Notes@HKU by Jax

Taxes and Subsidies

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=stts=s-t.

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

Wedge approach

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

ts=PCPP|ts| = |P_C - P_P|

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

Revenue, cost and burden

The government revenue from tax / cost of subsidy is tsQ|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 tsts changes.

Deadweight loss / gain

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

DWL=12×ts×(QQe)ηs,ηdDWL = \frac{1}{2} \times ts \times (Q^* - Q_e) \propto \eta_s, \eta_d

Where QeQ_e is the equilibrium quantity without tax / subsidy, and η\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:

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