Why a binding price ceiling or price floor causes a deadweight loss

Surplus and deadweight loss. A market's gains are measured by two surpluses. Consumer surplus is what buyers gain: on a diagram, the region lying under the demand curve but over the market price. Producer surplus is what sellers gain: the region lying between the market price above and the supply curve below. Adding the two gives total surplus. Each point on the demand curve shows what a buyer is willing to pay for that unit, and each point on the supply curve what it costs a seller to provide it. When a policy stops units from being traded that buyers value at more than they cost to produce, the surplus those units would have created is lost to everyone. This fall in total surplus, caused by lost production and consumption, is the deadweight loss, as with a tax that cuts the quantity traded.

When a price control binds. A price ceiling has an effect only when it is fixed below the equilibrium price, and a price floor only when it is fixed above it. A ceiling above equilibrium, or a floor below it, leaves the market at its equilibrium and causes no deadweight loss. A binding control does cause one, because the quantity actually traded is set by the short side of the market, whichever of buyers and sellers wants less at the controlled price, and that is less than the equilibrium quantity.

Price ceiling. At a ceiling below equilibrium, buyers want more than sellers offer, so there is excess demand, a shortage. Buyers cannot buy more than sellers supply, so the quantity traded falls to the quantity supplied at the ceiling. The units between that quantity and the equilibrium quantity are no longer produced, although buyers value each of them above its cost of production: their surplus is the deadweight loss of the ceiling. Part of the remaining surplus also shifts from sellers to the buyers who still get the good, but that shift is a transfer, not a loss. On top of this, rationing brings long queues at ration shops and can create a black market.

Price floor. At a floor above equilibrium, sellers offer more than buyers want, so there is excess supply. Unless someone else, such as the government, buys the excess, sellers cannot sell more than buyers purchase, so the quantity sold falls to the quantity demanded at the floor. Again, units that buyers value above their cost are not exchanged, and the surplus they would have yielded is the deadweight loss. Where the floor is an agricultural support price, the government has to buy the unsold surplus at the fixed price to keep the floor in place; private buyers still take only the quantity they demand at the floor, and the rest goes into government stocks. The analysis below is of a floor without such purchases.

Example (our own). In the market for a pulse such as tur dal, let demand be Qd = 100 − P and supply Qs = P − 20, with P in ₹ per kg and Q in lakh kg. Equilibrium is at P = ₹60 and Q = 40 lakh kg, with consumer surplus ½ × 40 × (100 − 60) = 800 and producer surplus ½ × 40 × (60 − 20) = 800, a total of ₹1,600 lakh.

(₹ lakh. Under the ceiling the 30 lakh kg are taken to reach the buyers who value them most; under the floor, output is taken to equal the 30 lakh kg sold.)

• Ceiling at ₹50: sellers supply 50 − 20 = 30 and buyers want 100 − 50 = 50, a shortage of 20. Only 30 is traded. At the 30th unit buyers would pay 100 − 30 = ₹70, while it costs sellers 30 + 20 = ₹50. The 10 lakh kg between 30 and 40 are lost, and the deadweight loss is the triangle ½ × 10 × (70 − 50) = ₹100 lakh, that is ₹1 crore.
• Floor at ₹70: buyers want 100 − 70 = 30 and sellers offer 70 − 20 = 50, an excess supply of 20. Only 30 is sold, the same 10 lakh kg of trades are lost, and the deadweight loss is again ₹100 lakh.

Conclusion. A price control causes a deadweight loss only when it binds. It then holds the quantity traded below the equilibrium quantity, at the level the short side of the market chooses (for a floor, unless the government buys the excess), so trades that would have benefited both buyers and sellers do not take place. The surplus those trades would have created is the deadweight loss; the gain of one side at the other's expense is only a transfer.