Consumer and Producer Surplus

a: A study of a country's colleges and universities resulted in the demand equation

D(q) = 20,000 2q,

where D(q) is the average annual tuition (plus fees) per year a public college or university charges and q is the enrollment at the college or university. Officials at Enormous State University have developed a policy whereby the number of students q it will accept per year at a tuition level of S(q) dollars

is given by S(q) = 9,600 + 0.5q.

Find the market equilibrium price and quantity and the consumers' and producer's surpluses at this tuition level. What is the total social gain at the equilibrium price?

market equilibrium price$__________

market equilibrium quantity____________ students

consumers' surplus$________

producers' surplus$_____

total social gain______________________

b: A fast-food outlet finds that the demand equation for its new side dish, "Sweetdough Tidbit," is given by

p = 54/(q+1)^2

where p is the price (in cents) per serving and q is the number of servings that can be sold per hour at this price. At the same time, the franchise is prepared to sell q = 0.5p 1 servings per hour at a price of p cents. Find the equilibrium price p, the consumers' surplus CS and the producers' surplus PS at this price level. What is the total social gain at the equilibrium price?

equilibrium price _________

consumers' surplus_______________ producers' surplus__________

total social gain __________