Elasticity, Taxes, and Deadweight Loss

Elasticity, taxes, and deadweight loss Elasticity is not just a theoretical concept. It is critically important for understanding the consequences of tax policy: who actually pays taxes, what distortions they create, and the size of welfare losses.

Tax Incidence and Elasticity

Tax incidence is the distribution of the tax burden between buyers and sellers. The key insight: legal responsibility (who pays the tax to the government) does not determine the economic burden (who actually bears the costs).

Formula for burden distribution:

Share of buyers = PES / (PES + |PED|)

Share of sellers = |PED| / (PES + |PED|)

Intuition: the party less able to "escape" the tax (less elastic) bears more of the burden.

Examples of Tax Incidence

• Tax on cigarettes:

  • Demand is inelastic (addiction): |PED| ≈ 0.4
  • Supply is relatively elastic
  • Most of the tax falls on smokers
  • The price rises by almost the full amount of the tax

• Tax on luxury yachts (USA, 1990):

  • Demand is very elastic (easy to forgo buying a yacht)
  • Supply is relatively inelastic (specialized shipyards)
  • Sales collapsed, shipyards closed
  • Tax was repealed — did not generate revenue, destroyed jobs

• Tax on labor (payroll tax):

  • Labor supply is relatively inelastic (people need jobs)
  • Most of the burden falls on workers, even if the employer remits the payment
  • This explains why “employer taxes” reduce wages

Deadweight Loss (DWL)

Deadweight loss is the loss of welfare that nobody receives. It is not a redistribution (from buyers/sellers to the government), but a pure loss.

Source of DWL: a tax creates a “wedge” between the buyer’s price and the seller’s price. This distorts decisions:

• Some transactions that would be beneficial without the tax do not occur
• Buyers willing to pay more than sellers' costs but less than the tax-inclusive price do not buy
• Sellers willing to sell for less than the buyer’s price but more than their net-of-tax price do not sell

Graphically: DWL is the triangle between the demand and supply curves, between the old and new quantity.

DWL formula:

$ \text{DWL} \approx \frac{1}{2} \times t \times \Delta Q $

where $t$ is the per-unit tax, $\Delta Q$ is the reduction in quantity.

DWL and Elasticity

The key relationship: the more elastic demand and supply are, the greater the DWL for the same tax.

Why? Elastic curves mean quantity reacts strongly to price changes. Tax greatly reduces $Q$, creating a large triangle of loss.

With inelastic curves: quantity changes little, DWL is minimal. The tax looks more like redistribution than distortion.

Policy conclusion (Ramsey rule): To minimize DWL, taxes should be higher on goods with inelastic demand/supply.

DWL and Tax Size

An important insight: DWL grows faster than the tax!

DWL is proportional to $t^2$ (the square of the tax rate).

Doubling the tax quadruples DWL.

Consequence: many small taxes are more efficient than one large tax. It is better to spread the tax burden across many bases.

Laffer curve: At a sufficiently high tax, DWL is so large (transactions do not occur) that tax revenue falls. There is a rate that maximizes revenue.

Subsidies and DWL

Subsidies are the mirror image of taxes. They also create DWL:

• Subsidy: increases quantity above the efficient level
• Goods are produced whose costs exceed their value to consumers
• Overpayment for units that are not worth it

Subsidy DWL: the triangle between the curves, from equilibrium to the subsidized quantity.

Examples: agricultural subsidies lead to overproduction, fuel subsidies — to excessive consumption.

Efficiency vs. Equity

Trade-off: Taxes that minimize DWL (on inelastic goods) are often regressive — they fall on the poor (necessities are inelastic). Progressive taxes (on income, luxury) create more distortions but are considered fairer.

Lump-sum taxes (same amount from everyone) create no distortions at all (no quantity response), but are extremely regressive.

Political choice: Society decides how to balance efficiency and equity. Economics shows trade-offs but does not give the answer.

For the Investor

Analysis of tax changes:

• Who will actually bear the burden of a new tax?
• Companies with inelastic demand can pass the tax on
• Companies in competitive industries (elastic demand) cannot

Assessment of regulatory risk:

• Industries with high DWL — candidates for reform
• Subsidized industries — risk of subsidy removal

Understanding elasticity helps assess the impact on profit.

Pricing power again: The ability to pass on tax = pricing power. This is an additional test of competitive position.