The simple public finance of the matter, of course, would have the taxes apply to online purchases in order to avoid the distortion associated with applying the tax to some sellers but not all.
A similar line of argument works against state laws that apply different sales tax rates to different goods. Perhaps the feds could pass a law allowing state collection of sales taxes for online purchases but only if they apply their sales tax equally to all purchases of whatever product from whatever seller.
"only if they apply their sales tax equally to all purchases of whatever product from whatever seller."
Including buildings? Rent? Used goods? Wages? Shares of stock?
Just as firms adjust prices to take account of elasticities, states need flexibility in setting sales taxes. For example, if New York had a sales tax and had to apply it to shares of stock, they would quickly lose the NYSE.
As Georgists point out, you could tax a good with completely inelastic supply at a very high rate with no distortion, only redistribution. The same tax on a good with elastic supply would cause a lot of distortion.
Of course, once you allow differences, politics will take over and tax rates will be set according to influence, not some economist's estimate of supply elasticity. But I don't think it is obvious that this would be worse than a uniform tax on everything.
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