The market for a good is described by the demand equation $Q_d = 120 - 2P$ and the supply equation $Q_s = -20 + 3P$, where $P$ is the price in dollars per unit. Production of the good generates a negative externality that imposes a cost of $4 per unit on society. The government decides to impose a specific tax $t$ per unit to internalise the externality.

(a) What is the optimal specific tax?
(b) Calculate the new consumer price, producer price, equilibrium quantity, consumer surplus, producer surplus and tax revenue after the tax is imposed.
(c) Compute the dead‑weight loss arising from the tax and state the net welfare loss, taking the externality into account.

Question

The market for a good is described by the demand equation $Q_d = 120 - 2P$ and the supply equation $Q_s = -20 + 3P$, where $P$ is the price in dollars per unit. Production of the good generates a negative externality that imposes a cost of $4 per unit on society. The government decides to impose a specific tax $t$ per unit to internalise the externality.

(a) What is the optimal specific tax?
(b) Calculate the new consumer price, producer price, equilibrium quantity, consumer surplus, producer surplus and tax revenue after the tax is imposed.
(c) Compute the dead‑weight loss arising from the tax and state the net welfare loss, taking the externality into account.

Accepted Answer

Optimal tax = $4 per unit. After the tax: consumer price = $30.40, producer price = $26.40, quantity = 59.2 units. Consumer surplus ≈ $876.16, producer surplus ≈ $584.10, tax revenue = $236.80. Dead‑weight loss = $9.60, net welfare loss = $0 (the externality is fully internalised).

Gce Model Questions Vol1 2018 Economics Question 17

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