplus: the

More information

Rutgers University Economics 102: Introductory Microeconomics Professor Altshuler Fall 2003

Rutgers University Economics 102: Introductory Microeconomics Professor Altshuler Fall 2003 Rutgers University Economics 102: Introductory Microeconomics Professor Altshuler Fall 2003 Answers to Problem Set 10 Chapter 15 1. The following table shows revenue, costs, and profits, where quantities

More information

CE 231 NOMINAL AND EFFECTIVE INTEREST RATE STATEMENTS. r = interest rate per period x number of periods

CE 231 NOMINAL AND EFFECTIVE INTEREST RATE STATEMENTS. r = interest rate per period x number of periods CE 231 NOMINAL AND EFFECTIVE INTEREST RATE STATEMENTS The primary difference between simple and compound interest is that compound interest includes interest on the interest earned in the previous record,

More information

1 of 20 12/1/2013 1:02 PM

1 of 20 12/1/2013 1:02 PM 1 of 20 12/1/2013 1:02 PM The willingness to work a certain amount of time at a given wage rate is known as Labor supply. Labor Derived supply. Derived Labor supply is the willingness and ability to work

More information

Solving Quadratic Equations by Graphing. Consider an equation of the form. y ax 2 bx c a 0. In an equation of the form

Solving Quadratic Equations by Graphing. Consider an equation of the form. y ax 2 bx c a 0. In an equation of the form SECTION 11.3 Solving Quadratic Equations b Graphing 11.3 OBJECTIVES 1. Find an ais of smmetr 2. Find a verte 3. Graph a parabola 4. Solve quadratic equations b graphing 5. Solve an application involving

More information

Saints Christmas Trees Pricing Analysis Michael Pepe, Siena College, USA Arindam Mandal, Siena College, USA

Saints Christmas Trees Pricing Analysis Michael Pepe, Siena College, USA Arindam Mandal, Siena College, USA Saints Christmas Trees Pricing Analysis Michael Pepe, Siena College, USA Arindam Mandal, Siena College, USA ABSTRACT This teaching case and assignment pertains to various areas of pricing analysis that

More information

Chapter. Cost-Volume-Profit Relationships

Chapter. Cost-Volume-Profit Relationships Chapter 6 Cost-Volume-Profit Relationships 6-2 LEARNING OBJECTIVES After studying this chapter, you should be able to: 1. Explain how changes in activity affect contribution margin. 2. Compute the contribution

More information

Math 141 Final Exam Review

Math 141 Final Exam Review Math 141 Final Eam Review Problems appearing on your in-class final will be similar to those here but will have numbers and functions changed. 1. (.1) Use the graph below to find the following: a) lim

More information

Oligopoly. What Is Oligopoly? What is Oligopoly?

Oligopoly. What Is Oligopoly? What is Oligopoly? CHAPTER 13B After studying this chapter you will be able to Oligopoly Define and identify oligopoly Explain two traditional oligopoly models Use game theory to explain how price and output are determined

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Chapter 11 Perfect Competition - Sample Questions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Perfect competition is an industry with A) a

More information

Price Elasticity of Demand

Price Elasticity of Demand 04 Elasticity Price Elasticity of Demand Measures buyers responsiveness to price changes Elastic demand Sensitive to price changes Large change in quantity Inelastic demand Insensitive to price changes

More information

Elasticity. Demand is inelastic if it does not respond much to price changes, and elastic if demand changes a lot when the price changes.

Elasticity. Demand is inelastic if it does not respond much to price changes, and elastic if demand changes a lot when the price changes. Elasticity The price elasticity of demand measures the sensitivity of the quantity demanded to changes in the price. Demand is inelastic if it does not respond much to price changes, and elastic if demand

More information

Solutions of Linear Equations in One Variable

Solutions of Linear Equations in One Variable 2. Solutions of Linear Equations in One Variable 2. OBJECTIVES. Identify a linear equation 2. Combine like terms to solve an equation We begin this chapter by considering one of the most important tools

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question on the accompanying scantron.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question on the accompanying scantron. Principles of Microeconomics Fall 2007, Quiz #6 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question on the accompanying scantron. 1) A monopoly is

More information

Principles of Economics: Micro: Exam #2: Chapters 1-10 Page 1 of 9

Principles of Economics: Micro: Exam #2: Chapters 1-10 Page 1 of 9 Principles of Economics: Micro: Exam #2: Chapters 1-10 Page 1 of 9 print name on the line above as your signature INSTRUCTIONS: 1. This Exam #2 must be completed within the allocated time (i.e., between

More information

Section B. Some Basic Economic Concepts

Section B. Some Basic Economic Concepts This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License. Your use of this material constitutes acceptance of that license and the conditions of use of materials on this

More information

Find the competitive equilibrium. The competitive equilibrium is where supply equals demand. Since MC=S, where MC = 2Q/3

Find the competitive equilibrium. The competitive equilibrium is where supply equals demand. Since MC=S, where MC = 2Q/3 Problem Set #13-Key Sonoma State University Economics 305-Intermediate Microeconomic Theory Dr. Cuellar (1) Consider the following demand and cost functions for a monopolistic firm. The industry demand

More information

Elasticity. Definition of the Price Elasticity of Demand: Formula for Elasticity: Types of Elasticity:

Elasticity. Definition of the Price Elasticity of Demand: Formula for Elasticity: Types of Elasticity: Elasticity efinition of the Elasticity of emand: The law of demand states that the quantity demanded of a good will vary inversely with the price of the good during a given time period, but it does not

More information

11 PERFECT COMPETITION. Chapter. Competition

11 PERFECT COMPETITION. Chapter. Competition Chapter 11 PERFECT COMPETITION Competition Topic: Perfect Competition 1) Perfect competition is an industry with A) a few firms producing identical goods B) a few firms producing goods that differ somewhat

More information

N. Gregory Mankiw Principles of Economics. Chapter 15. MONOPOLY

N. Gregory Mankiw Principles of Economics. Chapter 15. MONOPOLY N. Gregory Mankiw Principles of Economics Chapter 15. MONOPOLY Solutions to Problems and Applications 1. The following table shows revenue, costs, and profits, where quantities are in thousands, and total

More information

Section 2.5 Average Rate of Change

Section 2.5 Average Rate of Change Section.5 Average Rate of Change Suppose that the revenue realized on the sale of a company s product can be modeled by the function R( x) 600x 0.3x, where x is the number of units sold and R( x ) is given

More information

1-3 Absolute Value in Equations and Inequalities

1-3 Absolute Value in Equations and Inequalities SECTION 1 3 Absolute Value in Equations and Inequalities 103 1-3 Absolute Value in Equations and Inequalities Z Relating Absolute Value and Distance Z Solving Absolute Value Equations and Inequalities

More information

Chapter 6: Break-Even & CVP Analysis

Chapter 6: Break-Even & CVP Analysis HOSP 1107 (Business Math) Learning Centre Chapter 6: Break-Even & CVP Analysis One of the main concerns in running a business is achieving a desired level of profitability. Cost-volume profit analysis

More information

Learning Objectives for Section 1.1 Linear Equations and Inequalities

Learning Objectives for Section 1.1 Linear Equations and Inequalities Learning Objectives for Section 1.1 Linear Equations and Inequalities After this lecture and the assigned homework, you should be able to solve linear equations. solve linear inequalities. use interval

More information

Elasticity and Its Application

Elasticity and Its Application Elasticity and Its Application Chapter 5 All rights reserved. Copyright 2001 by Harcourt, Inc. Requests for permission to make copies of any part of the work should be mailed to: Permissions Department,

More information