Econ Lab · Taxation

Taxation and Incidence

Stay with the coffee market, and suppose the government puts a tax on every cup sold. Simple enough. But here is the question that trips almost everyone up. Who actually pays it? The cafe that hands the money to the tax office, or the customer at the counter?

The honest answer is both, and the split has almost nothing to do with who writes the cheque. Slide the tax up and watch where the two prices land.

02680100200300400
Cups of coffee\text{Cups of coffee}
Price per cup ($)\text{Price per cup (\$)}
DD
SS
S′S'
no-tax price\text{no-tax price}
Q=200Q = 200
4.04.0

No tax yet. The coffee market clears at 44 dollars a cup, where demand meets supply. Buyers pay exactly what cafes receive, and every cup that is worth making gets made.

Move the tax slider. The supply line lifts by the tax, and the gap between buyers and firms opens up.

Try it

Start with the tax at zero. The market sits at four dollars a cup, where demand meets supply. Now raise the tax. The supply line lifts by exactly the tax, because cafes need that much more per cup before they will brew the same quantity.

Two new prices appear. The higher one is what buyers pay. The lower one is what cafes keep after handing the tax over. The distance between them is the tax itself.

The wedge

That gap has a name. It is the tax wedge, and it is always exactly the size of the tax.

Pbuy−Psell=tP_{\text{buy}} - P_{\text{sell}} = t

Here demand and supply are equally steep, so the wedge opens symmetrically. Each dollar of tax pushes the buyer's price up by fifty cents and the cafe's price down by fifty cents.

Pbuy=4+t2,Psell=4−t2P_{\text{buy}} = 4 + \tfrac{t}{2}, \qquad P_{\text{sell}} = 4 - \tfrac{t}{2}

And the cups sold fall, because at the higher price buyers want less. Q=200−25 tQ = 200 - 25\,t.

Who really pays

Notice what did not matter. The law said cafes must remit the tax, yet buyers ended up carrying half of it through a higher price. The side that legally pays is not the side that economically bears it.

What decides the split is steepness. The side that cannot easily walk away, the steeper curve, ends up carrying more. If buyers could not give up their coffee, the price they pay would climb most of the way and cafes would barely feel it. Flip the steepness and the burden flips with it. The cheque-writer never changes, but the burden does.

What you just did

You worked out tax incidence by hand, the question of who really bears a tax once prices adjust. You also saw the first hint of a deeper cost. Quantity fell below where it sat with no tax, so some trades that were worth making no longer happen. That lost ground is the deadweight loss, and it is the next thing worth seeing.

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