Question

Suppose the market for bottled water is competitive and is characterized by the following demand and supply conditions. The inverse demand and supply curves are depicted below.

Demand: Q^D = 400 – 100 P

Supply:    Q^S = 280 + 20 P (for P > 0)

Price:

Quantity:

Consumer surplus:

Producer surplus:

Suppose in anticipation of an approaching hurricane, demand rises to Q^D = 800 – 100 P. What will happen in the market, including welfare effects, as measured by consumer and producer surplus?

New price:

New quantity:

New consumer surplus:

New producer surplus:

Answer 1

Given

Qd=400-100P
Qs=280+20P
The equilibrium is where the Qs=QD
280+20P=400-100P
100P+20P=400-280
120P=120
P=$1

Substituting the value of P in Qs
Qs=280+20P
Qs=280+20(1)
Qs=300
Since Qs=Qd=300

Consumer surplus is the area below the demand curve and above the price level
Consumer surplus=area of the triangle
Consumer surplus=0.5*(base)*(height)
Consumer surplus=0.5*(300)*(4-1)
Consumer surplus=450

Producer surplus the area above the supply curve and below the price level. (Since supply here is starting at a negative point we will only take the area which is in the positive quadrant)

Producer surplus=area of triangle+area of the rectangle
Producer surplus=0.5*(base)*(height)+Lenghth*Breadth
Producer surplus=0.5*(300-280)*(1)+(280*1)
Producer surplus=290

Given

Qd=800-100P
Qs=280+20P
The equilibrium is where the Qs=QD
280+20P=800-100P
100P+20P=800-280
120P=520
P=$4.33

Substituting the value of P in Qs
Qs=280+20P
Qs=280+20(4.33)
Qs=366.6
Since Qs=Qd=366.6

Consumer surplus is the area below the demand curve and above the price level
Consumer surplus=area of triangle
Consumer surplus=0.5*(base)*(height)
Consumer surplus=0.5*(366.67)*(8-4.33)
Consumer surplus=672.83

Producer surplus the area above the supply curve and below the price level. (Since supply here is starting at a negative point we will only take the area which is in the positive quadrant)

Producer surplus=area of triangle+area of the rectangle
Producer surplus=0.5*(base)*(height)+Lenghth*Breadth
Producer surplus=0.5*(366.67-280)*(4.33)+(280*4.33)
Producer surplus=1400.04