Per-Unit Tax

A per-unit tax is paid on every unit of output, so it adds to marginal cost: $MC^{\text{post-tax}} = MC + t$. The monopolist's optimal price rises by less than the full tax (typical pass-through under linear demand is $1/2$ the tax), and quantity falls. Contrast with a Lump-Sum Tax or profit tax, which leaves $MC$ — and therefore the optimal price and quantity — unchanged.

When to use

Use per-unit tax reasoning whenever the question describes a tax "per barrel", "per pack", or "per unit produced". The standard exam move: rewrite the FOC with $MC + t$ in place of $MC$, re-solve, and compare to the pre-tax price/quantity. Combined with the Lerner Index formula $P^* = MC/(1 - 1/|E|)$, a per-unit tax shifts $MC$ and therefore $P^*$.