consider the market for coffee at university the

Question

Consider the market for coffee at University. The market supply is given by:

Q_S = -20 + P_S,

where QS is the quantity supplied and PS is the price per cup of coffee received by coffee firms. The market demand curve (for students) is given by:

Q_D = 100 - P_D,

where QD is the quantity demanded and PD is the price per cup of coffee paid by students. Prices are in cents. Initially, suppose that there are no taxes or subsidies on coffee, so that P_D = P_S . Call this common price P.
a. What is the equilibrium price in this market?

b. How many cups of coffee are traded in equilibrium?

c. In order to encourage the drinking of coffee (to keep awake during class, except Econ 2316 (which never causes sleepiness!)) the university announces that it will reimburse each student 20 cents for each cup of coffee purchased. In the new equilibrium, what price do firms charge for cups of coffee?

d. What is the new equilibrium price to the students after subtracting the reimbursement?

e. How many cups of coffee are bought and sold in this new equilibrium?