Question

Suppose the supply curve for steel is given by P=Q and the demand for steel is given by P=100- 2Q. The production of steel is associated with a constant external cost of $10 per unit.
a. Calculate the private equilibrium. What are equilibrium price and quantity?
b. What is the deadweight loss associated with the private equilibrium. Calculate and draw a sketch.

Answer 1

Solution:

Supply curve: P = Q

Demand curve: P = 100 - 2Q

a) The supply curve denotes the private marginal cost and demand curve denotes the private marginal benefit (which is same as the social marginal benefit).

So private equilibrium can be obtained by equating the private marginal benefit and cost. Thus,

Q = 100 - 2Q

Q + 2Q = 100

So, Q = 100/3 = 33.33

Since P = Q = $33.33

So, equilibrium price is $33.33 and equilibrium quantity is 33.33 units (denoted by point E' in the below figure).

b) With the marginal external cost, MEC = $10

So, the social marginal cost, SMC = Q + 10

So social equilibrium occurs where Q + 10 = 100 - 2Q

Q + 2Q = 100 - 10

3Q = 90

Q = 90/3 = 30

So, in case, the social cost = 30 + 10 = $40

This optimal equilibrium is presented by point E. The grey area represents the deadweight loss.

Calculating dead weight loss:

Notice that it is sum of two right angled triangles; area of a right angled triangle = (1/2)*base*height

So, DWL = (1/2)*(33.33-30)*(43.33-40) + (1/2)*(33.33-30)*(40-33.33)

DWL = 5.54 + 11.11 = $16.65