Suppose a $3 per-unit tax is placed on this good. The tax causes the price paid by buyers to

Per Unit specific tax = $3 : Increases price paid by buyers by $3 (if demand is perfectly inelastic) OR Doesn't change buyers' paid price (if supply is perfectly inelastic) OR Partially increases price by <$3 (based on relative demand & supply inelasticity)

Explanation:

Indirect taxes (eg-specific per unit tax) is an example of tax whose incidence & impact fall on different people, burden can be shifted from sellers to buyers.

However burden of a per unit tax is beared by consumers or producers more, depends on relative inelasticity of demand and supply.

If demand is more inelastic, more tax burden is shifted to buyers & if supply is more inelastic, more tax burden is beared by the seller itself.

Reason : Because Elasticity is the responsiveness of buyers demand & sellers supply to product price, more burden is shifted to the economic agent (buyers / sellers) who are less sensitive / more insensitive to change in price for their demand / supply