Question

Suppose that the demand curve for chairs in Euroland is given by QD = 800,000 − 6,000P, and that the supply curve is given by QS = 14,500P - 225,000. The equilibrium price is €50.
The government is thinking about imposing a tax of €2.46 on chairs.

The price paid by buyers after the tax is

Answer 1

Answer:

The price paid by buyers after the tax is €51.74.

Explanation:

QD = 800,000 − 6,000P .................. (1)

QS = 14,500P - 225,000 ................... (2)

P* = equilibrium price = €50

Substituting P* into equation (1) to obtain equilibrium quantity, Q*, we have

Q* = 800,000 − 6,000(50)

Q* = 800,000 - 300,000

Q* = 500,0000

Rewrite equation (1), we have:

6,000P = 800,000 - QD

P = (800,000 / 6,000) - (1 / 6,000)QD

P = 133.333333333333 - 0.000166666666666667QD ............ (3)

Rewrite equation (2), we have:

14,500P = QS + 225,000

P = (1 / 14,500)QS + (225,000 / 14.500)

P = 0.0000689655172413793QS + 15.5172413793103 .......... (4)

With tax of €2.46, equation (4) becomes:

P = 0.0000689655172413793QS + 15.5172413793103 + 2.46

P = 0.0000689655172413793QS + 17.9772413793103

Equating equations (3) and (4), and solve for new equilibrium quantity after tax, QT, we have:

133.333333333333 - 0.000166666666666667QT = 0.0000689655172413793QT + 17.9772413793103

133.333333333333 - 17.9772413793103 = 0.000166666666666667QT + 0.0000689655172413793QT

115.356091954023 = 0.000235632183908046QT

QT = 115.356091954023 / 0.000235632183908046

QT = 489,560

To obtain the price paid by buyers after the tax, PT, we substitute QT = 489,560 for QD is equation (3) as follows

PT = 133.333333333333 - 0.000166666666666667(489,560)

PT = 133.333333333333 - 81.5933333333335

PT = 51.74

Therefore, the price paid by buyers after the tax is €51.74.