The market demand and supply functions for a commodity are given as Q_d = 120 - 2P and Q_s… — JAMB UTME

The market demand and supply functions for a commodity are given as $Q_d = 120 - 2P$ and $Q_s = 20 + 3P$ respectively, where $P$ is the price in Naira ( $\text{₦}$ ) and $Q$ is the quantity in units. If the government levies a specific sales tax of $\text{₦}10$ per unit on the producers, what is the per-unit tax burden borne by the consumer?

Answer: 6 ₦

Answer

The per-unit tax burden borne by the consumer is \text{₦}6.

The initial market clearing price is found by setting

120 - 2P = 20 + 3P

, which gives

P_1 = \text{₦}20

. With a specific tax of

\text{₦}10

per unit levied on producers, the price received by sellers becomes

P_s = P_c - 10

. Substituting into the supply equation gives

Q_s' = 20 + 3(P_c - 10) = 3P_c - 10

. Equating demand and post-tax supply gives

120 - 2P_c = 3P_c - 10 \implies 5P_c = 130 \implies P_c = \text{₦}26

. The consumer tax burden per unit is the price increase,

26 - 20 = \text{₦}6

Step-by-Step Solution

Calculate the pre-tax equilibrium price

Initial price

P_1 = \text{₦}20

Equating quantity demanded

Q_d = 120 - 2P

and quantity supplied

Q_s = 20 + 3P

gives

120 - 2P = 20 + 3P

, which solves to

P_1 = 20

Adjust the supply equation to account for the specific tax of \text{₦}10 per unit

New supply function

Q_s' = 3P_c - 10

Because the tax is paid by producers, the net price received by sellers is

P_s = P_c - 10

. Substituting

P_s

into

Q_s = 20 + 3P_s

yields

Q_s' = 20 + 3(P_c - 10) = 3P_c - 10

Calculate the post-tax equilibrium price paid by consumers (

P_c

)

Post-tax consumer price

P_c = \text{₦}26

Equating

Q_d

and

Q_s'

gives

120 - 2P_c = 3P_c - 10

, which simplifies to

5P_c = 130 \implies P_c = 26

Calculate the consumer's share of the per-unit tax incidence

Consumer tax incidence = \text{₦}6

The per-unit tax incidence on the consumer equals the net increase in market price paid,

P_c - P_1 = 26 - 20 = 6

Key Concept

Tax Incidence and Price Elasticity of Demand and Supply

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