A paper which is receiving considerable attention (see here, here and here) is Diamond and Saez's Journal of Economic Perspectives piece on optimal marginal tax rates. They put the rate at 73 percent, and declare it an optimum because it would maximize revenue that could then be used for other things. In particular, they argue that the utility lost to the rich would be much less than the utility gained by lower income people via government programs. I do believe that many government programs leave people better off, but I am skeptical about whether the optimal size of government is that which is supported by a revenue maximizing income tax.

In any event, one aspect of the paper bothers me: if one searches for the word "incidence," it is not found. Incidence reflects who really bears the burden of a tax. If one taxes a person or a business, they might absorb it, or they might pass it on to someone else.

The formula for the incidence of a tax on those who demand a taxed good is (Supply Elasticity)/(Supply Elasticity - Demand Elasticity). (I apologize for not having elegant formulas--I don't know how to paste them into Blogger). Because demand curves are generally downward sloping, demand elasticity has a negative sign, so in a sense, the incidence reflects how relatively elastic supply is relative to the sum of the absolute values of the elasticities of demand and supply.

Now let's think about supply elasticity at the revenue maximizing point. It is exactly one, in that the reduction in labor offered exactly offsets any increase in the rate. To illustrate, let us just assume for a moment that demand elasticity is -1. Then half the incidence of the tax is on the supplier of labor or capital (a.k.a. the rich) and half the incidence is on the demander. This means that the burden on the rich person is 36.5 percent, not 73 percent.

What we do know is that as tax rates fall, the supply elasticity of the wealthy falls. Why? Because we know at lower tax rates, raising rates raises revenue-the supply response to an increase in taxes is smaller. Let's assume that at a 50 percent marginal tax rate, the elasticity of labor supply for the rich is .25. Now the incidence on demanders is .25/1.25, or 20 percent of the tax burden; it is 80 percent on the rich. hence with a 50 percent tax rate, the effective tax on the rich is 40 percent, or higher than it would be with a 73 percent rate!

These arguments all depend on assumed elasticity parameters, and so it is important to estimate them as best as possible. I should also note that I am all for raising taxes, including on myself, to pay for the many government services that I do support. Somedays I think that if I could change the tax code, I would just raise my own taxes by ten percent and then have policy that assured that everyone with income greater than mine would pay an effective tax rate no lower than mine.

In any event, one aspect of the paper bothers me: if one searches for the word "incidence," it is not found. Incidence reflects who really bears the burden of a tax. If one taxes a person or a business, they might absorb it, or they might pass it on to someone else.

The formula for the incidence of a tax on those who demand a taxed good is (Supply Elasticity)/(Supply Elasticity - Demand Elasticity). (I apologize for not having elegant formulas--I don't know how to paste them into Blogger). Because demand curves are generally downward sloping, demand elasticity has a negative sign, so in a sense, the incidence reflects how relatively elastic supply is relative to the sum of the absolute values of the elasticities of demand and supply.

Now let's think about supply elasticity at the revenue maximizing point. It is exactly one, in that the reduction in labor offered exactly offsets any increase in the rate. To illustrate, let us just assume for a moment that demand elasticity is -1. Then half the incidence of the tax is on the supplier of labor or capital (a.k.a. the rich) and half the incidence is on the demander. This means that the burden on the rich person is 36.5 percent, not 73 percent.

What we do know is that as tax rates fall, the supply elasticity of the wealthy falls. Why? Because we know at lower tax rates, raising rates raises revenue-the supply response to an increase in taxes is smaller. Let's assume that at a 50 percent marginal tax rate, the elasticity of labor supply for the rich is .25. Now the incidence on demanders is .25/1.25, or 20 percent of the tax burden; it is 80 percent on the rich. hence with a 50 percent tax rate, the effective tax on the rich is 40 percent, or higher than it would be with a 73 percent rate!

These arguments all depend on assumed elasticity parameters, and so it is important to estimate them as best as possible. I should also note that I am all for raising taxes, including on myself, to pay for the many government services that I do support. Somedays I think that if I could change the tax code, I would just raise my own taxes by ten percent and then have policy that assured that everyone with income greater than mine would pay an effective tax rate no lower than mine.

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