# ECON200: Math for Economists

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.

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 cost-benefit analysis to make better decisions about the allocation decisions they face.

This unit should take approximately 8.75 hours to complete.

☐    Subunit 4.1: 1.75 hours

☐    Subunit 4.2: 2.5 hours

☐    Subunit 4.3: 4.5 hours

Unit4 Learning Outcomes
Upon successful completion of this unit, the student will be able to: - Develop a toolkit of quantitative methods to solve problems in resource allocation and product consumption. - Apply specific quantitative tools (cost-benefit analysis) to solve problems in choice theory. - Analyze differences in equity and fairness using economic definitions and tools. - Evaluate the optimal equity solution within the broader context of economic theory and practical applications.

4.1 Introduction to Game Theory vis-à-vis Equity and Fairness   - Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 7: Cake-Cutting” Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 7: Cake-Cutting” (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.

attributed to Yoram Bauman, and the original version can be found
[here](http://www.smallparty.org/yoram/quantum/).
``````
• 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.

4.2 Cake-Cutting: 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.

• 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)

Completing this assessment should take approximately 1 hour and 15 minutes.

Solutions: Answers are in the endnotes beginning on page 235.

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.

attributed to Yoram Bauman, and the original version can be found
[here](http://www.smallparty.org/yoram/quantum/).
``````
• 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)

Completing this assessment should take approximately 75 minutes.

Solutions: Answers are in the endnotes beginning on page 235.

• 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.