Question

The demand function for a product is given by p=80-0.5Q and the supply function is p=50+0.25Q,...

The demand function for a product is given by p=80-0.5Q and the supply function is p=50+0.25Q, where p is the price and Q is the quantity. Suppose that the government impose a tax of \$15 on every unit sold.

a) Find equilibrium price and quantity before imposing the tax.

b) Find price of buyer and seller and the quantity sold in the market after tax.

c) Find the tax burden on buyer and seller.

d) Find government revenue and deadweight loss (DWL) and the DWL as a percentage of tax revenue.

A. Solving fro equilibrium price and quantity,

80-0.5q = 50+0.25q

30 = 0.75q

Quantity = 40

Price = 50+0.25(40) = 60

B. Tax=15

Price before tax = 60

After tax,

Price customer pays = 65

Qty = 30

C.

Tax burden on buyer = 65-60 = 5

Tax burden on seller = 60-50 = 10

D.

Government Surplus = 30*15 = 450

DWL = 1/2 * 15 * 10 = 75 (Area of triangle = 1/2 * weight * height)

DWL in % = 75/450 = 16.67%