A study of a country's colleges and universities resulted in the demand equationq= 20,0002p,whereqis the enrollment at a public college or university andpis the average annual tuition (plus fees) it charges.Officials at Enormous State University have developed a policy whereby the number of students it will accept per year at a tuition level ofpdollars is given byq=6,500+ 0.5p.Find the equilibrium tuition pricep

and the consumers' and producers' surpluses at this tuition level. What is the total social gain at the equilibrium price? HINT [See Example 3.]

equilibrium tuition pricep=$

consumers' surplus CS=$

producers' surplus PS=$

total social gain = $