# ECON200: Math for Economists

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.

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.*

This unit should take approximately 24 hours to complete.

☐    Subunit 6.1: 4.17 hours

☐    Subunit 6.2: 4.5 hours

☐    Subunit 6.3: 3.67 hours

☐    Subunit 6.4: 3.5 hours

☐    Subunit 6.5: 2.75 hours

☐    Sub-subunit 6.5.1: 0.5 hours

☐    Sub-subunit 6.5.1: 4.83 hours

Unit6 Learning Outcomes
Upon successful completion of this unit, the student will be able to: - Develop a toolkit of quantitative methods to solve problems in microeconomics. - Apply specific quantitative tools (algebraic techniques, derivatives, partial derivatives, Lagrangian techniques) to solve problems in consumer theory. - Analyze differences in supply curves, demand curves, and utility functions using quantitative techniques. - Synthesize problem solutions in taxation, elasticity, and optimization by combining various elements of the quantitative toolkit as presented throughout the course.

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.

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

Instructions: The above link will bring you to lectures about how market equilibrium is calculated.

Watching these videos should take approximately 20 minutes.

• 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)

Completing this assessment should take approximately 2 hours.

Solutions: Answers are in the endnotes beginning on page 243.

• Assessment: University of California, Santa Cruz: Bob Baden’s ECON-100A: Intermediate Microeconomics: “Problem Set 2” Link: University of California, Santa Cruz: Bob Baden’s ECON-100A: Intermediate Microeconomics: “Problem Set 2” (PDF)

Completing this assessment should take approximately 1 hour and 30 minutes.

Solutions: Answers can be found at file “Problem Set 2 Answer Key.”

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.

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

Instructions: The above link will bring you to lectures about how taxation affects markets.

Watching these videos should take approximately 15 minutes.

• 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.

• 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)

Completing this assessment should take approximately 2 hours and 30 minutes.

Solutions: Answers are in the endnotes beginning on page 244.

• Assessment: University of California, Santa Cruz: Bob Baden’s ECON-100A: Intermediate Microeconomics: “Problem Set 5” Link: University of California, Santa Cruz: Bob Baden’s ECON-100A: Intermediate Microeconomics: “Problem Set 5” (PDF)

Completing this assessment should take approximately 1 hour.

Solutions: Answers can be found at file “Problem Set 5 Answer Key.”

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.

attributed to Yoram Bauman, and the original version can be found
[here](http://www.smallparty.org/yoram/quantum/).
``````
• Lecture: iTunes U: Harrisburg Area Community College, Department of Math: Susan Cooper-Nguyen’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 Cooper-Nguyen’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.

Instructions: Please review this entire presentation.  Consider the role of calculus in determining price elasticity.

Watching this presentation should take approximately 5 minutes.

• 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)

Completing this assessment should take approximately 1 hour and 30 minutes.

Solutions: Answers are in the endnotes beginning on page 248.

• 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)

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

Solutions: Answers are provided at the bottom of the page.

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.

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

Instructions: The above links will bring you to lectures about how market demand is calculated.

Watching these videos should take approximately 20 minutes.

• 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)

Completing this assessment should take approximately 1 hour and 30 minutes.

Solutions: Answers are in the endnotes beginning on page 249.

• 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.

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.

attributed to Yoram Bauman, and the original version can be found
[here](http://www.smallparty.org/yoram/quantum/).
``````
• Lecture: iTunes U: Harrisburg Area Community College, Department of Math: Susan Cooper-Nguyen’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 Cooper-Nguyen’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.

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.

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.

• 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)

Completing this assessment should take approximately 2 hours and 30 minutes.

Solutions: Answers are in the endnotes beginning on page 250.

• 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)