1.(16 points) Suppose that the government wishes to encourage the manufacture and sale of small cars.The current supply and demand of small cars are:

P^s = c + mQ, and P^d = a - bQ,

where Q is in millions of cars and P is in hundreds of dollars.

a.(4 pts) What is the current equilibrium price and quantity of small cars sold?

b.(8 pts) Now, suppose that the government is considering two alternative plans for encouraging small car sales.Under Plan A, every car manufacturer will receive a rebate of dollar amount S from the government for each small car sold. What are the new equilibrium prices and quantity, and what are the equilibrium effects of (a higher) S on prices and quantity?