# Taxes levied on sellers = Taxes levied on buyers

All page numbers refer to Principles of Microeconomics, 7 Ed, 2014, by NG Mankiw.

[p 125:] Taxes levied on sellers and taxes levied on buyers are equivalent.
[p 156:] ... When a tax is levied on buyers, the demand curve shifts downward by the size of the tax; when it is levied on sellers, the supply curve shifts upward by that amount. In either case, when the tax is enacted, the price paid by buyers rises, and the price received by sellers falls. ...

What's the intuition? I already proved this 'surprising conclusion' with a supply-demand graph (p 130, Question 6.7) and so ask NOT about a graphical or rigorous math proof.
I understand the para below, but don't comprehend how it intuitively explains the supply-demand mechanisms (the quote below concerns only how the tax is sent to the government)?

[p 125:] The equivalence of these two taxes is easy to understand if we imagine that the government collects the $0.50 ice-cream tax in a bowl on the counter of each ice cream store.' ..... • Why would I just not choose a seller in a lower tax area? Since when have all buyers of a given seller had to pay the same tax, or all possible sellers for a given buyer had to pay the same tax? Mar 7, 2015 at 18:10 ## 4 Answers Whether the tax is imposed on the buyer or the seller doesn't make any practical difference. It's just an accounting detail. One might even say, it's just an accounting trick. I haven't read this particular book but I imagine what he was driving at with the "bowl" example was this: Suppose that instead of filing tax forms, etc, the government collected taxes on the spot: There is a tax collector standing beside the counter with a bowl to collect the tax money. The price not including the tax is \$10. The government charges a \$1 tax. So, scenario 1: The government declares that the buyer must pay the tax. So when you buy the product, you hand the seller \$10, and then you drop \$1 into the tax man's bowl. Scenario 2: The government declares that the seller must pay the tax. So the seller increases the price to \$11. When you buy the product, you hand the seller \$11. He then drops \$1 into the tax man's bowl, and keeps the remaining \$10. Either way, the buyer has \$11 less cash, the seller has \$10 more cash, and the tax man has \$1 more cash. Whether the buyer hands the tax money directly to the tax man, or the buyer hands the money to the seller and the seller hands it to the tax man, makes very little practical difference.

We could discuss what portion of the tax is really born by the seller and what portion by the buyer. If today the tax is zero and tomorrow the government begins imposing a \$1 tax, it doesn't necessarily follow that the seller can continue to collect \$10 and the buyer will pay \$11. Increasing the cost to the buyer to \$11 would mean that fewer units are sold -- some number of people will not buy or will not buy as many for \$11. So the seller may conclude that to maintain sales sufficient to maximize his profits, he must drop the price to, say, \$9.60, so with tax the total price is now \$10.60, and the seller is paying 40 cents of the tax while the buyer is paying 60 cents. Or he may have to drop the price further, or not drop it as much. But whatever the optimum price ends up being, whether the government nominally collects the \$1 from the buyer or from the seller has nothing to do with how the tax is really being split between buyer and seller.

There is the technicality that there may be costs involved in record-keeping or other mechanics of the tax. Like if the seller is required to collect the tax and turn if over to the government, then the seller has additional book-keeping costs. If the buyer is expected to keep records and pay the tax, then the buyer has book-keeping costs. But this isn't the main point.

Both buyers and sellers have a degree of elasticity to the price - how much they change their demand/supply if the price changes a bit.

If you tax the buyer, that is like increasing the price - he will reduce his demand according to his elasticity. Given a shrinking Q, the seller will adjust the price to get the most out of the deal - according to his elasticity. They "split" the tax, if you will, according to their elasticity.

Whoever has the higher elasticity - whoever reacts more strongly to price changes, is the "winner" - the other one will try to compensate relatively more for the price change in order to have the total quantity not changed too much.

### Comparison with Bargaining

You and your buddy have a project going, involving a startup cost. You were planning to split it. Then, for some reason, the project cost increases. Whoever is worse at bargaining ("if you don't pay this much of the project cost, I leave"), will have to take the lion share of the costs. Here, there is no bargaining, but whoever "cares less about the price" is the one with the better bargaining power.

The key point is to remember that prices are determined by the equilibrium condition that quantity supplied must equal the quantity demanded. This is a fundamental proposition of price theory. The result that you speak of is a logical consequence of that condition given the standard framework. In the presence of taxes, the effective price that a buyer or seller changes. So, prices must adjust so that equilibrium is again reached. The result is that prices adjust in the same way, regardless of who remits the tax. Just think of it that way.

So, given the idea that prices adjust so that an equilibrium reaches, I think the best intuition beyond what has been given is to think of a tax as a wedge between the price buyers and sellers face. It doesn't matter whether you obtain that wedge by increasing buyers effective price or by lowering sellers' effecting price. Because prices will adjust to equilibrium, the only thing that matters in the end is the size (think width) of that wedge.

The intuition is that there is only one price in a transaction. The tax acts upon that price. Its a fiction that the tax is "paid by" either party individually. The tax is paid out of the money exchanged in the transaction. Whether the money is ultimately given to the government directly from the buyer or directly from the seller is completely different from who bears the cost of the tax.

In a perfect competition scenario, the sellers are all price takers and have no leeway to bear the cost of the tax, therefore the burden of the tax falls entirely on the buyer (in the form of a higher price). Of course, the sellers in the industry as a whole still pay a price by selling less units, and therefore some sellers will go out of business.

By contrast, in a more monopolistic scenario, the buyer bears part of the burden of the tax by paying a higher price, and the business pays part of the burden by selling a lower volume at a potentially lower profit margin.