Question

Consider the following supply and demand curves: Pd=500-Qd Ps=Qs-30 Suppose we impose a 30$ tax on this market. 1. determine the price that sellers receive under the tax. 2, determine the price that buyers pay given the tax. Determine the number of units transacted given the tax.

Answer 1

Pd = Price paid by consumer

Ps = price received by sellers

t = tax = $30 (Given)

After tax imposed:

Ps = Pd - t (Equation (1) )

Qs - 30 = 500 - Qd - 30.

Q - 30 = 470 - Q (Note: At equilibrium Qd = Qs = Q)

Q + Q = 470 + 30

2Q = 500

Q = (500/2)

Q = 250. (number of units transacted after the imposition of $30 tax)

Since, Qd = Qs = Q.

Then, Qd = 250, Qs = 250.

Put Qd = 250 in demand equation

Pd = 500 - Qd

Pd = 500 -250

Pd = 250 (price paid by consumer)

Now put Pd = 250 in equation (1)

Ps = Pd - t

Ps = 250 - 30

Ps = 220 (price received by seller)

Answers: (1) Price that seller receive under tax is $220

(2) Price that buyers pay given the tax is $250

(3) number of units transacted given the tax in 250.