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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.*

Unit 6 Time Advisory
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.  

 Terms of Use: The above reading 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/).
  • 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 ECON-100A: Intermediate Microeconomics: “Problem Set 2” Link: University of California, Santa Cruz: Bob Baden’s ECON-100A: 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.

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 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/).
  • 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 A-16.1–A-16.3 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 ECON-100A: Intermediate Microeconomics: “Problem Set 5” Link: University of California, Santa Cruz: Bob Baden’s ECON-100A: 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.

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 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/).
  • 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.

    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.

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 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/).
  • 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 Attribution-NonCommercial-ShareAlike 3.0 Unported License. They are attributed to Massachusetts Institute of Technology, and the original versions can be found here.

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 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/).
  • 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.

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

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.

    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 upper-left 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 Self-Test” Link: The Saylor Foundation’s “Unit 6 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.

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.