EC213: Public Economics: Taxation - PowerPoint by 28G69v

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									          EC313:
Public Economics: Taxation
 6. Optimal Taxation
 • Ramsey Taxation
 • Optimal user fees
 • Optimal income taxes
 • Time inconsistency problems
 • Tax evasion


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     C. Optimal Income Taxes
• Optimal income taxation is choosing the tax
  rates across income groups to maximize social
  welfare subject to a government revenue
  requirement.
  – A key concern in the analysis is vertical equity /
    ability to pay
  – Key consideration is efficiency
  – Many models to consider – we’re looking for general
    rules the models suggest
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          Optimal income taxes
     (example #1) Edgeworth’s Model
• Goal: Choose an optimal income tax rate t to maximize
  social welfare, assuming the social welfare function is
  Utilitarian
   W = U1 + U2 + …. + UN
• Assume the following for Ui:
   – Identical utility functions, depends only on income
   – Diminishing marginal utility of income
• Assume total income is fixed (no labour supply
  response to changes in after tax wages).

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         Optimal income taxes
    example #1 ( Edgeworth’s Model)
• The model suggests
   – To maximize social welfare, redistribute income so
     that each person’s marginal utility of income is the
     same
       taxes should be set so that after-tax incomes are
     equal
   – Implies marginal tax rate of 100% for those with
     above-average income.

• The unrealistic assumption is that total income (labor
  supply) is fixed.

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  Consider the 100% tax rate
Tax revenues




               0            τ*             100% Tax rate



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         Stern (1976) (example #2)
• Similar to Edgeworth model
• Assume individuals choose between income
  (consumption of goods) and leisure to maximize
  Ui
• Assume tax revenues collected from each
  individual is defined by
     Revenue = -α + t x Income
  – Linear income tax schedule, aka flat tax

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          Example #2 – Stern (1976)
Revenue
             Revenue=- α +t x Income




                                        (taxable) income
    α            For example, let α =100, t=.5
                 - Receive grant = $100 if income = 0
                 - Receive grant = $100 - .50 if earn $1
                 - Pay tax = 0 if earn $200
                 - Pay tax = $50 if earn $300
                 - Pay tax = $100 if earn $400

                 Everyone has 50% marginal tax rate
                 Different average tax rates
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          Example #2– Stern (1976)
• Assume government needs to collect 20% of pre-tax
  income, very (but not perfectly) inelastic labour
  supply (ε=0.1)
   – Optimal tax rate t=.19 to max. social welfare
• If higher labour supply elasticity assumed
   lower income tax rates
• If more egalitarian SWF (higher weight on poor)
   higher income tax rates
  Rawlsian  t=.80

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  Gruber and Saez (2000): Simulation exercise
                (example #3)
• Simulation exercises are the numerical simulation of
  economic agents’ behavior based on measured
  economic parameters.
• These are used to determine the optimal tax rates or
  other parameters of interest.
• Gruber and Saez (2000) considered a tax rate with:
   –   Guaranteed income level (α)
   –   Utilitarian SWF
   –   Revenue neutral
   –   Four income categories
• They weighed the equity-efficiency implications
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Tax payments    Gruber and Saez (2000)
     $46,650

                               The average rate does
                                 not exceed 47%.
     $34,400
                                                              t=49%




                    t=66%                   t=56%
     $10,320


                 $10,000


     -$4,200          $16,364 $32,000               $75,000    $100,000   Family income


     -$11,000
                                    The optimal income tax schedule
                                        starts off with a subsidy.
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    Gruber and Saez (2000)
               Optimal Tax Results
                         $32
                 $0       K        Guarante
                 To $10K To  $75K      ed
   Income       $10  To  $75  and   income
   groups        K  $32K K   Above    level
Marginal Tax
Rates           68      66       56      49   $11,000
Average Tax
Rates          -161     12       40      47
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      Gruber and Saez (2000)
• Gruber and Saez (2000) found that marginal tax
  rates were highest on the poor and lowest on the
  rich, while average tax rates rose with income
  (because of the loss of the grant).




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        Our existing system
(in a very rough and simple way…)
 Revenue




   A
                                   income

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 Optimal taxation – general results
• Optimal tax = maximize social welfare
• Constraint: taxation creates excess burden
  which reduces potential social welfare
• When labour supply is elastic
      lower income tax rates are optimal
• When preferences are more egalitarian
      higher income tax rates are optimal

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                    FYI
• Reading: Chapter 17 RDSB as per course
  outline




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