Question

Assume the government imposes a per-unit tax on good Y.

Will the price paid by consumers increase by the same amount as the tax? Explain.

Will the loss in consumer and producer surplus be greater than, less than, or equal to the tax revenue collected by the government

Answer 1

Short answers
- No — the consumer price will generally rise by some fraction of the tax, not necessarily the full amount. How the tax is split between consumers and producers (tax incidence) depends on the relative price elasticities of demand and supply.
- The loss in consumer plus producer surplus is greater than the tax revenue collected, except in special cases (e.g. perfectly inelastic supply or demand) where they can be equal.

Explanation — consumer price change
- With a per‑unit tax t, the price paid by buyers (p_b) and the price received by sellers (p_s) satisfy p_b = p_s + t. Equilibrium quantity moves to the point where demand at p_b equals supply at p_s.
- The amount p_b rises relative to the pre‑tax price depends on how much quantity adjusts in response to price changes. If demand is very inelastic (buyers don’t reduce quantity much), buyers will bear most of the tax (p_b rises almost by t). If supply is very inelastic, sellers bear most of the tax and p_b rises little.
- A standard elasticity expression for the fraction of the tax borne by consumers is:
consumer share = Es / (Es + |Ed|)
where Es = supply elasticity and |Ed| = absolute value of demand elasticity. So p_b increases by t·[Es/(Es+|Ed|)].
- Special cases: if demand is perfectly inelastic buyers pay the full tax; if supply is perfectly inelastic sellers pay the full tax.

Explanation — surplus loss vs. tax revenue
- The government revenue = t × Q_taxed (tax per unit times post‑tax quantity).
- Consumers’ surplus falls and producers’ surplus falls. Part of that fall is a transfer to the government (the tax revenue); the rest is a deadweight loss (DWL) caused by the reduction in mutually beneficial trades.
- Therefore total loss in CS + PS = tax revenue + deadweight loss. Since DWL > 0 whenever quantity traded falls (i.e. unless supply or demand is perfectly inelastic so quantity does not change), the combined loss in CS and PS is larger than the tax revenue in the usual case.
- Special case: if one side is perfectly inelastic so quantity doesn’t change, there is no DWL and the loss in CS+PS equals the tax revenue (the tax is a pure transfer).

Intuition: taxes reduce the traded quantity, destroying some gains from trade. Tax revenue is only the transferred part; the destroyed gains are the extra welfare loss beyond revenue.