Question

The private demand curve for flu shots is: P = 18 – 2Qd

The social demand curve for flu shots is: P = 21 – 2Qd

The private and social supply curve for flu shots is: P = 3 + Qs

a)      Draw a supply and demand model of the market for flu shots.

b)      Is there an externality in this market, if yes, is it positive or negative?

c)      Does the private market provide too many or too few flu shots from society’s perspective? What quantity of flu shots is optimal from the private market perspective? What quantity of flu shots is optimal from society’s perspective?

d)      What is a “Pigouvian” solution to this market failure?

Answer 1

(a)

From private demand equation, When Qd = 0, P = 18 (Vertical intercept of private demand curve)

From social demand equation, When Qd = 0, P = 21 (Vertical intercept of social demand curve)

From private supply equation, When Qs = 0, P = 3 (Vertical intercept of supply curve)

In following graph, the curves D(P), D(S) and S(P) represent private demand, social demand and private supply curves respectively.

(b) Since the private demand and social demand functions are different, and social demand lies above private demand curve, there is a positive externality in consumption.

(c) In private market equilibrium, D(P) equals S(P).

18 - 2Q = 3 + Q

3Q = 15

Q = 5

P = 3 + 5 = 8

In socially optimal outcome, D(S) equals S(P).

21 - 2Q = 3 + Q

3Q = 18

Q = 6

P = 3 + 6 = 9

Therefore, private market provides too few flu shots from society's perspective.

Optimal Private number of optimal shots = 5

Socially optimal number of shots = 6

(d) The Pigouvian solution to this market failure is to give of a subsidy which is equal to the difference between D(P) and D(S) functions, when output is socially optimal (equal to 6).

When Q = 6,

D(P) = 18 - (2 x 6) = 18 - 12 = 6

D(S) = 21 - (2 x 6) = 21 - 18 = 3

Pigouvian subsidy per unit = 6 - 3 = 3