HOLLYWOOD - OLIGOPOLY

Hollywood - Oligopoly



Hollywood - Oligopoly

How to Do Calculate The Gini Coefficient

The Gini Coefficient is calculated as follows. We find out the income of all the people in a country and then express this information as a cumulative percentage of people against the cumulative share of income earned. This gives us a Lorenz Curve which typically looks something like the following.

In plain English, the graph above indicates the proportion of the income going to the poorest people, middle-income people and richest people.

There will always be rich and poor, but we are interested in how evenly wealth is distributed and most governments put effort into keeping this coefficient as low as possible.

The Gini Coefficient ranges between 0 and 1 (or it can also be expressed as a number from 0 to 100) and is given by the ratio of the areas:

If A = 0, it means the Lorenz Curve is actually the Line of Equality. In this case, the Gini Coefficient is 0 and it means there is "perfect" distribution of income (everyone earns the same amount).

For example, say we have 10 people in a village and the income for the village is $100 per day. If every person shares this income evenly, they get $10 each per day.

So the income distribution would be as follows. ("Cumulative" just means add up the number you have so far for each step.)

Person

Proportion of population (%)

Cumulative proportion of population (%)

Income (%)

Cumulative income (%)

A

10%

10%

10%

10%

B

10%

20%

10%

20%

C

10%

30%

10%

30%

D

10%

40%

10%

40%

E

10%

50%

10%

50%

F

10%

60%

10%

60%

G

10%

70%

10%

70%

H

10%

80%

10%

80%

I

10%

90%

10%

90%

J

10%

100%

10%

100%

So for this society with perfectly-distributed income, we could draw a graph of the cumulative proportuion of population (on the horizontal axis) against the cumulative percentage of income (on the vertical axis) as follows.

Person

Proportion of population (%)

Cumulative proportion of population (%)

Income (%)

Cumulative income (%)

A

10%

10%

5%

5%

B

10%

20%

5%

10%

C

10%

30%

5%

15%

D

10%

40%

10%

25%

E

10%

50%

10%

35%

F

10%

60%

10%

45%

G

10%

70%

10%

55%

H

10%

80%

15%

70%

I

10%

90%

15%

85%

J

10%

100%

15%

100%

Let's graph it and see what it looks like.

In summary, the bottom 30% of the population earns 15% of the income, while the top 30% earns 45% of the income.

I've shaded 2 regions in the above graph, region A (with light magenta shading) and region B (with light green shading).

Recall the Gini Coefficient is the ratio of the areas:

Area A = 0.095 (from calculating area B - one triangle and 2 trapezoids - and subtracting it from 0.5)

Area (A + B) = 0.5 (this is half of the rectangle)

So the Gini Coefficient in this case is:

Let's take it another step. The three richer guys (H, I and J) have a fight and J wins. He demands 50% of the income and leaves it to H and I to distribute the rest.

Then H and I have a fight and I wins. He wants 33% and gives 10% to H and they decide to give what's left (1% or $1 a day) to each of the rest of the village.

(Millions of people live on less than $1 per day.)

Person

Proportion of population (%)

Cumulative proportion of population (%)

Income (%)

Cumulative income (%)

A

10%

10%

1%

1%

B

10%

20%

1%

2%

C

10%

30%

1%

3%

D

10%

40%

1%

4%

E

10%

50%

1%

5%

F

10%

60%

1%

6%

G

10%

70%

1%

7%

H

10%

80%

10%

17%

I

10%

90%

33%

50%

J

10%

100%

50%

100%

Now we have a very uneven income ...