Per-Unit Taxes and the Tax Wedge

A per-unit tax, say 3 dollars on every unit sold, does not just add 3 dollars to the old price. It wedges itself between two prices that used to be one: the price buyers pay (Pb) and the price sellers keep (Ps), with Pb - Ps = t. Both prices move from the old equilibrium, but usually not by the full tax. Quantity falls, because the new equilibrium is wherever Qd at Pb equals Qs at Ps, and that quantity is lower than before the tax existed.

To solve a tax problem, substitute Pb = Ps + t into the demand or supply equation and set Qd = Qs, then solve for Ps, then get Pb = Ps + t, then plug either price back in for the new quantity. Tax revenue is t times that new quantity. Graphically, the tax opens a rectangle between Pb and Ps across the new quantity — that is government revenue — and a triangle just to the right of the new quantity, between the old demand and supply curves, that is deadweight loss: trades that used to make both sides better off but no longer happen.

Who physically hands the money to the government is irrelevant. Supply and demand curves describe willingness to pay and willingness to accept, and those don't care about legal paperwork. The actual split of the burden, how much of the wedge falls on buyers versus sellers, depends only on relative elasticity: whichever side is less elastic, less able to walk away, absorbs more of the tax. Doubling the tax does not double the deadweight loss; the triangle's area grows with the square of the wedge, so it roughly quadruples.