Question

1. Consider a perfectly competitive market where the demand and supply curves are given by QD = 500 − P and QS = −100 + 2P , respectively. Suppose that the government decides to tax the producers by $60 per unit sold.
(a) Determine the pre-tax and after-tax equilibrium price and quantity.
(b) Determine the loss in net benefits due to the tax.
(c)Determine the percentage of the tax burden that falls on the consumers.

Answer 1

Qd = 500 - P

Qa = -100 + 2P

At equilibrium, demand equals supply

500 - P = -100 + 2P

P = 200

At this price, Q = 300

a) At a tax of $60, tax will be shared among both buyers as well as sellers which will fall in the ratio of (demand curve touching price axis - equilibrium price) to (equilibrium price - supply curve touching price axis) which is (500 - 200) / (200 - 50) = 300 / 150 = 2 / 1

Burden on consumers would be [2 / (2 + 1)] of total tax which is 66.67% totalling of 0.6667 * 60 = $40 while burden on producer is [1 / (2 + 1)] which is 33.33% totaling of 0.33 * 60 = 20

After tax, consume pay $240 while producer receive $180. Quantity trad(ed falls to 260 units

b) Loss in net benefits is area of portion E + F whose sum is (1/2) * (240 - 180) * (300 - 260) = 2,400

c) Tax burden on consumers falls is 66.67%