The tax collector knows whom to pursue; the economist still has to discover who pays. A shopkeeper sends the money to the treasury, but the customer may have handed over part of it in a higher price. A customer is charged at the till, but the shopkeeper may have conceded part of the charge through a lower price before tax. The receipt records the collection faithfully while leaving this division unresolved. The state's claim has entered the bargain, and the bargain can move around it. To follow the burden, we must compare the prices, quantities and incomes that result with those that would have prevailed without the claim.
A competitive market supplies a precise benchmark for that comparison. Suppose sellers respond to the price they keep, buyers to the full price they pay, and both know the tax. A unit tax then places a fixed difference between those two prices. The market must find a quantity at which willingness to pay covers both the seller’s marginal cost and the tax. Whether the seller sends the tax out of the amount collected or the buyer sends it separately leaves that condition unchanged. This equivalence depends on how the parties respond and how the market clears; the legal direction to remit the money does not, by itself, determine the economic division.
The side with fewer alternatives bears more of the price adjustment in this benchmark. If buyers readily turn to another good, an attempted price rise sends them away, pressing sellers to accept less. If suppliers can readily withdraw resources to another use, they have less reason to accept a reduced net price, pressing buyers to pay more. Relative responsiveness matters. A demand described as inelastic can still be more responsive than the supply facing it, and therefore leave much of the burden on sellers. The relevant comparison is between the two sides’ responses in the same market, over the same period, for the change being considered.
An invented market shows how a tax can be split even though only one party remits it. Let willingness to pay for the next unit be thirty pounds minus twice the quantity, and marginal cost six pounds plus the quantity. Without tax, eight units trade at fourteen pounds each. A tax of six pounds reduces trade to six units. Buyers now pay eighteen pounds; sellers retain twelve. The buyer price has risen four pounds and the seller price has fallen two. A law requiring sellers to send the whole six pounds to the treasury would therefore leave two-thirds of the unit charge reflected in the higher buyer price and one-third in the lower seller price. Requiring buyers to remit it would produce the same prices under the stated conditions.
The price division leaves a second division to be accounted for: the surplus lost by each side. Before the tax, buyers have sixty-four pounds of surplus and sellers thirty-two. Afterwards, their surpluses are thirty-six and eighteen, while the treasury has thirty-six. Buyers have lost twenty-eight pounds and sellers fourteen, a combined forty-two. Of that amount thirty-six has reached the state and six is the net gain lost on the two units no longer traded. Describing all forty-two as tax revenue would overstate the receipts; describing all forty-two as deadweight loss would erase the treasury. The burden on market participants includes the transfer and the foregone gain, while the latter is the loss left after the transfer has been brought back into the account.
The familiar elasticity formula is a local expression of this price adjustment. At the untaxed position in the example, the supply elasticity is one and three-quarters, while the absolute demand elasticity is seven-eighths. The buyer’s share of a small unit tax is supply elasticity divided by the sum of the two elasticities: two-thirds. The seller’s share is one-third. These are shares of the marginal price wedge, not a universal formula for each household’s complete welfare loss. A large tax may move the market to a place where the elasticities differ, and a household may be affected through several markets at once. Our straight-line example keeps the price fractions fixed; an actual estimate must establish the relevant response.
Time changes the alternatives behind those responses. A machine already installed may have little use elsewhere this month, while replacement investment can go elsewhere over the coming years. Buyers may initially have no convenient substitute and later learn to economise or change their equipment. A burden borne by the existing owners at first can therefore reach workers, customers or future investment differently as adjustment proceeds. Even the fixed-supply result needs its object and its model specified: a tax on the pure return to unimproved land differs from a tax on building or maintenance, and a tax that leaves the acreage unchanged may still alter investment elsewhere. The unchanged quantity of one resource cannot settle every effect on the incomes around it.
The treasury receives a payment from one hand; the bargain determines how many hands have borne it.
The benchmark also depends on buyers perceiving the price that the analyst has put into their demand curve. Chetty, Looney and Kroft examine a setting in which consumers respond differently to a posted price and a tax added to it. If buyers react little to the added tax, sellers face less pressure to cut their pretax price to clear the market. In the limiting case where the tax does not change demand at a given pretax price, that price need not move at all: buyers bear the whole additional payment. Which side is charged can then matter if it changes how conspicuously the charge enters the price. The old equivalence remains a useful comparison, but attention is one of the conditions that makes it work.
The recipient of a lower income must eventually be a person, though the tax may first appear in a firm’s accounts. Workers, customers and owners are possible bearers, and a single household can occupy all three positions. Following the burden therefore requires asking how wages, returns and purchase prices change together, rather than treating a charge on an organisation as though it stopped at its name. A tax in one market may also change the prices and rewards in another as spending and resources move. Fullerton and Metcalf make this wider accounting central to incidence: a partial market calculation is a starting point, while a distributional conclusion must identify the people and all the relevant changes in their opportunities.
The state’s use of the proceeds completes a different part of the account. Our treasury’s thirty-six pounds might finance something its taxpayers value, transfer purchasing power to other people, or purchase resources for a project whose benefits do not justify them. Holding spending fixed while studying a tax, studying a tax together with its spending, and replacing one tax with another are different comparisons. The loss of six pounds in the invented market is a cost of raising the revenue under its assumptions. It is not a judgment that every possible use of the revenue is worth less than that cost. Nor would the same sign follow if the charge were correcting a harm omitted from the private price, as The Loss showed.
The elasticity lesson is a statement about adjustment, rather than an instruction to tax whoever has the least freedom to escape. A small quantity response can mean little deadweight loss within a narrow market calculation, while a particular group still parts with a substantial share of its means. Judging that result requires information about resources, needs and the benefits financed by the tax. The fact that a burden can be collected with little movement along a curve does not determine who ought to carry it. Efficiency in raising revenue and justice in distributing it remain related questions with different answers to supply.
The law supplies an address for collection; the surplus account follows the consequences beyond it. Sometimes the statutory payer and the ultimate bearer coincide. Sometimes prices shift most of the burden elsewhere. The answer is earned by specifying the market, the period, the information and the fiscal alternative, then tracing the people affected. Even that account measures their losses in money they could command. The next plate turns to the willingness to pay itself, and asks how faithfully that command speaks for what they need.