17.01.2024 Tax Ineffiencies#

Tax system = balance equity and efficiency

without Taxes: Social Margin Benefit (SMB) = Social Marginal Cost (SMC)

with Taxes: Deadweight Loss, depends on

  • Tax height

  • elasticities (inelastic = lower DWL, higher tax rev)

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Deadweight Loss#

DWL Formula (not relevant!) $\( DWL = - \frac{ \eta_s \eta_d }{2(\eta_s - \eta_d)}\times \tau^2 \times \frac{ Q }{P} \)$

  • \(\eta\) = elasticities

  • \(\tau\) = Tax rate

Implications

  1. effiency depends on preexisting distortions

    • e.g. taxing positive externalities = very inefficient

  2. progressive tax system = higher DWL

    • higher tax rate for rich = higher DWL

  3. low long running taxes > short high taxes (e.g war financing)

empirical: DWL is smaller than in theory!

  • individuals perceive taxes different

  • they are used much better than private!

Optimal Commody Taxation#

by Frank Ramsay: ratio of marginal DWL = marginal Revenue

Formula:

\[ \frac{ MDWL_i }{MR_i} = \lambda \]

ratio \(\lambda\) = should besame for all goods

Example

\[ \frac{ MDWL_A }{MR_A} > \frac{ MDWL_B }{MR_B} \]

  • increase taxation on B

  • lower on A

-> elasticity rule: good with higher elast. = lower tax

  • but not good for equity (caviar = high elast, wheat = low)

Optimal Income Taxes#

optimal syste,

  • total income in society = fixed

  • same utility function

  • After = everyone same income

Lafffer Curve = bullshit, not empirical!

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What to include in Tax Policy

  • vertical equity = high tax on rich

  • behavioral responses

Formula: \(\frac{ MU }{MR} = \lambda\) same for all

Tax-Benefit Linkages#

Earmarked Taxes: taxes collected and spent for specific purpose (e.g social insurance)

  • lowers inefficiency

  • benefits are distributed back

Example: benefits are valued same as tax loss

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