Question

Suppose that a market is described by the following supply and demand equations:

Qs = 2P

Qd = 300 – P

A Php 1-tax is imposed on buyers, and another Php 1-tax is imposed on sellers.

1. Calculate the price received by sellers

2. Calculate the price received by sellers

3. Calculate the quantity sold in the market

4. Calculate the government's tax revenue

5. Calculate the loss in economic efficiency as a result of the tax

6. Calculate the total surplus of the market after the tax was imposed

7. Suppose that this market pertains to the market of some highly dangerous drug. Calculate the tax needed to make quantity sold equal to zero. (In economics, we say that the resulting tax "priced people out of the market")

Answer 1

Qs = 2P

Qd = 300 - P

At equilibrium, Qd = Qs

300 - P = 2P

P = 100

At this P, Q = 200

Total tax imposed is $2 ($1 on buyer and $1 on seller)

At a tax of $2 in market, 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 (300 - 100) / (100 - 0) = 200 / 100

Burden on consumers would be [200 / (200 + 100)] of total tax which is 66.67% of $2 which is $1.33 while burden on producer is [100 / (200 + 100)] of total tax which is 33.33% of $2 which is $0.67

1) Price received by seller falls to $99.33

2) Price paid by consumer rises to $101.33

3) Quantity sold is 198.66

4) Government tax revenue is area of portion B + C whose sum is $2 * 198.33 = $396.66

5) Loss of economic efficiency is area of portion D + E whose sum is (1/2) * $2 * (200 - 198.66) = $1.34

6) Total surplus of the market before tax is area of portion A + B + C + D + E + F whose sum is (1/2) * (300 - 0) * (200 - 0) = 30,000

Total surplus of the market before tax is area of portion A + B + C + F whose sum is (1/2) * (300 - 0) * (200 - 0) = 30,000 - Deadweight loss from tax = $30,000 - $1.34 = $29,998.66

7) Tax should be 300 which impose tax of $200 on consumer and $100 on producer which result in total surplus converting into deadweight loss and quantity sold is zero.