Question

# Suppose the market for soda is represented by the following supply and demand equations: QS =...

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?

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