Question

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

Q^{S} = 2P

Q^{D} = 400 - 3P

Solve for the equilibrium price and the equilibrium quantity.

Suppose that a tax of T is placed on buyers, so the new demand equation is

Q^{D} = 400 – 3(P+T)

Solve for the new equilibrium. What happens to the price received by sellers, the price paid by buyers, and the quantity sold?

Tax revenue is T x Q. Use your answer from part (b) to solve for tax revenue as a function of T. Graph this relationship for T between 0 and 400.

Answer #1

Qs = 2P

Qd = 400 - 3P

In equilibrium Qd = Qs

400 - 3P = 2P

5P = 400

P = 80

Q = 160

Now a tax of T is imposed,

Qd = 400 - 3(P+T)

Qs = 2P

Qd = Qs

400 - 3(P+T) = 2P

400 - 3P - 3T = 2P

5P = 400 - 3T

P = (400-3T)/5

Q = 2(400-3T)/5

Earlier the sellers were receiving price = 80, now they are receiving P = 80 - 0.6T

Earlier the consumer paid price = 80, Now they are paying P = P + T = 80 + 0.4T

Earlier quantity sold = 160, Now Q = 2(400-3T)/5 = 160 - 1.2T

Tax revenue TR = T*Q = T*(160 - 1.2T)

TR = 160T - 1.2T^{2}

TR is zero when T = 0 and T = 133.33. When T = 400, TR = -128000

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