# 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.

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.

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.

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.

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.

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.

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.

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

Watching these videos should take approximately 40 minutes.

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`````` Instructions: The above link will bring you to a video lecture

Watching these videos should take approximately 30 minutes.

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Watching these videos should take approximately 30 minutes.

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`````` Instructions: The above link will bring you to a video lecture

Watching this video should take approximately 10 minutes.

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• 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)

Completing this assessment should take approximately 2 hours.

Solutions: Answers are in the endnotes beginning on page 227.

• 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)

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.”