# Efficient Taxation

## Lump Sum Taxes

A lump sum (or poll) tax is when the government demands the same $X from each person. You'll see this one crop up quite a bit as favored by economists. The justification given is that, since these taxes are constant, they do not distort economic decisions, meaning there is no deadweight loss.

This is obviously ludicrous.

Someone working 40 hours per week for $10 per hour makes $20,800 per year. A $20,000 lump sum tax leaves only $800 to live on, which strongly suggests they will increase how much they work to survive (or somehow avoid paying the tax). This is a huge distortion. Compare to a billionaire, whose behavior wouldn't change at all.

As best I can tell, the popularity of this tax scheme is due exclusively to the second fundamental theorems of welfare economics Fundamental theorems of welfare economics:

Out of all possible Pareto optimal outcomes one can achieve any particular one by enacting a lump-sum wealth redistribution and then letting the market take over

TODO: Write why this is wrong.

## Taxing Land

The deadweight loss of a tax is determined by the elasticity of the supply and demand for that good. The less elastic these curves are the less deadweight loss a tax will impose Deadweight loss.

A natural implication of this line of reasoning is the government should tax goods with perfectly inelastic supply and demand. Land fits nicely - with some minor exceptions made for man-land. Note, however, that for the supply to be perfectly inelastic, we have to tax only the value of unimproved land. For instance, we wouldn't count the value of the buildings on a piece of land.

Another reason land is ideal for tax purposes is that its value is largely derived as an externality. For instance, if a Walmart opens up, homes around the new Walmart will likely rise in value. This is an unearned boon to those homeowners that Walmart can't internalize. In this sense, land ownership is a trillion dollar example of rent seeking, and, in fact, an entire ideology has evolved around this premise Georgism.

To clarify, the value of a plot created by improvements around that plot are fair game to tax since such taxes create no deadweight loss. The value created by improvements to that plot of land shouldn't be taxed.

Taxing land has two main downsides:

- Like all capital gains taxes, the entire cost of the tax is imposed on today's land owners.
- It is difficult to compute the value of a plot of land.

The first problem is one of fairness rather than practicality or efficiency, so we'll sidestep it. The second problem was provided an elegant solution by Arnold Harberger in 1965:

- Have everyone say how much their land is worth.
- Implement a tax as a fixed percent of the land's value.
- Force anyone to sell their property for the price they gave if someone else offers it.

This method ignores the distinction between taxing land and taxing unimproved land, which makes it distortionary, but it also has the interesting (if controversial) feature of eliminating the need for eminent domain: if you land is needed for a public work or shopping mall, the government or company just pay you want you said your home is worth. The downside, of course, is you are forced to sell at that price. You can imagine some poor family who values their home a great deal because its near their family/friends/work but can't afford the proper Harberger tax being evicted.

Whether you use a Harberger tax or not, the maximum possible revenue land taxes can raise equal to the interest rate times the value of all land since, a higher tax would make owning land a net-negative. In 2005, that value of real estate was about $36 trillion and about one third of that was land-value The value of land in the United States - that's about 2.7 and 0.9 times GDP.

The next question concerns what the "interest rate" is. Since the taxes are certain, we should look at the safest investments. Inflation-protected treasury bonds typically trade for around 0.6% interest DFII10. Adding 2% for inflation yields an interest rate of around 2.6%.

This all suggests a land value tax can raise at most 2.3% of GDP while a property tax is limited to about 7% of GDP. This is not nearly enough to fund existing government spending, which numbers around 33% of GDP Table 1.1.5 Table 3.1.

## Taxing Consumption

Taxing consumption has been the go-to choice for many economists for decades.

A flat consumption tax is appealing from an efficiency standpoint:

- It eliminates the potential of having a large tax bill at the end of the year.
- It dramatically reduces tax complexity relative to existing income tax schemes.
- Compared to capital gains and corporate profit taxes, consumption taxes don't distort how much people save

Finally, economists generally prefer low taxes on large tax bases to high taxes on small tax bases. There are two reasons for this.

First, deadweight loss grows quadratically with the tax rate but only linearly with the tax base. Therefore, for a given revenue, it is generally better to tax more things at lower rates.

Second, larger markets have lower elasticities, which (again) means they have lower deadweight loss.

By these metric, consumption taxes do pretty well given that consumption is around 60% of GDP. A practical benefit is that we can actually run our government on a consumption tax (at 55%) which was impossible with just a land tax.

Moreover, Frank Ramsey proved that to minimize deadweight loss Ramsey
the tax ad valorem on each commodity should be proportional to the sum of the reciprocals of its supply and demand elasticities

In other words, the optimal consumption tax on a good is given by

$$\frac{a}{1/\epsilon_S + 1/\epsilon_D}$$where $a$ is some constant set to raise enough revenue while $\epsilon_S$ and $\epsilon_D$ are the elasticity of supply and demand, respectively.

The basic idea going on here is that, as already mentioned, taxes on inelastic goods generate less deadweight loss, so they should be taxed more. In this way, the land-value tax is really just a special case of Ramsey's theory.

I've never heard of an economist explicitly endors Ramsey-esque taxation. It has numerous practical issues: How do we estimate the elasticity of all these goods? How do stores get told the tax rate for all their goods? How do we decide what the categories of goods are? How do we decide what goods are assigned to each category? However, it's worth mentioning because, whatever its pragmatic faults, it was widely-accepted as the *theoretical ideal* prior to 1976.

## The Atkinson-Stiglitz Theorem

In 1976, Atkinson and Stiglitz proved the Atkinson-Stiglitz theorem, which assumes several things (which we'll cover later) and ends up concluding that there is no reason to tax consumption if you implement an optimal income tax *even if you care about equality and not just efficiency*.

Now, the assumptions are fairly strong and the proof mathematical, but the conclusion should make some sense: Take two households that are identical in all non-consumption ways (same income, same wage-earners, same number of kids, same wealth, etc). The Ramsey approach suggests the household buying more inelastic goods should be taxed more.

TODO