Download consumer surplus

5.1 – An Economic Application:
Consumer Surplus and Producer Surplus
Consumer’s Demand Curve: a graph of 𝒑 = 𝑫 𝒙 , that shows the unit price that
the consumer is willing to pay for x number of units of a product
Producer’s Supply Curve: a graph of 𝒑 = 𝑺 𝒙 , that shows the unit price that the
producer is willing to accept for selling x number of units of a product
5.1 – An Economic Application:
Consumer Surplus and Producer Surplus
Consumer surplus is the difference between the amount that consumers
actually pay and the amount that they would have been willing to pay.
If p = D(x) describes the demand function for a commodity, then the
consumer surplus is defined for the point (Q, P) as:

Q
0
D( x)dx  QP.
5.1 – An Economic Application:
Consumer Surplus and Producer Surplus
Producer surplus is the difference between the amount that a producer
receives from the sale of a good and the lowest amount that producer is
willing to accept for that good.
If p = S(x) is the supply function for a commodity, then, the producer
surplus is defined for the point (Q, P) as:
Q
QP   S(x) dx.
0
5.1 – An Economic Application:
Consumer Surplus and Producer Surplus
The equilibrium point, (xE, pE), is the point at which the supply and
demand curves intersect.
In a competitive market, the unit price for a particular good will vary
until it settles at a point where the quantity demanded by consumers (at
current price) will equal the quantity supplied by producers (at current
price).
The result is an economic equilibrium for price and quantity.
5.1 – An Economic Application:
Consumer Surplus and Producer Surplus
The four basic laws of supply and demand are:
If demand increases (demand curve shifts to the right) and supply
remains unchanged, a shortage occurs, leading to a higher equilibrium
price.
If demand decreases (demand curve shifts to the left) and supply
remains unchanged, a surplus occurs, leading to a lower equilibrium
price.
If demand remains unchanged and supply increases (supply curve shifts
to the right), a surplus occurs, leading to a lower equilibrium price.
If demand remains unchanged and supply decreases (supply curve shifts
to the left), a shortage occurs, leading to a higher equilibrium price.
5.1 – An Economic Application:
Consumer Surplus and Producer Surplus
Given:
The consumer’s price function, 𝐷 𝑥 = 𝑥 − 4 2 and
the producer’s price function, 𝑆 𝑥 = 𝑥 2 + 2𝑥 + 6,
calculate the following:
a) The equilibrium point.
b) The consumer surplus at the equilibrium point.
c) The producer surplus at the equilibrium point.
equilibrium point
consumer
surplus
producer
surplus
5.1 – An Economic Application:
Consumer Surplus and Producer Surplus
Given:
The consumer’s price function, 𝐷 𝑥 = 𝑥 2 − 6𝑥 + 16 and
1
4
the producer’s price function, 𝑆 𝑥 = 𝑥 2 + 𝑥 + 4,
3
3
calculate the following:
a) The equilibrium point.
b) The consumer surplus at the equilibrium point.
c) The producer surplus at the equilibrium point.
consumer
surplus
producer
surplus
equilibrium point