The demand and supply curves in the market for college education determine the equilibrium price and quantity of education. Assume the student for college education is given by Dstu = P = 9500 – 500Q and the cost to society to of providing a college education or the social supply curve is given by Ssoc = P = 3500 + 1000Q; where P is the price of tuition per year and Q is the average number of years of college attendance. (a) Assuming the market for education is private, what is the equilibrium price of tuition and equilibrium quantity of education consumed? Solve numerically and show in a diagram. (b) Suppose that each year of college provides external benefits equal to $4500. The social demand would be Dsoc = 14,000 – 500Q. What is the socially optimum average number of years of college? What tuition must be charged to supply that quantity? Solve numerically then show in the same diagram as in (a). (c) What dollar amount of subsidy will lead to social optimum? Solve numerically then show in the same diagram as in (a)?