Subsidy and Welfare (Consumer and Producer Surplus)

Idea

A subsidy paid to producers shifts the supply curve down and to the right, lowering the price consumers pay and raising the quantity traded. Both consumer and producer surplus rise as a result.

Mechanism

With supply at $S_1$ the market clears at the original equilibrium. A per-unit subsidy shifts supply to $S_2$ , so the new equilibrium is at a lower consumer price and a higher quantity.

Consumer surplus rises. Consumers buy more at a lower price, so the area between the demand curve and the price they pay expands.
Producer surplus rises. Producers sell more and, inclusive of the subsidy, receive a higher effective price per unit, so the area between the price they receive and the supply curve expands.

Diagram

A per-unit subsidy shifts supply from S1 to S2, moving equilibrium from B (price P1, quantity Q1) to C (consumer price P2, quantity Q2); producers receive P2+S. Consumer surplus rises by P1BCP2; producer surplus rises by P2+S·E·B·P1.

Considerations

The figures here are schematic: the named surplus areas are what the diagram supplies, while the magnitude of each gain, and the cost of the subsidy to the government, belong in prose for any worked case. A subsidy’s welfare gains to consumers and producers must be weighed against the opportunity cost of the public funds financing it.