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ECON200: Math for Economists

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 well-being. 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.

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 Time Advisory
Completing this unit should take approximately 10.75 hours.

☐    Subunit 1.1: 0.5 hours
☐    Subunit 1.1.1: 2.67 hours

☐    Subunit 1.1.2: 1.33 hours

☐    Subunit 1.2: 0.1 hours

☐    Subunit 1.3: 1 hour
☐    Subunit 1.3.1: 0.67 hours

☐    Subunit 1.3.2: 0.5 hours

☐    Subunit 1.3.3: 0.33 hours

☐    Subunit 1.3.4: 3.67 hours

Unit1 Learning Outcomes
Upon successful completion of this unit, you will be able to: - develop a toolkit of quantitative methods to solve optimization problems in macroeconomics and microeconomics; - apply specific quantitative tools (decision trees, algebraic equations, derivatives, integrals) to solve problems in macroeconomics and microeconomics; and - analyze specific problems in microeconomics and macroeconomics from an algebraic and calculus perspective and interpret the similarities and differences among tools.

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 Attribution-NonCommercial 3.0
License](http://creativecommons.org/licenses/by-nc/3.0/).  It is
attributed to Yoram Bauman, and the original version can be found
[here](http://www.smallparty.org/yoram/quantum/).

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.

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.

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.

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.

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.

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.

1.3.3 Integration   - Web Media: YouTube: Khan Academy’s “The Indefinite Integral or Anti-Derivative” and “Introduction to Definite Integrals” Link: YouTube: Khan Academy’s “The Indefinite Integral or Anti-Derivative” 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.

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 C-1.1–C-1.12 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 WEB-pages for the course BEE 1024: Mathematics for Economists: “Week 2 Exercises” Link: University of Exeter: Juliette Stephenson’s WEB-pages 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 Self-Test” Link: The Saylor Foundation’s “Unit 1 Self-Test”

    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.