Question

Suppose the internal supply curve is given by P=6+(2/3)Q, the internal demand curve is given by P=12-(1/3)Q, and the social supply curve is given by P=9+(2/3)Q.

a.     (3 points) Algebraically solve for the coordinates of the market equilibrium and the coordinates of the social optimum.

b.     (3 points) Labelling everything, graph these three curves and clearly indicate the market equilibrium, the social optimum, and the triangle corresponding to the deadweight loss. (In the interest of time, you do NOT have to draw this to scale, but clearly label the values of the intercepts and equilibria for full credit.)

c.     (1 point) Do these curves represent a market with a positive or a negative externality? How can you tell?

d.     (3 points) Please calculate the deadweight loss that is associated with this externality. SHOW YOUR WORK for credit.

Answer 1

Demand: P= 12-(Q/3)

X Intercept (keeping P=0) = 36

Y Intercept (Keeping Q=0) = 12

Social Supply: P= 9+ (2Q/3)

X Intercept (keeping P=0)= -13.5

Y Intercept (keeping Q=0) = 9

Internal Supply: P= 6+(2Q/3)

X Intercept ( Keeping P=0)= -9

Y Intercept (keeping Q=0)= 6

Answer a)

Market equilibrium: Demand=Internal Supply

12-(Q/3)=6+(2Q/3)

(36-Q)/3 = (18+2Q)/3

36-Q= 18+2Q

Q= 6

P= 12-(Q/3)

P= 10

Social optimum: Demand= Social supply

12-(Q/3)= 9+(2Q/3)

(36-Q)/3= (27+2Q)/3

36-Q= 27+2Q

Q*= 3

P*=12-(Q/3)

P*= 11

Answer b)

Answer c) This is a market for negative externality and this is because in case of negative externalities the amount of privately optimal output is greater than the socially optimal output i.e there is over production/ consumption due to which resources are over exploited.

Answer d) Dead weight loss= Area of triangle ABC

DWL= (1/2)*BASE*HEIGHT

BASE= 13-10= 3

HEIGHT= 6-3= 3

DWL= (1/2)*3*3 = 4.5