Friday, September 17, 2010

If You Lower The Excise Tax On A Good By $1.00, Does A Firm Save $1.00 On Each Unit Sold?

Probably not. This issue came up in an article that I linked on Wed. One of the things it said was:

"Crapo's bill would cut the federal excise tax on brewers' first 60,000 barrels of beer in half to $3.50, saving brewers up to $210,000 a year."

One thing we know in economics is that if we enact a tax in the first place, most likely some of the tax is paid by the seller and some is paid by the buyer. We can see this by looking at the following graph. Suppose an excise tax of $1.00 is imposed on this good. The immediate effect is to shift up the supply curve by $1.00. As you can see, the new price is now $6.00 where as before the tax it was $5.50. That means the buyer is paying $0.50 more than before. Then the seller gets $0.50 less.

Before the tax, when a consumer bought the good, they paid $5.50. Now they pay $6.00. But the seller has to give the government $1.00 of that, leaving them with $5.00 or $0.50 less than they got before. Now how this relates to the barley tax is explained below the graph.

Suppose, initially, for the sake of simplicity, that in the market represented by the graph above, the government now eliminates the $1.00 tax on the first 20 units sold. That basically means that we are back to S1 and a price of $5.50. The sellers collectively save $5.00. Why? Because they lost $0.50 per unit before the tax was eliminated and they sold 10 units. Now they sell 11 units and pay no tax. So they are $5.00 better off. But, if we went along with the way the article reads, we would say that the sellers save $10. That is impossible, since they did not lose $10 to begin with. So it would be impossible for the barley growers to save $3.50 per unit sold if that is how much the tax was reduced.

But let's try eliminating the tax on the first 5 units sold, kind of like the proposed change to the barley tax. So there will only be a $1.00 tax on units 6-10. It think that part of the supply curve shifts down by $1.00, but only up to a Q of 5. Then the rest of the supply line is still S2. The graph below shows this. The equilibrium price is still $6.00 and the equilibrium quantity is still 10. Businesses pay $0.50 per unit from the tax on the last 5 units sold so their total cost from the tax is $2.50. So cutting the tax only saves them $2.50 since before this change of not taxing the first 5 units, they paid $5.00. Now they pay $2.50 or $2.50 less than before.

This means that the barley growers cannot save $3.50 per unit over 60,000 units for a total savings of $210,000. It will be less than that.

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