Question

2.  The private marginal benefits for the flu vaccine is estimated to be MBp= 200-Q  where Q is the number of flu vaccines. The private marginal cost of producing the flu vaccine is MCp= 20. Because flu vaccines also reduce the probability that someone nearby receives the flu, there is a positive external benefit of MBe=100. No other externalities exist in the market.  

a. Solve for the market equilibrium price and quantity for flu vaccines. Solve the socially optimal level of price and quantity of flu vaccines (hint: MBS is the sum of MBP and MBE ).  

b. Graph all the curves and identify the deadweight loss area. Given the deadweight loss area you have identified in the graph, calculate the deadweight loss in the market.

Answer 1

MBp = 200-Q

MBe= 100

MBS = MBP+ MBE

= (200-Q+100)= 300-Q

(a) For the market equilibrium: MBP = MC

MC = 20 (Given)

200-Q = 20

Q= 180 flu vaccines. (Market equilibrium quantity)

P= 200-180= 20 (Market equilibrium price)

For the socially optimal level : MSB=MC

300-Q=20

Q= 280 flu vaccines (Socially optimal quantity)

P= 300-280= 20 (Socially optimal price)

(b) At Q=180 , MSB= 300-180-120

Deadweight loss is shown by the area of triangle .

DWL = (0.5)(120-20)(280-180)= (0.5)(100)(100)= $5000.