Consumer and Producer Surplus

Willingness to pay and consumer surplus

Willingness to pay is the highest price a buyer would pay for one unit of a good. It is the buyer's own valuation, and it depends on tastes, income, and how much they want the good right now.

Why does it exist? Because the market charges one price to everyone. Buyers who value the good more than that price get a bonus, and the bonus is their surplus.

Add up the surplus of every buyer in a market and you get the market's consumer surplus. Because buyers differ, the demand curve is really a ladder of willingness to pay: the first buyers value the good a lot, and later buyers value it less.

Producer surplus

Sellers have a mirror-image idea. The lowest price a seller would accept for one unit is the seller's minimum acceptable price. It equals the seller's cost for that unit, including opportunity cost.

If a food truck can make a taco for $\$2$ and sells it for $\$6$, the truck gets $\$4$ of producer surplus on that taco. Producer surplus is not the same as profit, because it ignores fixed costs. It is a gain measured against the cost of each extra unit.

The supply curve is a ladder of costs. The first sellers have low costs, and later sellers have higher costs, which is why the supply curve slopes up.

Surplus on a graph

In a graph with Quantity on the horizontal axis and Price ($) on the vertical axis, surplus becomes an area.

• Consumer surplus is the area below the demand curve and above the price.

• Producer surplus is the area above the supply curve and below the price.

• Total surplus (TS) is $CS + PS$. It measures the total gain from trade in the market.

Here is the sneaker market where demand is $P = 100 - 2Q$ and supply is $P = 20 + 2Q$ (with $Q$ in thousands of pairs).

Both surplus areas are triangles, so use

The base is the quantity traded (the horizontal side along the price line). The height is the vertical distance between the price and the curve's vertical intercept.

Surplus also works with a table of individual buyers and sellers. Add up each buyer's $\text{WTP} - \text{price}$ and each seller's $\text{price} - \text{cost}$, counting only the people who actually trade. A buyer trades if $\text{WTP} \ge \text{price}$, and a seller trades if $\text{cost} \le \text{price}$.

Efficiency and deadweight loss

At equilibrium, total surplus is as large as it can be. We call this outcome efficient. When a policy keeps some mutually beneficial trades from happening, total surplus shrinks.

A price ceiling

A price ceiling is a maximum legal price. It is binding when it is set below the equilibrium price. Let's put a ceiling of $\$40$ on the sneaker market.

At $\$40$ sellers supply only $Q = 10$, because $20 + 2Q = 40$. Buyers want $Q = 30$, because $100 - 2Q = 40$. There is a shortage, and the quantity traded is the smaller number, 10, since nobody can force sellers to supply more.

If the 10 thousand pairs go to the buyers with the highest willingness to pay, the demand curve at $Q = 10$ is at $P = 100 - 20 = 80$.

• $CS = \text{triangle} + \text{rectangle} = \tfrac{1}{2}(10)(100 - 80) + 10(80 - 40) = 100 + 400 = 500$

• $PS = \tfrac{1}{2}(10)(40 - 20) = 100$

• $TS = 600$, compared with $800$ before. So $DWL = 800 - 600 = 200$, which is $\$200{,}000$.

Notice the rectangle in the consumer surplus: it is the price savings of the buyers who still get a pair ($\$40$ less than the old price on each of 10 thousand pairs). It is a transfer from producers to those buyers, not a net gain for the market. Consumer surplus rises for the buyers who still get a pair (from 400 to 500), but total surplus falls because the trades between Q = 10 and Q = 20 are lost. The DWL triangle is exactly the trades between $Q = 10$ and $Q = 20$ that no longer happen.

A per-unit tax

Now suppose the government taxes sellers $\$12$ per pair. Sellers' costs rise by $\$12$ per unit, so the supply curve shifts up by $12$: $P = 32 + 2Q$.

Why is there a DWL at all? The tax drives a wedge of $\$12$ between what buyers pay and what sellers keep. Trades between $Q = 17$ and $Q = 20$ were worth more to buyers than they cost sellers, but not by $\$12$, so they disappear. In fact $DWL = \tfrac{1}{2} \times 12 \times 3 = 18$, the triangle whose height is the tax and whose base is the drop in quantity.

New technology

Surplus also helps us see who gains from good news. When technology lowers every cost by $\$12$, supply shifts down and the price falls. In a market with demand $P = 60 - 3Q$ and supply $P = 12 + Q$, the equilibrium is $Q = 12$, $P = \$24$. After the improvement, supply becomes $P = Q$ and the equilibrium is $Q = 15$, $P = \$15$. The price fell $\$9$ of the $\$12$ cost cut, so most of the gain goes to buyers, because demand is steeper than supply. Check the gains. Before: $CS = \tfrac{1}{2}(12)(36) = 216$ and $PS = \tfrac{1}{2}(12)(12) = 72$. After: $CS = \tfrac{1}{2}(15)(45) = 337.5$ and $PS = \tfrac{1}{2}(15)(15) = 112.5$. So consumers gain $337.5 - 216 = 121.5$ and producers gain $112.5 - 72 = 40.5$, in millions of dollars per month.

Back to the football ticket: the $\$5$ difference between your $\$15$ and the $\$10$ price is your consumer surplus. Add that up for every fan, add the school's gains, and you have the total surplus of the ticket market.

Summary

• Consumer surplus = willingness to pay − price paid. On a graph it is the area under demand and above the price.

• Producer surplus = price received − minimum acceptable price (cost). On a graph it is the area above supply and below the price.

• Total surplus = CS + PS. It is largest at the market equilibrium, which is efficient.

• For linear curves, each surplus is a triangle: $\tfrac{1}{2} \times \text{base} \times \text{height}$, where the base is the quantity traded.

• Deadweight loss is the lost total surplus when a price ceiling, a tax, or another distortion blocks mutually beneficial trades. Tax revenue still counts as part of total surplus.