Question

The inverse demand function for a medication is p = 10000 - 0.5Q, where p is the market price and Q is quantity demanded

MC = 100 + 0.05Q.

What is the competitive market price and quantity in this market, and producer and consumer surplus and social welfare?         

Suppose production creates an externality. You can assume marginal external costs are simply MEC = 400. Based on this information, what is your estimate for a regulated market outcome where marginal social costs include both marginal production costs and marginal external costs. What is social welfare with this regulated market, where social welfare = PS + CS + EXT, where EXT is the value of externality that exists in regulated market.

Answer 1

P= 10000-0.5Q

MC= 100+0.05Q

In Equilibrium, Price= MC

10000-0.5Q= 100+0.05Q

Q= 18000

Price= 10000-0.5×18000=1000

Competitive Market Price= 1000, Competitive Market Quantity= 18000.

Producer Surplus= 0.5×(1000-100)×18000= 8100000

Consumer Surplus= 0.5×(10000-1000)×18000= 81000000

Social Welfare= 8100000+81000000=89100000

In regulated Market, Suppose Governement impose tax per unit equal to Externality (Marginal External Cost) of 400

Thus, Marginal Social Cost= MC+400= 100+0.05Q+400

At social optimum, Marginal Social Cost= P

500+0.05Q= 10000-0.5Q

Q= 17272.7

P= 10000-0.5×17272.7=1363.6

Socially Optimal Price= 1363.6

Socially Optimal Quantity= 17272.7

Price which Producers receive= 100+0.05×17272.7= 963.6

Producer Surplus= 0.5× ( 963.6-100)× 17272.7= 7458351.8

Consumer Surplus= 0.5×(10000-1363.6)× 17272.7= 74586973.1

Social Welfare= Consumer Surplus+Producer Surplus+Externality= 7458351.8+74586973.1+ 400= 82045724.9