Question

Consider a hypothetical market for the hepatitis A vaccine. The market demand (or private marginal benefit schedule) is given as: P = 80 -0.25Qd where Qd denotes the number of vaccinations demanded per month and P is the price per vaccination. The market supply for the vaccine (the private marginal cost schedule) is: P = 15 + 0.4Qs where Qs denotes the number of vaccinations supplied per month. a. Sketch a graph of the market and solve for the number of vaccinations purchased per month. b. The hepatitis A vaccination generates external benefits. Suppose the external marginal benefit schedule is given as: MEB = 35 -0.15Q. Find the efficient number of vaccinations per month. c. Suppose the government decides to subsidize the price of the hepatitis vaccination. Find the optimal subsidy. Who gains and loses under this plan?

Answer 1

A) Equilibrium number of vaccinations (E in diagram) to be purchased can be calculated as follows:

PMB = PMC 80 -0.25Q = 15 +0.4Q 65 = 0.650 Q* = 100

The graph of the market can be shown below:

Cost and benefit SMB PMC 1007 PMB E' 100 120 150 200 250 Quantity

B) The social marginal benefit can be calculated by adding the private marginal benefit and marginal external benefit. (E’ in the diagram)

SMB = PMB + MEB = 80 -0.25Q + 35 -0.150 = 115 -0.4Q For socially efficient number of vaccinations: SMB = PMC 115 -0.4Q = 15 +0.40 Q* = 125

C) Optimal subsidy equals the MEB at socially efficient equilibrium number of vaccinations.

So, S* = 35 -0.15 x 125 = 16.25 S per unit

Government has to provide subsidy of $16.25 per unit. So, it loses, and the producers would gain.