The market for a good is described by the demand equation $Q_d = 120 - 2P$ and the supply equation $Q_s = 20 + P$. The government imposes a specific tax of $t$ Naira per unit on sellers.

(a) Express the equilibrium price paid by buyers ($P_b$) and the price received by sellers ($P_s$) in terms of $t$.

(b) Derive the tax‑revenue function $R(t)$.

(c) Determine the value of $t$ that maximises tax revenue and compute the maximum revenue (to two decimal places).

(d) For that optimal tax, calculate the dead‑weight loss (DWL) as the loss in total surplus relative to the no‑tax equilibrium. Give the DWL rounded to the nearest Naira.

Question

The market for a good is described by the demand equation $Q_d = 120 - 2P$ and the supply equation $Q_s = 20 + P$. The government imposes a specific tax of $t$ Naira per unit on sellers.

(a) Express the equilibrium price paid by buyers ($P_b$) and the price received by sellers ($P_s$) in terms of $t$.

(b) Derive the tax‑revenue function $R(t)$.

(c) Determine the value of $t$ that maximises tax revenue and compute the maximum revenue (to two decimal places).

(d) For that optimal tax, calculate the dead‑weight loss (DWL) as the loss in total surplus relative to the no‑tax equilibrium. Give the DWL rounded to the nearest Naira.

Accepted Answer

Optimal tax = 40 Naira; Maximum revenue = 1066.67 Naira; Dead‑weight loss = 533 Naira

Neco Model Questions Vol1 2018 Economics Question 6

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