Question

Consider a market with demand and supply functions:

Supply function: ? = 40? − 40

Demand function: ? = 200 − 20�

a. Find deadweight loss of the price floor. [Hint: Deadweight loss is a region lost because of no trade.]

Welfare effects of a tax

Now, the government repeals the price floor and imposes a sales tax of $3 per good on buyers-side.

b. Draw a new demand curve with old demand and supply curves. Find the new equilibrium quantity when the tax is imposed. [Hint: The demand curve shifts down by $3 due to the tax. Use the new demand function: ? = 140 − 20?.]

c. When the tax is imposed, find the price buyers pay and the price sellers receive.

d. Of $3 tax, how much buyers and sellers pay, respectively?

e. Find and calculate the new consumer surplus, producer surplus, government revenue, total surplus and deadweight loss under the tax.

Answer 1

Supply: Q= 40P - 40

Demand: Q = 200 - 20P

Equilibrium occurs when demand = supply

40P - 40 = 200 - 20P

P = 4

At this price, Q = 120

A) If a price floor of $3 is imposed, there is supply of 80 units while at this quantity, price consumer willing to pay is 6. Deadweight loss is the area of shaded triangular portion whose sum is (1/2) * (120 - 80) * (6 - 3) = 60

B) If tax imposed of $3 shifts the demand curve to its left from D to D1 which shifts the equilibrium where price is 3 and quantity traded is 80 units.

C) Price buyer pay rises to $6 while price seller receive falls to $3

D) Buyer pay $2 of the tax while seller pay $1.

E) Before tax:

• Consumer surplus is area of portion A + B + C + D + G whose sum is (1/2) * (120 - 0) * (10 - 4) = 360
• Producer surplus is area of portion E + F + H + I whose sum is (1/2) * (120 - 0) * (4 - 1) = 180

After tax:

• Consumer surplus is area of portion A + B whose sum is (1/2) * (80 - 0) * (10 - 6) = 160
• Producer surplus is area of portion I whose sum is (1/2) * (80 - 0) * (3 - 1) = 80
• Government revenue is area of portion C + D + E + F whose sum is (6 - 3) * (80 - 0) = 240
• Deadweight loss is area of portion (1/2) * (120 - 80) * (6 - 3) = 60