subsidy in a single market
A subsidy is the mirror image of a tax: instead of the government taking money on each unit traded, it pays money on each unit. The aim is usually to make something cheaper or more plentiful than the market would manage on its own — to encourage things society wants more of, such as renewable energy, vaccines, public transport, staple foods, or education. If a tax is a wedge the government drives between buyer and seller to discourage trade, a subsidy is a wedge that pulls them together to encourage it.
Follow the money. Give sellers 1 dollar for every solar panel they sell. This is like a fall in their costs, so they're willing to supply more at any price — the supply curve effectively shifts down by the subsidy. The new equilibrium has a lower price for buyers and more panels sold. But here's the symmetry with tax incidence: the benefit splits between buyers and sellers, and the split is set by relative elasticity, not by who legally pockets the cheque. Buyers might see the price drop by 60 cents while sellers keep 40 cents of the dollar — and it would come out the same if the subsidy were legally paid to buyers instead. The more inelastic side captures the larger share of the gain.
Subsidies are everywhere in real economies and they can be genuinely justified — especially to correct a market failure, like rewarding activities with positive spillovers (a vaccinated person protects others; clean energy benefits everyone). But honesty requires naming the costs. Someone has to fund the subsidy: taxpayers. Subsidies can prop up inefficient producers, get captured by well-connected industries, distort choices, and prove almost impossible to remove once people depend on them (fuel subsidies are notorious for this). And because they push the market to trade more than the unaided equilibrium, a subsidy on an ordinary good actually creates its own deadweight loss — the cost to taxpayers exceeds the combined gain to buyers and sellers. The case for a subsidy rests on the benefit it buys outweighing that bill.
A government pays farmers a per-bushel subsidy on wheat. Wheat gets cheaper for buyers and farmers sell more — but taxpayers foot the bill, and how much of the benefit reaches eaters versus farmers depends on the elasticities, not on who receives the cheque.
Like a tax in reverse: it lowers the price and lifts the quantity, with the split set by elasticity.
A subsidy isn't free money — taxpayers fund it, and on an ordinary good it creates its own deadweight loss by pushing trade beyond the efficient level. The good case for one is correcting a market failure (positive externalities), where the social benefit can outweigh that cost.