Section 14.10: Consumer and Producer Surplus.
Consider the graphic below, where p = D(q) is the demand curve and p = S(q) is the supply curve.
The demand curve is a representation of how units people are willing to purchase at a given price. For example, at point
(10, 33.28), people are willing to buy 10 units a price of $33.28.
The supply curve is a representation of how many items a producer is willing to sell at a given price. For example, at point
(5, 12.01), the producer is willing to sell five units at a price of $12.01.
The point E is where the two graphs intersect and is called the equilibrium point, with ordered pair (qE , pE ).
For this section, we will assume that the market is at this equilibrium point.
Consumer Surplus.
Let us consider the point on the demand curve. Consumers were willing to buy 10 units and pay $33.28 per unit for the
product. They are then pleasantly surprised that the item is actually on the market for $18.30. This means that at this point,
there is a consumer surplus of $14.98.
The total consumer surplus is the region between the demand curve and the equilibrium line p = pE . Using definite integrals,
this can be computed as:
Z qE
Consumer Surplus =
(D(q) − pE ) dq
0
Producer Surplus.
Now let us consider the five units on the supply curve. The producer was wiling to produce 5 items at $12.01. They are then
pleasantly surprised that they could sell these five items at $18.30. This means that at this point, there is a producer surplus
of $6.29.
The total producer surplus is the region between the equilibrium line p = pE and the supply curve S(q). Using definite
integrals, this can be computed as:
Z qE
Consumer Surplus =
(pE − S(q)) dq
0
Graphically, you have the following:
Notice that regions to the right of the equilibrium point are not considered. The demand function is below the equilibrium
price, so the consumers will not purchase the item.
Steps to computing Consumer and Producer Surplus:
• Determine the equilibrium point by determining where the consumer and producer functions intersect. You will need
both ordered pairs: (qE , pE ).
• Apply the given formulas and integrate accordingly. You may have to use integration techniques other than the power
rule.
• Note: By definition, both consumer and producer surpluses must be positive.
Examples: Determine the equilibrium points for the given supply S(q) and demand D(q) curves.
1. S(q) = q 2 + 25q + 80, D(q) = 360 − q − q 2
2. S(q) = 2.1q−3.5 , D(q) = 21.3−.3q
Examples: Determine the total consumer and producer surplus for the given supply S(q) and demand D(q) curves.
3. S(q) = 6 + 1.2q, D(q) = 22 − 0.8q
4. S(q) = 400 + q 2 , D(q) = 2200 − q 2
5. S(q) =
√
1
q + 5, D(q) = 400 − q
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