Subsidies

1. Because the payment lowers unit costs, the supply curve shifts vertically downwards by the amount of the subsidy per unit, the mirror image of an indirect tax.
2. The new equilibrium has a lower price for consumers and a higher quantity traded.
3. The effective price producers receive is the new market price + the subsidy per unit.

Sharing the benefit

1. The consumer gain is the fall (−) in the price they pay, and the producer gain is the rise (+) in the price they keep after the subsidy.
2. As with a tax, the more inelastic side of the market captures the larger share of the benefit.
3. The total cost to the government is the subsidy per unit multiplied by the new higher quantity.

Benefit shares

$$Consumer\; share=\frac{\Delta P_c}{subsidy\; per\; unit}Producer\; share=\frac{\Delta P_p}{subsidy\; per\; unit}$$

Government cost

$$Government\; cost=subsidy\; per\; unit\times Q$$

Why governments subsidise

1. Subsidies encourage consumption of goods with positive externalities, such as vaccinations or public transport, moving output towards the social optimum.
2. They can make necessities more affordable and protect the incomes of key producers such as farmers.
3. They can also support new or strategic industries until they become competitive.

Do subsidies work?

1. A subsidy does raise output and consumption towards the social optimum, and it works best when demand is price-elastic, because then a given fall in price produces a large rise in quantity, so subsidising public transport or renewable energy can shift behaviour substantially and spread the external benefit widely.
2. If demand or supply is inelastic the quantity effect is small and most of the money simply raises producer revenue or cuts the consumer price without changing behaviour, so the subsidy is poor value, and it carries an opportunity cost because the same funds could support other public spending.
3. Subsidies can also keep inefficient firms in business, dull the incentive to cut costs, and are politically hard to remove once granted, so they risk becoming a permanent drain and a source of government failure.
4. On balance a subsidy is justified where a good generates clear positive externalities and demand is responsive enough for the payment to change behaviour, but its net value depends on the elasticity of demand and supply, the size and accuracy of the payment, the opportunity cost of the funds, and whether it can be withdrawn once the market matures.