Question

5) (28 points) Suppose the demand and supply for flu shots are given by pd = 1200-Q ps = 440 + Q Suppose flu shots generate a positive externality, and the marginal external benefit (MEB) is MEB=60 -0.050. (a) Derive the marginal social benefit (MSB) curve. (b) Draw the Demand, Supply, and MSB curves on the same graph (with P on the vertical axis and Q on the horizontal axis) and clearly indicate the curves in your graph. (c) Calculate the free market/competitive production level and price. Show the competitive market equilibrium on the graph in part b, and call this point "A." Clearly indicate that point A is the free market equilibrium on your graph. (d) Calculate the socially optimal production level and price. Show the socially optimum equilibrium on the graph in part b, and call this point "B." Clearly indicate that point B is the socially optimum equilibrium on your graph. (e) Calculate the deadweight loss (DWL) from an underproduction of flu shots in the free market equilibrium. Clearly indicate the DWL on your graph in part a (Hint: it is a triangle). (1) What if the government used a subsidy of $S per flu shot to encourage the socially optimum production level? What should that subsidy (S) be?

Answer 1

a. MSB=MPB+MEB=1200-Q+60-0.05Q=1260-1.05Q

b.

Price 12001 MPB. MSB. MPO 1000 DWLLY 800 -600- 200 400 600 800 1000 1200 Quantity

c. Free market equilibrium

MPB=MPC

1200-Q=440+Q

Q*= (1200-440)/2

Equilibrium quantity Q*= 380

Equilibrium Price P*=440+380= $820

d. Socially optimal Equilibrium

MSB=MPC

1260-1.05Q=440+Q

Q=(1260-440)/2.05=400

Socially optimal Equilibrium quantity Q**= 400

Socially optimal Equilibrium Price= 440+400=$840

e. when Q=380, MSB=1260-1.05*380=861

Deadweight loss=0.5(400-380)(861-820)=$410

f. Subsidy will lead to upward shift in demand curve. This will increase the quantity of flu shots.

Subsidy= External benefit at socially optimal level= 60-0.05*400= $40

Per unit subsidy=$40