NotesAtHKU

Per unit tax and subsidies

A per unit tax $t is a tax of $t per unit of output. A per unit subsidy $s is a subsidy of $s per unit of output. Consider the quantity $ts=s-t$ .

The demand curve will be shifted vertically by $ts$ units, and the supply curve will be shifted vertically by $-ts$ units.

Wedge approach

Consider the new equilibrium point $(Q^*, P^*)$ . Let the wedge be $x=Q^*$ . $P_\text{Consumer}$ is the intersection of wedge and demand curve, and $P_\text{Producer}$ is the intersection of wedge and supply curve.

|ts| = |P_C - P_P|

The per unit share of tax burden / subsidy benefit can be found by $|P_D-P^*|$ and $|P^*-P_S|$ .

Revenue, cost and burden

The government revenue from tax / cost of subsidy is $|ts| Q^*$ . Inside the rectangle in the case of tax, the upper portion is the consumer burden / benefit (CB), and the lower portion is the producer burden / benefit (PB). It is reversed in the case of subsidy.

The less price elastic side of the market bears more burden of the tax / subsidy. If elasticity is unchanged, the ratio of burden remains unchanged even if $ts$ changes.

Deadweight loss / gain

The lost economic surplus when the socially optimal quantity of a good is not produced, given by:

DWL = \frac{1}{2} \times ts \times (Q^* - Q_e) \propto \eta_s, \eta_d

Where $Q_e$ is the equilibrium quantity without tax / subsidy, and $\eta$ is the elasticity of demand or supply.

To find the "total economic surplus to the society corresponding to a subsidy", we can use the formula:

\textbf{TES corresponding to ts} = \textbf{TES before ts} - \textbf{DWL}

Taxes and Subsidies

Per unit tax and subsidies

Wedge approach

Revenue, cost and burden

Deadweight loss / gain