Per-Unit Subsidy Market Effect Calculator

This calculator applies that wedge to a linear demand curve and a linear supply curve, then solves the resulting market equilibrium exactly. Enter the intercept and positive slope magnitude for each curve, along with the subsidy per item. The result shows the original benchmark, the new equilibrium quantity, both sides of the post-subsidy price, how the benefit is divided, and total government expenditure at the new quantity.

Describe the market with two linear curves

The calculator represents demand as Qd = a - bPb and supply as Qs = c + dPs. In these expressions, a is the demand intercept, b is the positive absolute demand slope, c is the supply intercept, and d is the positive supply slope. Pb means the price buyers pay, while Ps means the price sellers receive. Before a subsidy, those two prices are equal, so the original equilibrium comes from setting the two quantities equal at one market price. Enter quantities and prices in consistent units throughout. If quantity is measured in thousands of items, every quantity result and the expenditure calculation inherit that scale. Likewise, the subsidy must use the same currency-per-item unit as the prices implied by the curve coefficients. The slopes must be strictly positive because the model assumes demand falls as the buyer price rises and supply rises as the seller price rises. This is a partial-equilibrium model: it treats the two curves as fixed and does not estimate how income, technology, expectations, or related markets might shift them after the policy begins.

Interpret the subsidy wedge and the new equilibrium

A subsidy of s per unit means sellers receive s more than buyers pay, so Ps = Pb + s. The calculator substitutes this relationship into the supply curve and sets subsidized supply equal to demand. It then reports the new equilibrium quantity, the buyer price, and the seller price. Their difference should equal the subsidy, apart from harmless display rounding. The original equilibrium is included as a benchmark, making the reported changes easy to interpret. A negative buyer price change means buyers pay less than before; a positive seller price change means sellers receive more. The buyer benefit per unit and seller benefit per unit express those same changes as positive shares of the subsidy. Their sum equals the subsidy in the standard interior solution. Incidence does not depend on whether a law says the payment goes to buyers or sellers: within this frictionless linear model, the relative slopes determine how the benefit is split. The side of the market that responds less strongly to price generally captures more of the subsidy because its quantity is less elastic locally.

Use the result carefully for policy analysis

Total government expenditure is calculated as the subsidy per unit multiplied by the new equilibrium quantity. This is the direct fiscal outlay in the model, not a complete welfare estimate. It does not subtract tax revenue changes, administrative costs, fraud, financing costs, or spillovers. The quantity change shows the modeled increase in transactions, but it is not by itself the social benefit of the program. For a fuller welfare analysis, compare changes in consumer and producer surplus with government expenditure and any external benefits or costs. Also check whether the new prices and quantity remain plausible over the relevant range. Linear curves are local approximations and can imply unrealistic negative prices or extrapolated quantities when the subsidy is very large. A mathematically valid result can therefore be economically unsuitable if the policy moves the market far beyond the observations used to estimate the curves. Run alternative slope estimates or subsidy sizes to see how sensitive incidence and expenditure are. For API automation, each calculation costs $0.002; keep the same unit conventions across scenarios so comparisons remain meaningful.