# The Firm

Materials for class on Thursday, October 3, 2019

## Contents

## Slides

Download the slides from today’s class.

## Calculating Gini coefficients

You can see global inequality statistics at Wikipedia. There are several columns here—the World Bank and CIA both calculate Gini coefficients (multiplied by 100 to be on a 0–100 scale), and the R/P columns are the 90/10 ratios you calculated in Problem Set 1 (income held by top 10% compared to income held by bottom 10%).

Here’s an example of how to calculate Gini coefficients in Excel:

Instead of using calculus to find the area under Lorenz curve, we used this formula where \(x\) = income, \(y\) = cumulative proportion of the population, and \(\mu_x\) = mean of income:

\[ \text{Gini} = \frac{2}{\mu_x} \text{Cov}(x, y) \]

You can also do this in R with the **ineq** package:

```
library(ineq)
# List of incomes
incomes <- c(10000, 20000, 50000, 100000, 200000)
# Calculate Gini coefficient
gini_coef <- Gini(incomes)
gini_coef
```

`## [1] 0.4842105`

```
# Plot Lorenz curve
plot(Lc(incomes), xlab = "Proportion of population", ylab = "Proportion of income")
text(x = 0.2, y = 0.8, labels = paste("Gini:", round(gini_coef, 3)))
```

## Clearest and muddiest things

Go to this form and answer these three questions:

- What was the muddiest thing from class today? What are you still wondering about?
- What was the clearest thing from class today?
- What was the most exciting thing you learned?

I’ll compile the questions and send out answers after class.