Market Equilibrium with a Per-Unit Tax Calculator

Enter each curve's quantity intercept and price slope, plus the tax charged on every unit. The result gives the original equilibrium, the after-tax equilibrium quantity, the buyer price, the seller price, each side's per-unit burden, and total tax revenue. It is designed for economics exercises, policy scenarios, and repeatable automated calculations.

Represent the linear market consistently

The calculator writes demand as Qd = a - bPb and supply as Qs = c + dPs. Here, a is demand quantity when the buyer price is zero, b is the positive absolute slope of demand, c is supply quantity when the seller price is zero, and d is the positive slope of supply. Pb is the amount buyers pay per unit, while Ps is the amount sellers keep per unit. Before tax, Pb and Ps are the same market price. Keep every input in compatible units. If prices are dollars per item, the tax must also be dollars per item. If quantity is measured in thousands of items, intercepts, equilibrium quantities, and tax revenue all retain that scale. Enter slope magnitudes as positive numbers; the minus sign in the demand equation already captures the downward direction. The calculator treats the curves as fixed, competitive schedules. It does not infer the coefficients from observations or account for simultaneous shifts in income, technology, expectations, market structure, product quality, or related markets. Those changes require new curve inputs rather than a different interpretation of the same result.

Solve and interpret the tax wedge

A tax of t per unit creates the relationship Pb = Ps + t: buyers pay the seller price plus the tax wedge. Substituting that relationship into demand and setting demand equal to supply produces the after-tax equilibrium. The returned buyer price minus the seller price equals the tax, apart from harmless rounding at the twelfth decimal place. The original no-tax price is also reported, which makes incidence visible. The buyer tax burden per unit is the buyer price minus the original price. The seller tax burden per unit is the original price minus the seller price. In an interior competitive solution, those two burdens add to the statutory tax. This division does not depend on whether the law formally requires buyers or sellers to remit the payment. The relative slopes determine economic incidence because the less price-responsive side changes its behavior less and generally bears more of the wedge. Quantity change is reported as the after-tax quantity minus the initial quantity, so a standard positive tax normally produces a negative value. Tax revenue equals the tax per unit multiplied by the after-tax quantity, not the quantity that existed before taxation.

Recognize the model's policy limits

Use the output as a transparent partial-equilibrium benchmark, not as a complete forecast or welfare verdict. A linear curve may approximate behavior well near observed prices yet become unrealistic when a large tax pushes the solution far outside the estimation range. The calculator rejects a negative equilibrium quantity, but mathematically possible negative prices are retained because some electricity, waste, storage, or disposal markets can exhibit them. Review whether such prices make sense for the market being studied. Tax revenue is a gross collection estimate; it does not subtract administration, enforcement, avoidance, evasion, collection delays, or changes elsewhere in the tax system. Likewise, the quantity decline is not itself deadweight loss. A full welfare analysis would calculate changes in consumer surplus and producer surplus, include government revenue, and consider external costs or benefits. Real policies may also feature exemptions, thresholds, ad valorem rates, imperfect competition, inventories, cross-border trade, capacity constraints, or different short-run and long-run responses. When inputs are uncertain, run several plausible slope and tax scenarios, preserve the chosen units, and document the source and valid range of every coefficient. Each automated API calculation costs $0.002.