What does a subsidy look like on a supply and demand graph?
A per-unit subsidy to producers shifts the supply curve down (to the right) by the amount of the subsidy. Quantity rises, buyers pay less, sellers receive more, the government pays subsidy times quantity, and a deadweight loss triangle appears between the old and new quantity.
Start with the standard market graph: price on the vertical axis, quantity on the horizontal axis, a downward-sloping demand curve, and an upward-sloping supply curve labeled S. A per-unit subsidy paid to producers lowers what it costs them to supply each unit, so draw a second supply curve, labeled S1, sitting below the original by exactly the subsidy per unit. Down and to the right describe the same shift. The new equilibrium is where demand crosses S1, at a larger quantity than before.
Three prices now matter, and each one sits on a specific curve. The original equilibrium price is where demand crosses S. The price buyers pay is read off the demand curve at the new quantity, and it is lower than the original price. The price sellers receive is read off the original supply curve S at that same new quantity, and it is higher than the original price. The vertical gap between the seller price and the buyer price at the new quantity equals the subsidy per unit, the same wedge a tax creates but flipped, which the excise tax vs subsidy comparison lays out side by side.
A worked example makes the areas concrete. Let demand be P = 120 - Q and supply be P = 20 + Q. Setting them equal gives 120 - Q = 20 + Q, so Q = 50 and P = $70. A $10 per-unit subsidy moves supply to P = 10 + Q, and 120 - Q = 10 + Q gives Q = 55. Buyers now pay 120 - 55 = $65, sellers receive $65 + $10 = $75 (check: 20 + 55 = 75 on the original supply curve), and the gap is the $10 subsidy.
The government's cost is the rectangle with width equal to the new quantity and height equal to the subsidy, running from the buyer price up to the seller price: $10 times 55 = $550. Consumer surplus grows by the strip between $70 and $65 out to the new quantity, (50 + 55) / 2 times 5 = $262.50, and producer surplus grows by the strip between $70 and $75, also $262.50. Together that is $525 of gains against $550 of spending. The missing $25 is the deadweight loss: a small triangle between the old quantity (50) and the new quantity (55), with its left corner at the original equilibrium and its right side running from the buyer price up to the seller price above Q = 55. Its area is 0.5 times 5 times 10 = $25. Those extra 5 units cost more to produce than buyers value them.
That deadweight loss assumes the market had no externality to begin with. If the good creates a positive externality, a subsidy equal to the marginal external benefit moves output toward the socially optimal quantity and removes a deadweight loss instead of creating one. To check the numbers on your own curves, use the per-unit subsidy calculator, and drag the curves on the supply and demand sandbox to see the shift.
This also answers the common homework question about a subsidy to milk producers meant to lower the price of milk. The factor that changes the supply of milk is the subsidy itself, which lowers producers' effective cost of production, one of the determinants of supply. Supply increases, the curve shifts right, and the price of milk falls. Demand does not shift: the lower price only moves buyers down along the existing demand curve to a larger quantity demanded.
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Related questions
- Does a subsidy shift the supply curve right or down?
- Both, because they describe the same shift. A per-unit subsidy lowers the price producers need for every quantity by the subsidy amount, so the curve moves straight down by that amount, which also places it to the right of the original curve at every price.
- Who gets more of the benefit from a subsidy, buyers or sellers?
- The side of the market with the less elastic curve captures more of the subsidy. In the example above, demand and supply have slopes of the same size, so the $10 subsidy splits evenly: buyers pay $5 less and sellers receive $5 more.
- What if the subsidy is paid to consumers instead of producers?
- Then the demand curve shifts up by the subsidy per unit instead of supply shifting down. The new quantity, the price buyers pay after the subsidy, the price sellers receive, the government's cost, and the deadweight loss all come out the same as in the producer case.
- Why is there a deadweight loss if more people get the good?
- Because the extra units past the original equilibrium cost more to produce, read off the original supply curve, than buyers value them, read off the demand curve. Society spends more on those units than they are worth, so total surplus falls by the triangle between the two quantities.