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 function, When Qd = 0, P = 18 (Vertical intercept)

From social demand function, When Qd = 0, P = 21 (Vertical intercept)

From private supply function, When Qs = 0, P = 3 (Vertical intercept)

In following graph, D(P), D(S) and S(P) are private demand, social demand and private supply curves with above intercepts.

(b) Since there is a social demand which lies above private demand curve, there is a positive externality.

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

18 - 2Q = 3 + Q

3Q = 15

Q = 5

P = 3 + 5 = 8

In social optimal, D(S) = S(P)

21 - 2Q = 3 + Q

3Q = 18

Q = 6

P = 3 + 6 = 9

Therefore, private market produces too few shots.

Private optimal shots = 5

Socially optimal shots = 6

(d) The Pigouvian solution is imposition of a subsidy equal to vertical distance between D(P) and D(S) when output is socially optimal (= 6).

When Q = 6,

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

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

Unit subsidy = 6 - 3 = 3