A subsidy is a payment from the government to a firm, made directly or through lower taxes, when the firm carries out certain actions.
Indirect tax
An indirect tax is a tax on spending on goods and services, collected from producers, such as VAT or excise duty.
A subsidy on each unit produced
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BeforeBefore the subsidy, demand D meets supply S1 at price P1 and quantity Q1.
A subsidy per unit shifts supply down by the subsidy, so the price consumers pay falls from P1 to P2 and quantity rises from Q1 to Q2.
Government subsidies reduce the cost of production. Firms will supply each quantity for the old price minus the subsidy, so supply shifts down by the subsidy per unit, which is the same as a shift to the right.
Consumers pay P2, and producers receive P3, which is P2 plus the subsidy and higher than P1. The cost to the government is the subsidy per unit times Q2: the rectangle between P3 and P2, from zero to Q2.
Consumers gain most from a cost cut when demand is inelastic, because the shift in supply then brings a much lower price. When demand is elastic, the price falls only slightly and quantity rises instead.