Archive page for ECON 384

**Note on textbook:** This semester we are using Pemberton & Rau’s “Mathematics for Economists.” You can get a discount for this book, by first registering for the CORE Team Econ textbook which we will also use. The CORE book is free, but you have to register to get the deal. After registering, you can get the discounted copy of P&R at for $35. Links to relevant sections are provided throughout. While it might be confusing, I am doing this in an effort to minimize costs to you. The CORE book will be used to reintroduce you to the intro concepts that are a prerequisite for this course (and often forgotten).

### Link to course on Canvas

### Syllabus

### Mathematica Download and Help

### Exercise & Problem Solutions for Pemberton & Rau

Pemberton & Rau 3rd Edition Exercise Solutions, and 4th Edition Exercise Solutions Pemberton & Rau 3rd Edition Problem Solutions, and 4th Edition Problem Solutions

## Sections

### Section 1: Linear equations: slope/intercept, solving systems of equations, inequalities

#### Reading:

- Pemberton & Rau: Chapter 1 & 2
- CORE Unit 8. With the CORE readings, you might have to go backwards to read more and understand a model.

#### Lecture:

#### Leibniz - CORE supplements showing economics & math working together

- Core Econ (Ch 8.4.1) Leibniz - Market Supply
- Core Econ (Ch 8.4.2) Leibniz - Market Equilibrium
- Core Econ (Ch 8.6.1) Leibniz - Shifts in Demand and Supply
- Summation on Khan Academy

### Section 2: Sets and functions, quadratics and logs, series.

#### Reading:

#### Lecture:

#### Leibniz

- Core Econ (Ch 3.6.1) Leibniz - Modeling Technological Change
- Core Econ (Ch 11.8.1) Leibniz - Price Bubbles

### Section 3: Differentiation: first, second, product, quotient rules.

#### Reading:

#### Lecture:

#### Leibniz

- Core Econ (Ch 2.7.1) Leibniz - The Production Function
- Core Econ (Ch 3.1.1) Leibniz - Average and Marginal Productivity
- Core Econ (Ch 3.1.2) Leibniz - Diminishing Marginal Productivity
- Core Econ (Ch 3.6.1) Leibniz - Modeling Technological Change (same as above)
- Core Econ (Ch 6.7.1) Leibniz - Profit Wages and Effort
- Core Econ (Ch 7.3.1) Leibniz - Average and Marginal Cost Curves
- Core Econ (Ch 7.5.1) Leibniz - Profit Maximizing Price
- Core Econ (Ch 7.6.1) Leibniz - Marginal Revenue and Marginal Cost
- Core Econ (Ch 7.8.1) Leibniz - Elasticity of Demand
- Core Econ (Ch 8.4.1) Leibniz - Market Supply Curve (same as above)

### Section 4: Optimization, exponential and log functions.

#### Reading:

#### Lecture:

#### Leibniz

- Core Econ (Ch 3.1.2) Leibniz - Diminishing Marginal Productivity (same as above)
- Core Econ (Ch 3.1.3) Leibniz - Concave and Convex Functions
- Core Econ (Ch 3.4.1) Leibniz - Marginal Rate of Transformation
- Core Econ (Ch 3.5.1) Leibniz - Optimal Allocation of Free Time
- Core Econ (Ch 6.7.1) Leibniz - Profit Wages and Effort (same as above)
- Core Econ (Ch 7.3.1) Leibniz - Average and Marginal Cost Curves (same as above)
- Core Econ (Ch 7.4.1) Leibniz - Isoprofit Curves and Their Slopes
- Core Econ (Ch 7.5.1) Leibniz - Profit Maximizing Price (same as above)
- Core Econ (Ch 7.6.1) Leibniz - Marginal Revenue and Marginal Cost (same as above)
- Core Econ (Ch 8.5.1) Leibniz - Gains From Trade

### Section 5: Matrix algebra

#### Reading:

- Pemberton & Rau: Chapters 11, 12, & 13

#### Lecture:

- Lecture 5: Mathematica (nb)
- Lecture 5: Powerpoint
- Lecture 5b: Mathematica (nb)
- Lecture 5b: Powerpoint
- Doing this in R

#### Supplements: OLS in Matrix form

### Section 6: Functions of several variables, differentiation, chain rule, partial derivatives, Hessians, constrained optimization

#### Reading:

#### Lecture:

- Lecture 6: Mathematica (nb)
- Lecture 6a: Mathematica partials (nb)
- Lecture 6b: Mathematica regression (nb)
- Lecture 6c: Mathematica (nb)

#### Leibniz

- Core Econ (Ch 3.7.1) Leibniz - Mathematics of Income and Substitution Effects
- Core Econ (Ch 4.4.1) Leibniz - Social Preferences and Altruism
- Core Econ (Ch 8.6.1) Leibniz - Shifts in Demand and Supply (same as above)

### Section 7: Basic integration and applications to statistics

#### Reading:

- Pemberton & Rau: Chapters 19 & 20
- CORE 8.5

#### Lecture:

#### Leibniz

- Core Econ (Ch 8.5.1) Leibniz - Gains From Trade (same as above)

## Software Downloads

### Mathematica

Mathematica is software that is used for a wide variety of mathematical and economic purposes including running simulations, solving linear algebra problems, performing regression analysis, building models, to name only a few. Mathematica is incredibly powerful, and will help you to check through taking derivations, solving integrals, examining non-linear problems, and graphically displaying your work. We will only begin to touch on what Mathematica can do.

You can download Mathematica for free at http://www.jmu.edu/computing/download/.

#### Required Readings

Mathematica Solutions to Economics Site

### R (just “R”)

R is free software used for statistical computing and graphics. While SAS is very powerful software for running prepackaged econometric estimations, R can perform many advanced features that you cannot easily do in SAS. To be fair, SAS is probably able to do almost everything we are going to do with R, but as an experienced user of SAS I can tell you that it can be like trying to hammer a nail with a screwdriver to do the same work in SAS that you can do in R. We are only going to scratch the surface of what you can do with R, but I hope that you are able to apply what you learn here beyond this course. R is open-source software, meaning it is free for you to use for almost any purpose (except redistribution in many cases) and on any platform (Mac, PC, Linux). For those considering graduate work in economics or another mathematically inclined field, you will be able to use R without the restriction of having to pay for it. SAS is very expensive, and is not provided by many employers. The primary benefit of R is the community of open-source programmers who help expand the software. We will use R to experiment with algorithms, matrix manipulation, and Monte Carlo simulation.