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# The Laffer Curve & Examples

The Laffer Curve is named this way due to his main supporter and researcher about that theory, Arthur Laffer.

It is a theoretical representation of the relationship between Gov. Revenues and Taxes. The representation tries to prove that there is an optimal point when maximizing revenues by changing the income tax, and not always the increase in taxation will generate more revenues.

The Laffer curve is a simple curve that tries to expose the pros and cons of changing taxes and takes into account that there are external factors when you change it, such as:

• Tax Evasion;
• Tax Avoidance;
• etc...

Many have tried to find an optimal tax rate for their country, but putting the Laffer curve in practice has been very hard and almost impossible to predict.

The Laffer curve works in theory, since in economics, we have to assume ceteris paribus, everything else remains the same and when we change the tax rate, other facts do not change, which in reality, is impossible.

## Examples of the Laffer Curve

Some times the best way to understand something is seeing it working. So I will do some practical examples and show what is the base of the Laffer Curve, and why many people criticize it.

## Example 1 - Basic Laffer

This is a simple example of how the Laffer Curve can be shown.

In this example, these are the data for the graph:

There is a City-state with a population of 500.000 tax payers.

The average income per year is \$50.000

It will be assumed that the income of each taxpayer will be the same always. Although according to Laffer if taxes are too high, the tax payer will not feel motivated to work, but we will only check the tax evasion influence.

There is only one type of tax, it is income tax, which can change to prove the Laffer Curve.

We will use the Ceteris Paribus assumption, nothing else will influence this example.

## Other Data

As the taxes increases 10%, the tax evasion increases in an arithmetic progression, there is a risk of being caught according to the tax evasion, since more tax evaders are harder to catch than just a few. The fine for not paying in time is the double of the taxes you would have to pay.

For example, at a 20% tax rate the tax payer has two options.

• Not Paying (Receives: 50%*50.000 + 50%*(50.000-20%*2*50.000))

This leads to the same "expected" earnings but some people are more risk takers than others. So in the following table we have the Income Tax, the rate of Tax Evasion, the risk rate of being caught and the Revenues, if taxes were linear.

Raw Revenues:

Income Tax * Tax Payers(500.000) * Av. Income (\$50.000)

The fines are calculated as it follows:

(Tax Evasion)% * 2(Fine is double tax) * (Risk of Being Caught)% * Raw Revenues

Laffer Revenue Curve:

Raw Revenues + Fines - Tax Evasion% * Raw Revenues

Income Tax
Tax Evasion
Risk being caught
Fines
Raw Revenues
According Laffer curve
0%
0%
-
-
-

10%
2%
59%
58.800.000
2.500.000.000
2.508.800.000
20%
3%
58%
174.600.000
5.000.000.000
5.024.600.000
30%
5%
57%
427.500.000
7.500.000.000
7.552.500.000
40%
8%
55%
883.200.000
10.000.000.000
10.083.200.000
50%
13%
52%
1.696.500.000
12.500.000.000
12.571.500.000
60%
21%
47%
2.986.200.000
15.000.000.000
14.836.200.000
70%
34%
40%
4.712.400.000
17.500.000.000
16.262.400.000
80%
55%
27%
5.940.000.000
20.000.000.000
14.940.000.000
90%
89%
7%
2.643.300.000
22.500.000.000
5.118.300.000
100%
100%
0%
2.999.700
25.000.000.000
5.499.700

## Example 2 - Government Welfare

In this example I will show one reason why the Laffer curve is not taken so seriously to some economists. This example that includes Government Welfare is more likely to happen in European countries.

I will include the Living Costs, and Government Help for the Living Costs.

The basic living costs will be \$25.000, the government help will be the same as the tax rate.

Assuming as in the example 1, 500.000 tax payers with a \$50.000 fixed income.

The arithmetic effect was shown on the Raw Revenues, the economic effect will consider tax evasion and the decrease in motivation for work as taxes raise.

## Other data

The tax rates will be the same as before.

The tax evasion will be much less since the Gov. will help in the Living Costs.

The chance of being caught will vary because as the Gov. has more money, it can have a more efficient Tax Collector system.

Tax Rate
Tax Evasion
Chances Being Caught
Fines
Gov. Revenue
Gov. Welfare
Gov. Balance

0%
0%
100%
-
-
-
-

10%
1%
98%
49.000.000
2.524.000.000
1.250.000.000
1.274.000.000

20%
2%
95%
190.000.000
5.090.000.000
2.500.000.000
2.590.000.000

30%
5%
85%
637.500.000
7.762.500.000
3.750.000.000
4.012.500.000

40%
10%
75%
1.500.000.000
10.500.000.000
5.000.000.000
5.500.000.000

50%
15%
60%
2.250.000.000
12.875.000.000
6.250.000.000
6.625.000.000

60%
20%
50%
3.000.000.000
15.000.000.000
7.500.000.000
7.500.000.000

70%
25%
40%
3.500.000.000
16.625.000.000
8.750.000.000
7.875.000.000

80%
30%
35%
4.200.000.000
18.200.000.000
10.000.000.000
8.200.000.000

90%
40%
30%
5.400.000.000
18.900.000.000
11.250.000.000
7.650.000.000

100%
50%
25%
6.250.000.000
18.750.000.000
12.500.000.000
6.250.000.000

## Laffer Curve Example 2

As we can see in the graph, the Gov. Revenues increase as the taxes increase, but since there are tax evaders, there is an optimal point below 100%, which shows that sometimes the best thing is to decrease taxes.

Although it is not similar to a Laffer curve, it is similar to Half Laffer Curve. More similar to the Laffer curve would be the Gov. Balance, that varies since there is an expenditure(Gov. Welfare) that increases with the increase in taxation.

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