# Goat Economics: Why the Laffer Curve Is No Joke

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Goat herding is one of the world's oldest economic professions.  It is because goats are excellent at reproduction, and easy to feed and raise. A female goat will on average birth around 2 kids per year. Simple math would suggest that if you start with 2 goats, you can double your herd each year. Thus in 10 years you will be quite wealthy with over 1000 goats (2^10 = 1024).

But as one can imagine, it turns out that goat herding is a little more complicated than that. First, the normal life expectancy of a goat is around 10 years.  This means you will lose about 10% of a herd to old age annually. Additionally, while goats may birth two kids per year, the viability rate is around 75% such that each female will only net an average of 1.5. Still, if you do the calculations, starting with 10 female goats you will have around 1496 female goats after 10 years.

Since raising goats is a rather simple economic activity, it is easy to model the impact of taxation on goat farming. Assuming the government comes and takes various numbers of the new goats (income) each year in goat taxes, one can easily calculate the impact of the size of the herd, and ultimately how much total revenue the government would receive over 10 years at various tax rates. It turns out that the optimum tax rate is in the 20-30% range to maximize total 10 year revenue.

The reason the tax revenue drops above a 30% rate is simple. If the government takes more new goats in taxes, the goat farmer has fewer goats to breed the following year. The smaller herd produces fewer new goats to tax each subsequent year. As a farmer, it also greatly reduces the size of the herd (wealth). Below is the cumulative ten year tax revenue when starting with 10 female goats, the tax collected in year 10, and the herd size after ten years:

For goat farming, the chart above clearly shows that tax rates above 30% make both the goat herder and the government poorer. In fact, long term revenues (year 10 revenues) are better around a 20% tax rate.

It is worth noting the wealth effect in this example. For a tax rate of 30% vs. 20%, the extra revenue is 7 goats over 10 years for the government, but the size of the herd shrinks by 232 goats for the goat farmer. In this example, there is a definite multiplier effect for additional government spending. Government spending destroys wealth at a multiple of what it collects from the farmer.

This type of revenue curve is exactly what Arthur Laffer would predict with the Laffer Curve. Laffer stated that there are two known revenue points for tax rates. At a 0% tax rate, tax revenue is zero; and at a 100% tax rate, the tax revenue is zero. Somewhere in between these two limits there is a maximum revenue point for taxation.

It should also be noted that the curve listed above is not the Laffer Curve, but rather the physical limit for goat herding. The Laffer curve would suggest the actual goat herding activity would drop as tax rates go up due to a disincentive to work. On this basis, the optimum tax rate would be lower than the physical limit peak. This is a significant point in light of the current debate around increasing tax revenues. The Democrats only want to increase tax rates on the wealthy who are already on the downward slope of the curve while doing nothing to increase tax rates on the famous 47% who pay no income taxes. Based on this curve, one would expect income tax revenues to drop if they are successful.

For a goat farmer, government is necessary and does play a very worthwhile role. The government prevents foreign armies from invading and taking the goats (national defense), other people from stealing the goats (justice), or someone from running the goat farmer off the land he uses to raise goats (protect property rights).

In this example with goat farming, it does not matter whether the government is getting goats through taxing new ones(income tax), borrowing goats from the herd (deficit spending), or stealing the goats at night (monetizing debt). When the government takes goats by any means, it destroys wealth and lowers future tax revenues. The most important feature to stimulate the size of the goat herd and thus increase tax revenue is to reduce the number of goats taken by the government each year (reduce spending).

As much as I hate to say it, when I see our president and Congress raising tax rates on the rich to stimulate revenues, it really gets my goat.

Charlie Musick (musickcd@bellsouth.net) is a chemical engineer in research & development.

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