# Market size and income distribution

Looking at US income distribution data from here on a distribution plot was informative. The question was:

What would the market size be if we targeted individuals above \$100k of annual income ?

We see that the answer is ~ 5.5% of income earning individuals which turns out to be about 12 million folks. It is interesting to note how quickly the market size drops off if the product is designed and priced to target higher income levels.

`Annual Income  % Individuals`
```Above \$25k          47%
Above \$50k          21%
Above \$75k          10%
Above \$100k          5%
Above \$200k          1%```

TECHNICAL TRIVIA : The shape of the curve fits the exponential function quite accurately. This means that the whole curve is defined by a single number (the mean income) along with the formula:

```F = exp[I/I_m]
F - fraction of people above a certain income level
I - income level
I_m - mean income of population```

Knowing the mean income (~\$32k) you can calculate the fraction of people with income above any level with the above formula. Interestingly, the exponential distribution is also used for predicting failure rates of light bulbs and electronic components. How many bulbs will glow for say 100,000 hours can be calculated simply from the average life of a bulb.

POLICY IMPLICATION : This makes me wonder if fiscal and tax policies that favor the middle class or favor the rich may be exactly equivalent. The whole income distribution curve moves in a related way. In other words, if the mean income goes up, the number of millionaires goes up correspondingly. More millionaires will also result in an exactly corresponding increase in mean income. Think about it.