Question

Suppose the market for soda is represented by the following supply and demand equations:
QS = 35P – 39.75 and QD = 10.25 – 5P, where P is price per bottle and Q measures bottles per second.

a. What are the value of consumer and producer surplus?

b. If the government imposes a $0.50 tax per bottle, what are the value of consumer and producer surplus?

c. What is the deadweight loss from the tax? How much revenue does the tax yield?

Answer 1

From the supply and demand equations, we find the current equilibrium

QS = QD

35P – 39.75 = 10.25 – 5P

40P = 50

P = 1.25 and Q = 10.25 - 5*1.25 = 4 units.

a) CS = 0.5*(max price - current price)*qty = 0.5*(2.05 - 1.25)*4 = 1.6.

PS = 0.5*(current price - minimum price)*qty = 0.5*(1.25 - 1.13)*4 = 0.228

b) A tax shifts the demand functions leftwards

QS = QD

35P – 39.75 = 10.25 – 5(P+0.5)

35P - 39.75 = 10.25 - 5P - 2.5

40P = 47.5

P = 1.1875 (sellers receive) and Q = 35*1.1875 - 39.75 = 1.8125 units.

Price that buyers pay = 1.1875 + 0.5 = $1.6875

CS = 0.5*(2.05 - 1.6875)*1.8125 = $0.328516

PS = 0.5*(1.6875 - 1.13)*1.8125 = $0.505234

c) DWL = 0.5*tax*qty change = 0.5*0.50*(4 - 1.8125) = 0.546875

Revenue = tax * quantity = 0.50*1.8125 = 0.90625