Question

Suppose you are an aide to a U.S Senator who is concerned about the impact of a recently proposed excise tax on the welfare of her constituents. You explain to the Senator that one way of measuring the impact of her constituents is to determine how the tax change affect the level of consumer surplus enjoyed by the constituents. Based on your arguments, you are given the go-ahead to conduct a formal analysis and obtain the following estimate of demand and supply:

Q=900-50P

Q=50P-100

A) What are the equilibrium quantity and equilibrium price?

B) How much consumer surplus exists in this market?

Answer 1

a) Set D=S

900-50P = 50P-100

900+100 = 50P+50P

1000 = 100P

P = 1000/100 = 10

Q = 900-50*10 = 400

b) Maximum reservation price = 900/50 = 18

Consumer surplus = 0.5*400*(18-10) = 200*8 = 1600