Math for Economists
Purpose of Course showclose
Math for Economists will help you assemble a toolkit of skills and techniques to solve fundamental problems in both macroeconomics and microeconomics. The material covers both precalculus and calculus concepts and should help you identify the best approach to solving problems. For example, an economist may be called upon to determine the right mix allocation of capital to a production process. The tools in this course will help you evaluate the options and select from the best alternatives. Advanced courses in economics typically utilize mathematical techniques beyond basic calculus; so, gaining practice in fundamental skills can serve as a good basis for further study. Of note, this course applies precalculus and calculus; this is different from “applied math,” which economists typically use to refer to probability and statistics.
This course begins with a survey of basic optimization tools and then applies them to solve problems over several periods in time. These optimization tools describe feasible choices and then direct you to the best possible solution. In essence, they will help you evaluate an economic environment and determine the best course of action. The role of risk in financial decisions is explored in relation to individual choices and macroeconomic processes. The equitable distribution of resources is then considered. In other words, this class will explore whether an optimal solution is indeed also fair to the participants and society. A specific application, game theory, is presented as one of the major recent advances in economic theory. The final topic returns to microeconomic problems such as taxes, elasticity, and specific types of supply and demand curves.
The materials included in the course offer a framework that you can use to apply quantitative skills. You should liberally use Saylor course materials (MA001, MA003, MA005, ECON103/MA101, and MA102) to refresh their general techniques. This course fits into the major as a bridge between quantitative theory and specific applications to problems in economics. Completing this course can greatly help students successfully build a toolkit for the intermediate courses, ECON201 and ECON202.
Course Information showclose
Course Designer: Professor Tony Pizur
Primary Resources: This course comprises a range of different free, online materials. However, the course makes primary use of the following:
 YouTube: Yale University, Department of Economics Lectures
 Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02
 Khan Academy “Economics Videos”
 Unit 1 SelfTest
 Unit 2 SelfTest
 Unit 3 SelfTest
 Unit 4 SelfTest
 Unit 5 SelfTest
 Unit 6 SelfTest
In order to pass this course, you will need to earn a 70% or higher on the Final Exam. Your score on the exam will be tabulated as soon as you complete it. If you do not pass the exam, you may take it again.
Time Commitment: This course should take you a total of approximately 84.25 hours to complete. Each unit includes a time advisory that lists the amount of time you are expected to spend on each subunit and assignment. These time advisories should help you plan your time accordingly. It may be useful to take a look at the time advisories before beginning this course in order to determine how much time you have over the next few weeks to complete each unit. Then, you can set goals for yourself. For example, Unit 1 should take you approximately 29 hours to complete. Perhaps you can sit down with your calendar and decide to complete Subunit 1.1 (a total of 10.75 hours) on Monday and Tuesday night, Subunit 1.2 (a total of 9.5 hours) on Wednesday and Thursday night, etc.
Tips/Suggestions: It is extremely important that you give each assignment the amount of reading and review necessary to grasp the main points and lines of enquiry. Also, on completing the assessments, take a moment to consider how the materials you have just studied relate to the topics covered in previous sections of the course.
Course Requirements showclose
√ have access to a computer;
√ have continuous broadband Internet access;
√ have the ability/permission to install plugins or software (e.g., Adobe Reader or Flash);
√ have the ability to download and save files and documents to a computer;
√ have the ability to open Microsoft files and documents (.doc, .ppt, .xls, etc.);
√ be competent in the English language;
√ have read the Saylor Student Handbook; and
√ have completed MA101: SingleVariable Calculus I. MA103: Multivariable Calculus is strongly recommended, though not required, prior to completion of this course.
Unit Outline show close
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Unit 1: Basic Tools of Optimization in Economics
Economics can be described as the study of how individuals, firms, and governments make the best choice among competing alternatives. Individuals seek to maximize utility or happiness, firms want to maximize profits, and governments attempt to maximize social wellbeing. Sometimes the possible and expected consequences of a choice can be quantified to help rank and determine the best, or optimal, selection. Economists use a variety of quantitative tools to evaluate alternatives, and this unit will build a foundation of basic optimization techniques. Calculus techniques are the primary methods in an economist’s toolkit.
Unit 1 Time Advisory show close
Calculus can be used to model most marginal decisions because derivatives measure the instantaneous rate of change. In other words, calculus describes what happens when we change “just a little more” of some variable in a process. Economists can then examine the whole range of choices – considering just a little bit more and more – until all options have been exhausted to determine the optimal one. Using advanced calculus, economists can isolate a single variable or input so that decisions can be broken down into their constituent components.
A good visual way of describing marginal choices is a decision tree. Decision trees map a formal process of possible expected outcomes of a decision. Their main value is identifying secondary and tertiary consequences of a choice. The additional, or marginal, benefits and costs at each step in the decision process can be clearly assigned. As a measure of risk, probabilities for possible outcomes can be calculated to help the decision maker identify the most likely scenarios. Remember that decision trees can be used to model almost any rational choice process.
Unit 1 Learning Outcomes show close

1.1 Decision Theory
 Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 1: Decision Theory”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 1: Decision Theory” (PDF)
Instructions: Read pages 13–28. Note that this reading covers the material you need to know for subunits 1.1–1.3.
Reading this chapter should take approximately 30 minutes.
Terms of Use: The resource above is licensed under a Creative Commons AttributionNonCommercial 3.0 License. It is attributed to Yoram Bauman, and the original version can be found here.
 Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 1: Decision Theory”

1.1.1 Individual Choice Optimization
Note: This subunit is covered by the reading assigned beneath subunit 1.1. Focus specifically on page 14 for a quick synopsis of individual choice optimization.
 Lecture: iTunes U: University of California, Berkeley’s Department of Economics: Glenn Woroch’s “Lecture 3” and “Lecture 5”
Link: iTunes U: University of California, Berkeley’s Department of Economics: Glenn Woroch’s “Lecture 3” and “Lecture 5” (iTunes)
Instructions: Click on the “View in iTunes” hyperlink for “Lecture 3” and “Lecture 5.”
Listening to the two lectures in their entirety should take approximately 2 hours.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: iTunes U: University of California, Berkeley’s Department of Economics: Glenn Woroch’s “Lecture 3” and “Lecture 5”

1.1.2 Firm Choice Optimization
Note: This subunit is covered by the reading assigned beneath subunit 1.1. Focus specifically on page 14 for a quick synopsis of firm choice optimization.
 Lecture: iTunes U: University of California, Berkeley’s Department of Economics: Glenn Woroch’s “Lecture 9”
Link: iTunes U: University of California, Berkeley’s Department of Economics: Glenn Woroch’s “Lecture 9” (iTunes)
Instructions: Click on the “View in iTunes” hyperlink for “Lecture 9.”
Listening to the entire lecture should take approximately 1 hour and 20 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: iTunes U: University of California, Berkeley’s Department of Economics: Glenn Woroch’s “Lecture 9”

1.2 Decision Trees
Note: This subunit is covered by the reading assigned beneath subunit 1.1. Focus specifically on pages 15–18 for a quick synopsis of decision trees.
 Web Media: YouTube: Knowledge Horizon: “Apply the Decision Tree Analysis Technique”
Link: YouTube: Knowledge Horizon: “Apply the Decision Tree Analysis Technique” (YouTube)
Instructions: Review this entire presentation. Consider the role of decision trees in selecting an optimal outcome. What role does marginal analysis play?
Watching this presentation should take approximately 5 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Web Media: YouTube: Knowledge Horizon: “Apply the Decision Tree Analysis Technique”

1.3 Optimization and Calculus
Note: This subunit is covered by the reading assigned beneath subunit 1.1. Focus specifically on pages 18–23 for an overview of key tools from calculus.
 Lecture: YouTube: Worldwide Center of Mathematics: “Worldwide Calculus: Optimization”
Link: YouTube: Worldwide Center of Mathematics: “Worldwide Calculus: Optimization” (YouTube)
Instructions: This link will directly bring you to a lecture about how calculus can be applied to optimization problems in economics. This video applies derivatives and their applications. If you need to brush up on your derivatives, you may want to first view the materials under subunits 1.3.1 to 1.3.4.
Watching this lecture should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: YouTube: Worldwide Center of Mathematics: “Worldwide Calculus: Optimization”

1.3.1 Derivatives
 Web Media: YouTube: Khan Academy’s “Calculus: Derivatives 1 (new HD version),” “Calculus: Derivatives 2 (new HD version),” and “Calculus: Derivatives 2.5 (new HD version)”
Link: YouTube: Khan Academy’s “Calculus: Derivatives 1 (new HD version)”, “Calculus: Derivatives 2 (new HD version)”, and “Calculus: Derivatives 2.5 (new HD version)” (YouTube)
Instructions: The above link will bring you to a video lecture about derivatives.
Watching these videos should take approximately 40 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Web Media: YouTube: Khan Academy’s “Calculus: Derivatives 1 (new HD version),” “Calculus: Derivatives 2 (new HD version),” and “Calculus: Derivatives 2.5 (new HD version)”

1.3.2 Partial Derivatives
 Web Media: YouTube: Khan Academy’s “Partial Derivatives” and “Partial Derivatives 2”
Link: YouTube: Khan Academy’s “Partial Derivatives” and “Partial Derivatives 2” (YouTube)
Instructions: The above link will bring you to a video lecture about partial derivatives.
Watching these videos should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Web Media: YouTube: Khan Academy’s “Partial Derivatives” and “Partial Derivatives 2”

1.3.3 Integration
 Web Media: YouTube: Khan Academy’s “The Indefinite Integral or AntiDerivative” and “Introduction to Definite Integrals”
Link: YouTube: Khan Academy’s “The Indefinite Integral or AntiDerivative” and “Introduction to Definite Integrals” (YouTube)
Instructions: The above link will bring you to a video lecture about opportunity costs.
Watching these videos should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Web Media: YouTube: Khan Academy’s “The Indefinite Integral or AntiDerivative” and “Introduction to Definite Integrals”

1.3.4 Application of Derivatives
 Web Media: YouTube: Khan Academy’s “Optimization Example 4”
Link: YouTube: Khan Academy’s “Optimization Example 4” (YouTube)
Instructions: The above link will bring you to a video lecture about an example of optimization.
Watching this video should take approximately 10 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 1 Problems”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 1 Problems” (PDF)
Instructions: Please go to the webpage and locate the Downloads section. Under “Quantum Microeconomics with calculus,” click on the “entire textbook” link to download the material. This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website. Complete problems C1.1–C1.12 on pages 24–27 in chapter 1.
Completing this assessment should take approximately 2 hours.
Solutions: Answers are in the endnotes beginning on page 227.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: University of Exeter: Juliette Stephenson’s WEBpages for the course BEE 1024: Mathematics for Economists: “Week 2 Exercises”
Link: University of Exeter: Juliette Stephenson’s WEBpages for the course BEE 1024: Mathematics for Economists: “Week 2 Exercises” (PDF)
Instructions: Please go to the webpage and locate the “Material for 2008” section. Under “Week 2,” click on the “Class exercises” and “Homework exercises” links to download the material. This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website. Complete all the problems.
Completing this assessment should take approximately 1 hour.
Solutions: Answers are available under “Week 2” and by clicking on “Solutions to class exercises” and “Solutions to homework exercises.”
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: The Saylor Foundation’s “Unit 1 SelfTest”
Link: The Saylor Foundation’s “Unit 1 SelfTest”
Instructions: Please complete these 10 multiple choice questions by selecting the best possible answer of those provided. It may be helpful to have pencil and paper available so you can sketch out and solve some of the problems.
Completing this assessment should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Web Media: YouTube: Khan Academy’s “Optimization Example 4”

Unit 2: Temporal Optimization
Humans perceive their environment in four dimensions. The first three – length, width, and height – define our physical universe. We can pinpoint any location using those three coordinates. The fourth dimension, time, is perceived as moving linearly in one direction. Humans can observe how things change over time, and economists try to explain and predict these changes using quantitative tools.
Unit 2 Time Advisory show close
The relative value of an asset will change over time. Some assets, like gold, remain fairly unchanged, while others decay, like a wood house. Even when assets don’t decay, their relative value to goods and services may change. For example, an ounce gold coin purchased in 2006 was worth about $600 and more than doubled in value in 2010. Present value calculations are used to figure out how much less (or more) an asset will be worth at a future time. These are important calculations for anyone saving their income.
How assets change over time has broader implications for whole societies. Economic growth models assume that investments in capital depreciate over time, and a sustainable growth pattern requires the correct rate of capital replacement. While simple models may explain growth over two periods, more dynamic ones explain changes over generations or even whole empires. Remember that economists try to assist people to make optimal choices not only today but also well into the future.
Unit 2 Learning Outcomes show close

2.1 Present Value
 Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 2: Optimization over Time”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 2: Optimization over Time” (PDF)
Instructions: Read pages 29–42. Note this reading also covers the material you need to know for subunits 2.1–2.3.
Reading this chapter should take approximately 1 hour.
Terms of Use: The above reading is licensed under a Creative Commons AttributionNonCommercial 3.0 License. It is attributed to Yoram Bauman, and the original version can be found here.  Lecture: YouTube: Yale University, Department of Economics: John Geanakoplos’ “05: Present Value Prices and the Real Rate of Interest”
Link: YouTube: Yale University, Department of Economics: John Geanakoplos’ “05: Present Value Prices and the Real Rate of Interest” (YouTube)
Also Available in:
Flash, HTML, MP3 or QuickTime
iTunes U
Instructions: Watch the entire lecture.
Watching this lecture should take approximately 1 hour and 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 2: Optimization over Time”

2.2 Distributions
Note: This subunit is covered by the reading assigned beneath subunit 2.1. Focus specifically on pages 30–32 for a discussion of lump sums, perpetuities, and annuities.
 Lecture: YouTube: Yale University, Department of Economics: John Geanakoplos’ “10: Dynamic Present Value”
Link: YouTube: Yale University, Department of Economics: John Geanakoplos’ “10: Dynamic Present Value” (YouTube)
Also Available in:
Flash, HTML, MP3 or QuickTime
iTunes U
Instructions: Watch the entire lecture.
Watching this lecture should take approximately 1 hour and 10 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 2 Problems”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 2 Problems” (PDF)
Instructions: Please go to the webpage and locate the Downloads section. Under “Quantum Microeconomics with calculus,” click on the “entire textbook” link to download the material. This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website. Complete problems 2.1–2.13 on pages 38–42 of chapter 2.
Completing this assessment should take approximately 2 hours.
Solutions: Answers are in the endnotes beginning on page 230.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: University of Exeter: Juliette Stephenson’s WEBpages for the course BEE 1024: Mathematics for Economists: “Week 6 Exercises”
Link: University of Exeter: Juliette Stephenson’s WEBpages for the course BEE 1024: Mathematics for Economists: “Week 6 Exercises” (PDF)
Instructions: Please go to the webpage and locate the Downloads section. Under “Week 6,” click on the “Class exercises” and “Homework exercises” links to download the material. This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website. Complete questions 1–5.
Completing this assessment should take approximately 60 minutes.
Solutions: Answers are available under “Week 6” and by clicking on “Solutions to class exercises” and “Solutions to homework exercises.” This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: YouTube: Yale University, Department of Economics: John Geanakoplos’ “10: Dynamic Present Value”

2.3 Applications of Concepts – Organic Growth Model
 Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 3: Math: Trees and Fish”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 3: Math: Trees and Fish” (PDF)
Instructions: Read pages 43–52.
Reading this chapter should take approximately 30 minutes.
Terms of Use: The above reading is licensed under a Creative Commons AttributionNonCommercial 3.0 License. It is attributed to Yoram Bauman, and the original version can be found here.  Lecture: YouTube: Yale University, Department of Economics: John Geanakoplos’ “12: Overlapping Generations Model of the Economy.”
Link: YouTube: Yale University, Department of Economics: John Geanakoplos’ “12: Overlapping Generations Model of the Economy” (YouTube)
Also Available in:
Flash, HTML, MP3 or QuickTime
iTunes U
Instructions: Watch the entire lecture.
Watching this lecture should take approximately 1 hour and 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 3 Problems”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 3 Problems” (PDF)
Instructions: Please go to the webpage and locate the Downloads section. Under “Quantum Microeconomics with calculus,” click on the “entire textbook” link to download the material. This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website. Complete problem 3.1, parts a–f, on pages 51–52 in chapter 3.
Completing this assessment should take approximately 45 minutes.
Solutions: Answers are in the endnotes beginning on page 232.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: The Saylor Foundation’s “Unit 2 SelfTest”
Link: The Saylor Foundation’s “Unit 2 SelfTest”
Instructions: Please complete these 10 multiple choice questions by selecting the best possible answer of those provided. It may be helpful to have pencil and paper available so you can sketch out and solve some of the problems.
Completing this assessment should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 3: Math: Trees and Fish”

Unit 3: Financial Theory, Risk, and Applications
Financial theory is predicated on the concept of inflation, or the general rise in prices over time. Inflation has the power to erode people’s savings or erase their debts. The rate of inflation varies over time, and its effects must be factored into a variety of quantitative economic models. In this unit, we will calculate the real value of a currency in two different ways and select which is best for various models.
Unit 3 Time Advisory show close
Risk is a measurable phenomenon. Every time a decision is made, there is a risk that the expected outcome will not be the actual result. In this respect, risk is everpresent because our environment is continually changing. The fairness of a system can be characterized by a risk and reward calculation, and models of risk tolerance can quantify an individual’s or firm’s appetite for risk.
Arbitrage is a typical example of a risk application. Generally defined as exploiting price differentials by buying a financial asset in one market and selling it in another, arbitrage involves calculating risk and reward. Economists will evaluate the similarities and differences in assets and markets over time to arrive at an optimal and potentially riskfree transaction.
Unit 3 Learning Outcomes show close

3.1 Inflation
 Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 4: In?ation”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 4: In?ation” (PDF)
Instructions: Read pages 53–58.
Reading this chapter should you approximately 15 minutes.
Terms of Use: The above reading is licensed under a Creative Commons AttributionNonCommercial 3.0 License. It is attributed to Yoram Bauman, and the original version can be found here.
 Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 4: In?ation”

3.1.1 Nominal and Real Interest Rates
 Web Media: YouTube: Khan Academy’s “Real and Nominal Return”
Link: YouTube: Khan Academy’s “Real and Nominal Return” (YouTube)
Instructions: The above link will bring you to a video lecture about how real and nominal rates are calculated.
Watching this video should take approximately 3 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Web Media: YouTube: Khan Academy’s “Real and Nominal Return”
 3.1.2 Applications of Inflation

3.1.2.1 Definition
 Web Media: YouTube: Khan Academy’s “Introduction to Inflation”
Link: YouTube: Khan Academy’s “Introduction to Inflation” (YouTube)
Instructions: The above link will bring you to a video lecture about inflation.
Watching this video should take approximately 10 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Web Media: YouTube: Khan Academy’s “Introduction to Inflation”

3.1.2.2 Historical Data Usage
 Web Media: YouTube: Khan Academy’s “Inflation Data”
Link: YouTube: Khan Academy’s “Inflation Data” (YouTube)
Instructions: The above link will bring you to a video lecture about how to use inflation statistics in the United States.
Watching this video should take approximately 5 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Web Media: YouTube: Khan Academy’s “Inflation Data”

3.1.2.3 Significance of Problem
 Web Media: YouTube: Khan Academy’s “Moderate Inflation in a Good Economy”
Link: YouTube: Khan Academy’s “Moderate Inflation in a Good Economy” (YouTube)
Instructions: The above link will bring you to a video lecture about why some inflation may be a sign of a healthy economy.
Watching this video should take approximately 5 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Web Media: YouTube: Khan Academy’s “Moderate Inflation in a Good Economy”

3.1.3 Mathematical Techniques
 Assessment: Math for Life: Ian Morrison’s Sample Chapter, “Time is Money”
Link: Math for Life: Ian Morrison’s Sample Chapter, “Time is Money” (PDF)
Instructions: Please go to the webpage and locate the “Contents” button toward the bottom of the page and click on it. Then click on “Inflation” under section 1.5. This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website. Complete questions 1.5.7, 1.5.8, and 1.5.9 on pages 8–10 in section 1.5, “Inflation.”
Completing this assessment should take approximately 30 minutes.
Solutions: Answers are available after each problem.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Web Media: YouTube: Khan Academy’s “Calculating Real Return in Last Year Dollars”
Link: YouTube: Khan Academy’s “Calculating Real Return in Last Year Dollars” (YouTube)
Instructions: The above link will bring you to a video lecture about how to calculate real returns from one year to the next.
Watching this video should take approximately 5 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 4”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 4” (PDF)
Instructions: Please go to the webpage and locate the Downloads section. Under “Quantum Microeconomics with calculus,” click on the “entire textbook” link to download the material. This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website. Complete problems 4.1–4.4 on pages 57–58 in chapter 4.
Completing this assessment should take approximately 1 hour and 15 minutes.
Solutions: Answers are in the endnotes beginning on page 232.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Assessment: Math for Life: Ian Morrison’s Sample Chapter, “Time is Money”

3.2 Risk
 Lecture: YouTube: Yale University, Department of Economics: John Geanakoplos’ “14: Quantifying Uncertainty and Risk”
Link: YouTube: Yale University, Department of Economics: John Geanakoplos’ “14: Quantifying Uncertainty and Risk” (YouTube)
Also Available in:
Flash, HTML, MP3 or QuickTime
iTunes U
Instructions: Watch the entire lecture.
Watching this lecture should take approximately 1 hour and 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 5: Optimization and Risk”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 5: Optimization and Risk” (PDF)
Instructions: Read pages 59–66.
Reading this chapter should take approximately 30 minutes.
Terms of Use: The above reading is licensed under a Creative Commons AttributionNonCommercial 3.0 License. It is attributed to Yoram Bauman, and the original version can be found here.  Assessment: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 5 Problems”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 5 Problems” (PDF)
Instructions: Please go to the webpage and locate the Downloads section. Under “Quantum Microeconomics with calculus,” click on the “entire textbook” link to download the material. This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website. Complete problems 5.1–5.4 and 5.7–5.10 on pages 64–67 in chapter 5.
Completing this assessment should take approximately 120 minutes.
Solutions: Answers are in the endnotes beginning on page 233.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: The College of William & Mary: Robert Archibald’s Econ304: Intermediate Macro Theory: “Problem Set 3”
Link: The College of William & Mary: Robert Archibald’s Econ304: Intermediate Macro Theory: “Problem Set 3” (HTML)
Instructions: Please click on the link and complete questions 1 through 6 of Problem Set 3.
Completing this assessment should take approximately 1 hour.
Solutions: Answers are available under “Problem Set 3 – Expectations, Present Values – Answers” (HTML).
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: YouTube: Yale University, Department of Economics: John Geanakoplos’ “14: Quantifying Uncertainty and Risk”

3.3 Arbitrage
 Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 6: Transition: Arbitrage”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 6: Transition: Arbitrage” (PDF)
Instructions: Read pages 67–72.
Reading this chapter should take approximately 20 minutes.
Terms of Use: The above reading is licensed under a Creative Commons AttributionNonCommercial 3.0 License. It is attributed to Yoram Bauman, and the original version can be found here.  Lecture: YouTube: Yale University, Department of Economics: John Geanakoplos’ “09: Yield Curve Arbitrage”
Link: YouTube: Yale University, Department of Economics: John Geanakoplos’ “09: Yield Curve Arbitrage” (YouTube)
Also Available in:
Flash, HTML, MP3 or QuickTime
iTunes U
Instructions: Watch the entire lecture.
Watching this lecture should take approximately 1 hour and 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 6 Problems”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 6 Problems” (PDF)
Instructions: Please go to the webpage and locate the Downloads section. Under “Quantum Microeconomics with calculus,” click on the “entire textbook” link to download the material. This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website. Complete problems 6.1–6.3 on page 73 in chapter 6.
Completing this assessment should take approximately 45 minutes.
Solutions: Answers are in the endnotes beginning on page 234.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: New York University Stern School of Business: Lasse Heje Pedersen’s “Foundations for Financial Markets”
Link: New York University Stern School of Business: Lasse Heje Pedersen’s “Foundations for Financial Markets” (PDF)
Instructions: Please go to the webpage and locate file “P07.pdf.” This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website. Complete questions 1 through 3 of Problem Set 7.
Completing this assessment should take approximately 45 minutes.
Solutions: Answers can be found by clicking on the link “S07.pdf.”
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: The Saylor Foundation’s “Unit 3 SelfTest”
Link: The Saylor Foundation’s “Unit 3 SelfTest”
Instructions: Please complete these 10 multiple choice questions by selecting the best possible answer of those provided. It may be helpful to have pencil and paper available so you can sketch out and solve some of the problems.
Completing this assessment should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 6: Transition: Arbitrage”

Unit 4: Equitable Division of Resources and Consumption
Economics is sometimes classified as the science of scarcity. Everything in our universe is scarce. There is only so much fresh water, food, and energy on the planet. Because we are mortal, our time is scarce, and even intangible things like good ideas are not in infinite supply. Economists can quantify this scarcity to help individuals, companies, and governments make the optimal choices about how to divide our resources.
Unit 4 Time Advisory show close
Exactly how to divide up resources has been a constant debate since ancient times. Economists can view the problem on a very personal level, like how best to divide up a pizza pie among a group of children, or on a global scale, like assessing fishing rights in international waters. There is no one right way to measure fairness, and context must be considered. Nevertheless, the essential fairness of a decision can be measured using objective mathematical tools.
Vilfredo Federico Damaso Pareto was an Italian economist who spent much of his life measuring efficiency and fairness. He successfully quantified trade theories and distribution patterns of wealth in nations. Jeremy Bentham proposed a calculation system for pleasure and suffering to calculate “the greatest good for the greatest number.” Individuals can use a costbenefit analysis to make better decisions about the allocation decisions they face.
Unit 4 Learning Outcomes show close

4.1 Introduction to Game Theory visàvis Equity and Fairness
 Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 7: CakeCutting”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 7: CakeCutting” (PDF)
Instructions: Read pages 75–84. Note this reading also covers the material you need to know for subunits 4.1–4.2.
Reading this chapter should take approximately 30 minutes.
Terms of Use: The above reading is licensed under a Creative Commons AttributionNonCommercial 3.0 License. It is attributed to Yoram Bauman, and the original version can be found here.  Lecture: YouTube: Yale University, Department of Economics: Ben Polak’s “01: Introduction – Five First Lessons”
Link: YouTube: Yale University, Department of Economics: Ben Polak’s “01: Introduction – Five First Lessons” (YouTube)
Also Available in:
Flash, HTML, MP3 or QuickTime
iTunes U
Instructions: Watch the entire lecture.
Watching this lecture should take approximately 1 hour and 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 7: CakeCutting”

4.2 CakeCutting: The Problem of Fair Division
Note: This subunit is covered by the reading assigned beneath subunit 4.1. Focus on pages 79–83 to learn more about equity and fairness.
 Lecture: YouTube: Yale University, Department of Economics: John Geanakoplos’ “04: Efficiency, Assets, and Time”
Link: YouTube: Yale University, Department of Economics: John Geanakoplos’ “04: Efficiency, Assets, and Time” (YouTube)
Also Available in:
Flash, HTML, MP3 or QuickTime
iTunes U
Instructions: Watch the entire lecture.
Watching this lecture should take approximately 1 hour and 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 7 Problems”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 7 Problems” (PDF)
Instructions: Please go to the webpage and locate the Downloads section. Under “Quantum Microeconomics with calculus,” click on the “entire textbook” link to download the material. This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website. Complete problems 7.1–7.3 on pages 83–85 in chapter 7.
Completing this assessment should take approximately 1 hour and 15 minutes.
Solutions: Answers are in the endnotes beginning on page 235.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: YouTube: Yale University, Department of Economics: John Geanakoplos’ “04: Efficiency, Assets, and Time”

4.3 Economics and Social Welfare
 Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 8: Economics and Social Welfare”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 8: Economics and Social Welfare” (PDF)
Instructions: Read pages 85–92.
Reading this chapter should take approximately 30 minutes.
Terms of Use: The above reading is licensed under a Creative Commons AttributionNonCommercial 3.0 License. It is attributed to Yoram Bauman, and the original version can be found here.  Assessment: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 8 Problems”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 8 Problems” (PDF)
Instructions: Please go to the webpage and locate the Downloads section. Under “Quantum Microeconomics with calculus,” click on the “entire textbook” link to download the material. This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website. Complete problems 8.1–8.3 on pages 92 to 93 in chapter 8.
Completing this assessment should take approximately 75 minutes.
Solutions: Answers are in the endnotes beginning on page 235.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: University of Pittsburgh: Michael LeGower’s “ECON 1100 – Intermediate Microeconomics: “Problem Set 6”
Link: University of Pittsburgh: Michael LeGower’s ECON 1100 – Intermediate Microeconomics: “Problem Set 6” (PDF)
Instructions: Please go to the webpage and locate the file “Problem Set #6.” This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website. Complete questions 1–3 of Problem Set 6.
Completing this assessment should take approximately 2 hours.
Solutions: Answers can be found by clicking on the link “Problem Set #6 with Answers.”
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: The Saylor Foundation’s “Unit 4 SelfTest”
Link: The Saylor Foundation’s “Unit 4 SelfTest”
Instructions: Please complete these 10 multiple choice questions by selecting the best possible answer of those provided. It may be helpful to have pencil and paper available so you can sketch out and solve some of the problems.
Completing this assessment should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 8: Economics and Social Welfare”

Unit 5: Game Theory
Game theory was first applied to economic problems by the NobelPrizewinning economist John Nash. His discoveries were dramatized in the movie A Beautiful Mind. In essence, game theory describes and predicts how participants will make decisions based on their expectations of consequences. In the classic game, the prisoner’s dilemma, two criminals either choose to confess or maintain innocence. There are four possible outcomes and associated benefits and costs with each. The choices can be quantified, and a “Nash equilibrium” can be calculated. Although abstract, this kind of game can describe behavior in oligopolies.
Unit 5 Time Advisory show close
Games can become substantially more complex as additional moves and choices are incorporated into models. Decision trees can be used to describe sequential move games, and a payoff matrix approximates simultaneous move games like the prisoner’s dilemma. Algorithms will provide some solutions to Nash equilibriums, while partial derivatives yield answers to other games. The right tool must be matched to each kind of game.
As a practical example, game theory can be used to describe some kinds of auctions. This kind of market has gained increasing popularity with the advent of online auctions at eBay. When calculating a price, the bidder must analyze available data, but some information is held back. The introduction of uncertainty into the process makes the optimal calculations extremely complex.
Unit 5 Learning Outcomes show close

5.1 Sequential Move Games
 Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 9: Sequential Move Games”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 9: Sequential Move Games” (PDF)
Instructions: Read pages 93–102. Note this reading covers the material you need to know for subunits 5.1–5.2.
Reading this chaptershould take approximately 30 minutes.
Terms of Use: The above reading is licensed under a Creative Commons AttributionNonCommercial 3.0 License. It is attributed to Yoram Bauman, and the original version can be found here.  Lecture: YouTube: Yale University, Department of Economics: Ben Polak’s “13: Sequential Games: Moral Hazard, Incentives, and Hungry Lions”
Link: YouTube: Yale University, Department of Economics: Ben Polak’s “13: Sequential Games: Moral Hazard, Incentives, and Hungry Lions” (YouTube)
Also Available in:
Flash, HTML, MP3 or QuickTime
iTunes U
Instructions: Watch the entire lecture.
Watching this lecture should take approximately 1 hour and 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 9: Sequential Move Games”

5.2 Backward Induction
Note: This subunit is covered by the reading assigned beneath subunit 5.1. Focus on pages 96–102 to learn more about backward induction.
 Lecture: YouTube: Yale University, Department of Economics: Ben Polak’s “14: Backward Induction: Commitment, Spies, and FirstMover Advantages”
Link: YouTube: Yale University, Department of Economics: Ben Polak’s “14: Backward Induction: Commitment, Spies, and FirstMover Advantages” (YouTube)
Also Available in:
Flash, HTML, MP3 or QuickTime
iTunes U
Instructions: Watch the entire lecture.
Watching this lecture should take approximately 1 hour and 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 9 Problems”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 9 Problems” (PDF)
Instructions: Please go to the webpage and locate the Downloads section. Under “Quantum Microeconomics with calculus,” click on the “entire textbook” link to download the material. This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website. Complete problems 9.1–9.12 on pages 98–104 in chapter 9.
Completing this assessment should take approximately 2 hours.
Solutions: Answers are in the endnotes beginning on page 236.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 10 Problems”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 10 Problems” (PDF)
Instructions: Please go to the webpage and locate the Downloads section. Under “Quantum Microeconomics with calculus,” click on the “entire textbook” link to download the material. This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website. Complete problems 10.1–10.2 on page 108 in chapter 10.
Completing this assessment should take approximately 45 minutes.
Solutions: Answers are in the endnotes beginning on page 238.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: University of California, Davis: Giacomo Bonanno’s Econ 122–Game Theory: “Week 5 Problems”
Link: University of California, Davis: Giacomo Bonanno’s Econ 122—Game Theory: “Week 5 Problems” (PDF)
Instructions: Please go to the webpage and locate file “week_ 5.pdf.” This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website. Complete questions 1–3.
Completing this assessment should take approximately 90 minutes.
Solutions: Answers can be found at file “week5_answ.pdf.”
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: YouTube: Yale University, Department of Economics: Ben Polak’s “14: Backward Induction: Commitment, Spies, and FirstMover Advantages”

5.3 Simultaneous Move Games
 Lecture: YouTube: Yale University, Department of Economics: Ben Polak’s “05: Nash Equilibrium: Bad Fashion and Bank Runs”
Link: YouTube: Yale University, Department of Economics: Ben Polak’s “05: Nash Equilibrium: Bad Fashion and Bank Runs” (YouTube)
Also Available in:
Flash, HTML, MP3 or QuickTime
iTunes U
Instructions: Watch the entire lecture.
Watching this lecture should take approximately 1 hour and 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 10: Simultaneous Move Games”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 10: Simultaneous Move Games” (PDF)
Instructions: Read pages 103–106.
Reading this chapter should take approximately 15 minutes.
Terms of Use: The above reading is licensed under a Creative Commons AttributionNonCommercial 3.0 License. It is attributed to Yoram Bauman, and the original version can be found here.  Assessment: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 12 Problems”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 12 Problems” (PDF)
Instructions: Please go to the webpage and locate the Downloads section. Under “Quantum Microeconomics with calculus,” click on the “entire textbook” link to download the material. This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website. Complete problems 12.1–12.10 and C12.1 and C12.2 on pages 128–131 in chapter 12.
Completing this assessment should take approximately 2 hours.
Solutions: Answers are in the endnotes beginning on page 238.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: University of California, Davis: Giacomo Bonanno’s “Econ 122–Game Theory”
Link: University of California, Davis: Giacomo Bonanno’s “Econ 122—Game Theory” (PDF)
Instructions: Please go to the webpage and locate file “week_ 4.pdf.” This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website. Complete questions 2–4.
Completing this assessment should take approximately 1 hour and 30 minutes.
Solutions: Answer can be found at file “week4_answ.pdf.”
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: YouTube: Yale University, Department of Economics: Ben Polak’s “05: Nash Equilibrium: Bad Fashion and Bank Runs”

5.4 Iterated Dominance and Nash Equilibrium
 Lecture: YouTube: Yale University, Department of Economics: Ben Polak’s “06: Nash Equilibrium: Dating and Cournot”
Link: YouTube: Yale University, Department of Economics: Ben Polak’s “06: Nash Equilibrium: Dating and Cournot” (YouTube)
Also Available in:
Flash, HTML, MP3 or QuickTime
iTunes U
Instructions: Watch the entire lecture.
Watching this lecture should take approximately 1 hour and 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 12: Iterated Dominance and Nash Equilibrium”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 12: Iterated Dominance and Nash Equilibrium” (PDF)
Instructions: Read pages 113–130. Note that this reading also covers the material you need to know for subunits 5.4.1–5.4.2.
Reading this chapter should take approximately 1 hour.
Terms of Use: The above reading is licensed under a Creative Commons AttributionNonCommercial 3.0 License. It is attributed to Yoram Bauman, and the original version can be found here.
 Lecture: YouTube: Yale University, Department of Economics: Ben Polak’s “06: Nash Equilibrium: Dating and Cournot”

5.4.1 Infinitely Repeated Games
Note: This subunit is covered by the reading assigned beneath subunit 5.4. Focus on pages 120–121 to learn more about infinitely repeated games.
 Lecture: YouTube: Yale University, Department of Economics: Ben Polak’s “21: Repeated Games: Cooperation vs. the End Game”
Link: YouTube: Yale University, Department of Economics: Ben Polak’s “21: Repeated Games: Cooperation vs. the End Game” (YouTube)
Also available in:
Flash, HTML, MP3 or QuickTime
iTunes U
Instructions: Watch the entire lecture.
Watching this lecture should take approximately 1 hour and 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: YouTube: Yale University, Department of Economics: Ben Polak’s “21: Repeated Games: Cooperation vs. the End Game”

5.4.2 Mixed Strategies
Note: This subunit is covered by the reading assigned beneath subunit 5.4. Focus on pages 122–127 to learn more about mixed strategies.
 Lecture: YouTube: Yale University, Department of Economics: Ben Polak’s “09: Mixed Strategies in Theory and Tennis”
Link: YouTube: Yale University, Department of Economics: Ben Polak’s “09: Mixed Strategies in Theory and Tennis” (YouTube)
Also available in:
Flash, HTML, MP3 or QuickTime
iTunes U
Instructions: Watch the entire lecture.
Watching this lecture should take approximately 1 hour and 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: YouTube: Yale University, Department of Economics: Ben Polak’s “09: Mixed Strategies in Theory and Tennis”

5.5 Auctions
 Lecture: YouTube: Yale University, Department of Economics: Ben Polak’s “24: Asymmetric Information: Auctions and the Winner’s Curse”
Link: YouTube: Yale University, Department of Economics: Ben Polak’s “24: Asymmetric Information: Auctions and the Winner’s Curse” (YouTube)
Also available in:
Flash, HTML, MP3 or QuickTime
iTunes U
Instructions: Watch the entire lecture.
Watching this lecture should take approximately 1 hour and 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 13: Application: Auctions”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 13: Application: Auctions” (PDF)
Instructions: Read pages 131–140.
Reading this chapter should take approximately 30 minutes.
Terms of Use: The above reading is licensed under a Creative Commons AttributionNonCommercial 3.0 License. It is attributed to Yoram Bauman, and the original version can be found here.  Assessment: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 13 Problems”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 13 Problems” (PDF)
Instructions: Please go to the webpage and locate the Downloads section. Under “Quantum Microeconomics with calculus,” click on the “entire textbook” link to download the material. This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website. Complete problems 13.1–13.5 on pages 140–142 in chapter 13.
Completing this assessment should take approximately 2 hours.
Solutions: Answers are in the endnotes beginning on page 242.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Paul Klemperer’s “Auctions: Theory and Practice”
Link: Paul Klemperer’s “Auctions: Theory and Practice” (PDF)
Instructions: Please go to the webpage and locate the file “Exercises.” This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website. Complete question 7.
Completing this assessment should take approximately 1 hour.
Solutions: Answers can be found in the “Solutions” PDF.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: The Saylor Foundation’s “Unit 5 SelfTest”
Link: The Saylor Foundation’s “Unit 5 SelfTest”
Instructions: Please complete these 10 multiple choice questions by selecting the best possible answer of those provided. It may be helpful to have pencil and paper available so you can sketch out and solve some of the problems.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: YouTube: Yale University, Department of Economics: Ben Polak’s “24: Asymmetric Information: Auctions and the Winner’s Curse”

Unit 6: Microeconomic Theory and Applications
Economists make many assumptions about the nature of supply and demand. Curves are smooth continuous functions and are nicely behaved in Euclidean space. A basic graphic argument can be constructed and then extrapolated to algebra and then calculus. In the real world, these assumptions and mathematical extrapolations often need modification, but it’s a good beginning point to understand how supply and demand behave in a perfect theoretical world.
Unit 6 Time Advisory show close
Joseph Louis Lagrange was an important mathematician in the eighteenth century; he developed a mathematical technique to calculate minimum and maximum points of a function. Originally applied in physics, his work has been used in a variety of fields, from quantum mechanics to the general theory of relativity. Because economists seek to maximize (or minimize) outcomes, Lagrangian techniques are a mainstay of any economic toolkit.
Calculus is the primary tool to calculate the instantaneous slope of a function at a given point. The slope reveals the rate of change and gives insight into marginal choices a consumer or firm makes. The double derivative describes the rate of change of the rate of change. While this may sound abstract, the information indicates whether the rate of change is increasing, decreasing, or remaining the same intensity. This has applications in consumer choice and profit maximization.
Unit 6 Learning Outcomes show close

6.1 Supply and Demand
 Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 15: Supply and Demand Basics”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 15: Supply and Demand Basics” (PDF)
Instructions: Read pages 147–154.
Reading this chapter shouldtake approximately 30 minutes.
Terms of Use: The above reading is licensed under a Creative Commons AttributionNonCommercial 3.0 License. It is attributed to Yoram Bauman, and the original version can be found here.  Web Media: YouTube: Khan Academy’s “Market Equilibrium” and “Changes in Market Equilibrium”
Link: YouTube: Khan Academy’s “Market Equilibrium” and “Changes in Market Equilibrium” (YouTube)
Instructions: The above link will bring you to lectures about how market equilibrium is calculated.
Watching these videos should take approximately 20 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 15 Problems”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 15 Problems” (PDF)
Instructions: Please go to the webpage and locate the Downloads section. Under “Quantum Microeconomics with calculus,” click on the “entire textbook” link to download the material. This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website. Complete problems 15.1–15.8 on pages 153–155 in chapter 15.
Completing this assessment should take approximately 2 hours.
Solutions: Answers are in the endnotes beginning on page 243.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: University of California, Santa Cruz: Bob Baden’s ECON100A: Intermediate Microeconomics: “Problem Set 2”
Link: University of California, Santa Cruz: Bob Baden’s ECON100A: Intermediate Microeconomics: “Problem Set 2” (PDF)
Instructions: Please go to the webpage and locate file “Problem Set 2.” This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website. Complete questions 1–4.
Completing this assessment should take approximately 1 hour and 30 minutes.
Solutions: Answers can be found at file “Problem Set 2 Answer Key.”
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 15: Supply and Demand Basics”

6.2 Taxes
 Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 16: Taxes”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 16: Taxes” (PDF)
Instructions: Read pages 155–164.
Reading this chapter should take approximately 30 minutes.
Terms of Use: The above reading is licensed under a Creative Commons AttributionNonCommercial 3.0 License. It is attributed to Yoram Bauman, and the original version can be found here.  Web Media: YouTube: Khan Academy’s “Taxation and Dead Weight Loss” and “Percentage Tax on Hamburgers”
Link: YouTube: Khan Academy’s “Taxation and Dead Weight Loss” and “Percentage Tax on Hamburgers” (YouTube)
Instructions: The above link will bring you to lectures about how taxation affects markets.
Watching these videos should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Web Media: YouTube: Intromediate Microeconomics’ “3. Why Taxes on Producers and Taxes on Consumers Have the Same Effect” and “14. More on Tax Incidence”
Link: YouTube: Intromediate Microeconomics’ “3. Why Taxes on Producers and Taxes on Consumers Have the Same Effect” and “14. More on Tax Incidence” (YouTube)
Instructions: Please review these presentations in their entirety. Consider the role of calculus in determining supply.
Watching these videos should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 16 Problems”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 16 Problems” (PDF)
Instructions: Please go to the webpage and locate the Downloads section. Under “Quantum Microeconomics with calculus,” click on the “entire textbook” link to download the material. This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website. Complete problems 16.1–16.8 and A16.1–A16.3 on pages 163–166 in chapter 16.
Completing this assessment should take approximately 2 hours and 30 minutes.
Solutions: Answers are in the endnotes beginning on page 244.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: University of California, Santa Cruz: Bob Baden’s ECON100A: Intermediate Microeconomics: “Problem Set 5”
Link: University of California, Santa Cruz: Bob Baden’s ECON100A: Intermediate Microeconomics: “Problem Set 5” (PDF)
Instructions: Please go to the webpage and locate file “Problem Set 5.” This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website. Complete questions 1, 4, and 5.
Completing this assessment should take approximately 1 hour.
Solutions: Answers can be found at file “Problem Set 5 Answer Key.”
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 16: Taxes”

6.3 Elasticities
 Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 17: Elasticities”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 17: Elasticities” (PDF)
Instructions: Read pages 165–172.
Reading this chaptershould take approximately 30 minutes.
Terms of Use: The above reading is licensed under a Creative Commons AttributionNonCommercial 3.0 License. It is attributed to Yoram Bauman, and the original version can be found here.  Lecture: iTunes U: Harrisburg Area Community College, Department of Math: Susan CooperNguyen’s “14: Elasticity of Demand – Part 1” and “15: Elasticity of Demand – Part 2”
Link: iTunes U: Harrisburg Area Community College, Department of Math: Susan CooperNguyen’s “14: Elasticity of Demand – Part 1” and “15: Elasticity of Demand – Part 2” (iTunes)
Instructions: Please click on the “View in iTunes” hyperlink for “13: Elasticity of Demand – Part 1” and “15: Elasticity of Demand – Part 2.” Listen to the lectures in their entirety.
Listening to these lectures should take approximately 20 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Web Media: YouTube: themathmaster’s “Business Calculus Topic 4.4 Lesson”
Link: YouTube: themathmaster: “Business Calculus Topic 4.4 Lesson” (YouTube)
Instructions: Please review this entire presentation. Consider the role of calculus in determining price elasticity.
Watching this presentation should take approximately 5 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 17 Problems”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 17 Problems” (PDF)
Instructions: Please go to the webpage and locate the Downloads section. Under “Quantum Microeconomics with calculus,” click on the “entire textbook” link to download the material. This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website. Complete problems 17.1–17.5 on pages 173–174 in chapter 17.
Completing this assessment should take approximately 1 hour and 30 minutes.
Solutions: Answers are in the endnotes beginning on page 248.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Fort Lewis College: Prof. Deborah Walker’s ECON262: Principles of Microeconomics: “Practice Problems on Elasticity”
Link: Fort Lewis College: Prof. Deborah Walker’s ECON262: Principles of Microeconomics: “Practice Problems on Elasticity” (HTML)
Instructions: Please click on the link above and complete questions 1–5.
Completing this assessment should take approximately 1 hour and 15 minutes.
Solutions: Answers are provided at the bottom of the page.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 17: Elasticities”

6.4 Individual and Market Demand Curves
 Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 18: Supply and Demand Details”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter Eighteen: Supply and Demand Details” (PDF)
Instructions: Read pages 173–180.
Reading this chaptershould take approximately 30 minutes.
Terms of Use: The above reading is licensed under a Creative Commons AttributionNonCommercial 3.0 License. It is attributed to Yoram Bauman, and the original version can be found here.  Web Media: YouTube: Khan Academy’s “Aggregate Demand” and “Shifts in Aggregate Demand”
Link: YouTube: Khan Academy’s “Aggregate Demand” and “Shifts in Aggregate Demand” (YouTube)
Instructions: The above links will bring you to lectures about how market demand is calculated.
Watching these videos should take approximately 20 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 18 Problems”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 18 Problems” (PDF)
Instructions: Please go to the webpage and locate the Downloads section. Under “Quantum Microeconomics with calculus,” click on the “entire textbook” link to download the material. This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website. Complete problems 18.1–18.3 on pages 181–182 in chapter 18.
Completing this assessment should take approximately 1 hour and 30 minutes.
Solutions: Answers are in the endnotes beginning on page 249.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Massachusetts Institute of Technology, Department of Economics: “Principles of Microeconomics Exam 2”
Link: Massachusetts Institute of Technology, Department of Economics: “Principles of Microeconomics Exam 2” (PDF)
Instructions: Complete questions 2 and 4. Once you are done, check your answers against the solutions file.
Completing these questions should take approximately 1 hour and 15 minutes.
Terms of Use: These articles are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 Unported License. They are attributed to Massachusetts Institute of Technology, and the original versions can be found here.
 Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 18: Supply and Demand Details”

6.5 Deriving Supply and Demand Curves
 Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 20: Math: Deriving Supply and Demand Curves” and “Appendix A”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 20: Math: Deriving Supply and Demand Curves” and “Appendix A” (PDF)
Instructions: Read pages 187–208 and 213–225. Note that this reading will also cover the material you need to know for subunits 6.5.1–6.5.2.
Reading these chapters should take approximately 2 hours.
Terms of Use: The above reading is licensed under a Creative Commons AttributionNonCommercial 3.0 License. It is attributed to Yoram Bauman, and the original version can be found here.  Lecture: iTunes U: Harrisburg Area Community College, Department of Math: Susan CooperNguyen’s “Lecture 17: First Derivative Test – Part 1,” “Lecture 18: First Derivative Test – Part 2,” and Lecture 19: “1st and 2nd Derivative Tests”
Link: iTunes U: Harrisburg Area Community College, Department of Math: Susan CooperNguyen’s “Lecture 17: First Derivative Test – Part 1”, “Lecture 18: First Derivative Test – Part 2”, and “Lecture 19: 1st and 2nd Derivative Tests” (iTunes)
Instructions: Please click on the “View in iTunes” hyperlinks for “Lecture 17: First Derivative Test – Part 1,” “Lecture 18: First Derivative Test – Part 2,” and “Lecture 19: 1st and 2nd Derivative Tests.”
Watching these lectures should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 20: Math: Deriving Supply and Demand Curves” and “Appendix A”

6.5.1 Foundations of Demand
Note: This subunit is covered by the reading assigned beneath subunit 6.5. Focus on pages 189–197 to learn more about the foundations of demand.
 Web Media: YouTube: Intromediate Microeconomics’ “9. Foundations of Demand Basics,” “9a. Deriving Demand using Calculus,” “9b. CobbDouglas Utility and Demand,” and “9c. Quasilinear Utility and Demand”
Link: YouTube: Intromediate Microeconomics’ “9. Foundations of Demand Basics”, “9a. Deriving Demand using Calculus”, “9b. CobbDouglas Utility and Demand”, and “9c. Quasilinear Utility and Demand” (YouTube)
Instructions: Please review these presentations in their entirety. Consider the role of calculus in determining demand.
Watching these videos should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Web Media: YouTube: Intromediate Microeconomics’ “9. Foundations of Demand Basics,” “9a. Deriving Demand using Calculus,” “9b. CobbDouglas Utility and Demand,” and “9c. Quasilinear Utility and Demand”

6.5.2 Foundations of Supply
Note: This subunit is covered by the reading assigned beneath subunit 6.5. Focus on pages 197 to 199 to learn more about the foundations of supply.
 Web Media: YouTube: Intromediate Microeconomics’ “17. Mapping Consumer Theory to Producer Theory” and “17a. Cost Minimization, Production and Lagrangians”
Link: YouTube: Intromediate Microeconomics’ “17. Mapping Consumer Theory to Producer Theory” and “17a. Cost Minimization, Production and Lagrangians” (YouTube)
Instructions: Please review these presentations in their entirety. Consider the role of calculus in determining supply.
Watching these videos should take approximately 20 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 20 Problems”
Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 20 Problems” (PDF)
Instructions: Please go to the webpage and locate the Downloads section. Under “Quantum Microeconomics with calculus,” click on the “entire textbook” link to download the material. This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website. Complete problems C20.1–C20.11 on pages 205–209 in chapter 20.
Completing this assessment should take approximately 2 hours and 30 minutes.
Solutions: Answers are in the endnotes beginning on page 250.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Columbia University’s “Problem Set: Economic Interpretation of Calculus Operations – Multivariate”
Link: Columbia University’s “Problem Set: Economic Interpretation of Calculus Operations – Multivariate” (HTML)
Instructions: Please click on the link above and complete questions 1–3.
Completing this assessment should take approximately 1 hour and 30 minutes.
Solutions: Answers can be found at the link “Show Solutions” in the upperleft corner of the page.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: The Saylor Foundation’s “Unit 6 SelfTest”
Link: The Saylor Foundation’s “Unit 6 SelfTest”
Instructions: Please complete these 10 multiple choice questions by selecting the best possible answer of those provided. It may be helpful to have pencil and paper available so you can sketch out and solve some of the problems.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Web Media: YouTube: Intromediate Microeconomics’ “17. Mapping Consumer Theory to Producer Theory” and “17a. Cost Minimization, Production and Lagrangians”

Final Exam
 Final Exam: The Saylor Foundation’s “ECON200 Final Exam”
Link: The Saylor Foundation’s “ECON200 Final Exam”
Instructions: You must be logged into your Saylor Foundation School account in order to access this exam. If you do not yet have an account, you will be able to create one, free of charge, after clicking the link.
 Final Exam: The Saylor Foundation’s “ECON200 Final Exam”