Suppose the market demand and market supply curves are given by the equations: Q

Question

Suppose the market demand and market supply curves are given by the equations:

Qd = 200 - P

Qs = 3P

and a tax of T is placed on buyers so that the demand curve becomes:

Qd = 200 - (P + T)

What price will sellers receive and what price will buyers pay after the tax is imposed? What quantity will be bought and sold after the tax is imposed? How much tax revenue will be collected after this tax is imposed? What will be the deadweight loss from this tax?

Answer:

Buyers will pay (200 + 3T) / 4

Sellers will receive (200 - T)

The quantity will be (600 - 3T) / 4

The tax revenue will be (600T - 3T2) / 4

Deadweight loss will be 3T2 / 8

(Why?)

Explanation / Answer

(All your answers are wrong.)

Correct answers are as below:

Let P be the price received by sellers and (P + T) be the price paid by buyers.

Qd (New) = Qs

200 – (P + T) = 3P

4P = (200 – T)

P = 50 – T/4

Now, P + T = (50 – T/4) + T = 50 + 3T/4

Quantity = 3P = 3 × (50 – T/4) = 150 – 3T/4

Answers: Buyers will pay (50 + 3T/4)

                Sellers will receive (50 – T/4)

                Quantity is (150 – 3T/4)

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