Theory of Income Taxation

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					Theory of Income Taxation

        Lecture 11
Definition of Income
Haig-Simons Definition
• Two steps are necessary before defining a
  comprehensive measure of income.
• First the taxpaying unit must be selected.
• For this discussion the taxpaying unit is
  considered to be the individual.
• Second the time period relevant for
  measuring personal income must be defined.
• For this discussion the time period is
  considered to be one year.
• As defined by Henry Simons, income is an
  indicator of the ”exercise of control over the
  use of society’s scarce resources. ”
• Income can be spent, there by converting
  perched empowering to consumption, or it
  can be stored for future use as savings.
• Thus income can be measured according to
  sources or it uses.
• Sources of income, calculated from the
  beginning to the end of the accounting
  period, are
• earnings from the sales of productive
• transfers from either government or
  individuals; and
• increases in the value of assets owned by the
• Uses of income include
• consumption, or purchase, of goods and
• taxes;
• donations; and
• savings (increased holdings of assets over
  liabilities constitutes savings). Savings
  represents an increase in a person’s net
• Comprehensive income is the sum of a
  person’s annual consumption expenditures
  and the increment in that person’s net worth
  in a given year.
• I = C + DNW
• Comprehensive income must be adjusted for
  inflation to accurately measure increases in
  potential purchasing power.
• The concept of comprehensive income is also
  called the Haig-Simons definition of income.
• Income is any payment or increment in a person’s
  net worth that increases that person’s ability to
  purchase or use goods and services in a given year.
• Capital gains are increases in the value of assets
  over the accounting. Comprehensive income
  measures capital gains on assets as the accrue
  regardless of whether the asset is sold or changed;
  that is, it includes both the realized capital gains and
  unrealized capital gains.
• The logic behind including unrealized capital gains
  income is that any increase in the valued assets, be it
  converted to cash or not, increases the individuals
  potential to purchase items in a given year.
• Net capital gains on capital gains minus capital
• Earnings include both income from labor and
  income from capital.
• Labor income is measured by wages and
  salaries from the sale of labor services;
• Capital income represents the sum of interest
  and dividends and rents.
• Transfers are payments for which no good or
  services received in return.
• Gifts are transfers, as our government
  payments to individual such as cash
  assistance to the poor.
• Comprehensive income deducts the
  transaction costs incurred in earning income.
• Sources = Earnings + Transfers + Net capital
             gains – Cost of Acquiring Income

• Uses = Consumption + Gifts and Donations +
         Savings-Cost of Acquiring Income
Example of the Comprehensive
    Definition of Income
• Suppose that in a given year a person orange
  $20,000 from the sale of labor services and also
  learns of thousand dollars in interest from
  certificates of deposit, which represent fund’s
  loaned to a bank.
• The total earnings for this person therefore equals
• The person also receives $2,000 as a gift from his
  parents that year to help with his expenses.
• He also was unemployed for one month during the
  year, during which time he received $800 in
  unemployment insurance payments from the
• Both the $2,000 gift and the $800
  unemployment insurance payments would be
  regarded as transfers and therefore would be
  included in his comprehensive income.
• Transfer income is $2800.
• The person earns capital gains of $1500 and
  incurs $600 in capital losses from stock
  market transactions.
• The net realized capital gains is therefore
• Suppose the value of the stock he owns but
  does not sell falls by $500. He would incur
  the unrealized capital losses of that amount on
  unsold stock.
• Over the same year, market appraisal
  indicates that the value of this person’s home
  you has increased by $2,000. The net
  unrealized capital gain their for would be
  $2,000-$500 = $1500.
• This individual’s comprehensive income
  would be equal to $26,200.
       Source Side
Income Component Dollar Amount
Labor Services       $21,000
Transfers             2, 800
Net Realized            900
Capital Gain
Unrealized Capital     1500
Comprehensive        $26, 200
              Use Side
Use Component     Dollar Amount
Consumption       $21,200
Savings            2, 500
Taxes               2,500

Comprehensive     $26, 200
Problems of Measurement
Unrealized Capital Gains
• The Haig-Simon definition of income would require
  that both realized an unrealized capital gains be
  included in income; a mechanism would have to be
  developed to measure increments in the value of all
  capital assets held by individuals as these gains or
  losses accrue.
• Also the gains would have to be adjusted for
  inflation to determine the real increases in
  consumption capabilities.
• While determining unrealized gains may not be so
  difficult for stocks which are traded on the
  secondary market, it could be quite difficult for
  antiques, jewelry, and livestock.
Costs of Earning Income
• All expenditures that are made neither for
  consumption nor for adding to net worth
  would be deducted as expenses from income.
• Such expenses might include such items as
  tools, work clothes, union dues, child care
  expenses, and such legitimate travel expenses
  as commuting cost to and from work.
• Some tools that an individual uses in work
  also might be used for personal purposes and
  therefore would be considered consumption
• The acquisition of skills in trading program
  supporting continued education adds to the
  individual’s human capital; thus expenditures for
  such activities might be legitimately deducted from
  income insofar as they will result in higher earnings
  that will be subject to future taxation.
• However, education that produces human capital
  for home use is not legitimately deductible if the
  increased consumption enjoyment stemming from
  taking craft courses and various how-to-do-it
  courses escapes taxation.
• Income-in-kind used in coming in the form of
  goods and services rather than cash payments.
• Difficult problems arise in measuring and
  tracing various forms of income- in-kind.
• Income-in-kind often results from home
  production of goods and services.
• Persons make things for themselves or
  provide themselves with services rather than
  purchasing those goods and services from
  others in the market.
• A comprehensive income tax base would
  include these services.
• Individuals who own their own homes receive
  income-in-kind in the form of imputed rent
  which represents the flow of housing services
  that individuals in effect sell to themselves as
  a force they are both landlord and tenant.
• Failing to subject such income-in-kind to
  taxation acts as a subsidy to undertake such
  activity and results in distortions and resource
• It is just not feasible to tax all income-in-kind.
• Thus the ultimate line between what is or is not
  income is likely to be drawn by arbitrary decisions.
• Fringe benefits provided by employers for their
  employees are fairly easy to tax.
• On the other hand, nonpecuniary returns associated
  with various occupations are more difficult to tax.
  Nonpecuniary returns represent satisfaction that
  individuals receive from their employment that is
  not reflected in their wages.
• Real pay levels may be different from the same
  pecuniary income.
• Resources may be attracted to occupations
  with relatively more nonpecuniary (nontaxed)
• When income-in-kind for various jobs escape
  taxation, the tax system encourages
  individuals to enter those jobs, and it
  encourages employers to provide
  nonpecuniary benefits in lieu of taxable
  monetary benefits.
     A General Tax on a
   Comprehensive Income:
Economic Effects of a Flat-Rate
        Income Tax
• A general proportional tax on comprehensive
  income is a flat rate on all income regardless
  of its source or use.
• Because all income is taxed at the same rate
  regardless of its source, the ratio of the price
  of labor to the price of capital is not distorted
  by the tax.
• Because taxes paid are independent of the use
  to which income is put, the comprehensive
  income tax does not distort the relative prices
  of consumption of goods and services.
• Although no loss in efficiency will occur in
  the way individual spend their income or earn
  it, the tax is likely to distort the choices that
  are made concerning the allocation of time
  between work and leisure and between
  consumption and savings or productive
• The flat tax rate on comprehensive income
  can therefore prevent labor markets and
  investment markets from attaining efficiency.
Taxation of Labor Earnings and
   the Work Leisure Choice
• Labor income has a dominant component of
  comprehensive income. It represents about
  60% of the nation’s gross income.
• So efficiency losses caused by taxation of
  labor income is of serious concern.
• In this analysis, each worker is presumed to
  allocate time between work and leisure to
  maximize utility.
• The equilibrium allocation of time depends on
  individual preferences and the wage a worker
  can earn per hour.
• The impact of income taxation on Detroit’s to
  work cannot be predicted unequivocally.
• The tax sets up both income and substitution
  effects; these work in opposite directions on
  workers’ forces to work.
• The equilibrium allocation of time depends
  on individual preferences and the wage a
  worker can earn per hour.
Income        J

    T    {                 B         U2
             IN                 E'

                  0   L1       L2              Leisure Hours
For any point other than the intercept point along HJ,
the individual’s income can be expressed as

             I  w(24  L)
L is the amount of leisure per day and w is the wage rate per hour.
The slope of the budget line is the rate of return on work effort, w.
The equilibrium condition for the utility maximizing allocation of
time between work and leisure is

                  w  MRSLI
The introduction of a flat-rate tax on the workers labor income
of t percent reduces the return to work effort at all levels of work.
The net wage received by the worker after payment of the income
tax is

                 wN  wG(1  t )
 This rotates the line that depicts the market possibilities for
 transforming leisure into income through work effort from
 HJ down to HJ’. The equation for this line now becomes

               I  wG(1  t )(24  L)
The new equilibrium for the worker now occurs at point E’.
The new equilibrium condition is

            wG(1  t )  MRSLI
• Be proportional income tax has the font effects:
• A reduction in utility fromU2 to U1.(This ignores any
  benefits from government expenditures accrue into the
• An increase in leisure hours per day from L1 to L2. This
  worker therefore chooses to work fewer hours per day as a
  result of the tax on labor earnings.
• A consequent reduction in actual labor earnings per day
  fromI1 to IG because of the reduction in hours worked.
  Because taxes are levied on IG, net income available to spend
  falls to IN.
Income and Substitution Effects
 of the Tax on Labor Earnings
• The tax can be viewed as lowering the
  opportunity cost of an hour of leisure by
  reducing the wages that the worker receives
  from wg to wg(1-t).
• The income tax results in a substitution
  effect that is unfavorable to work effort.
• The tax reduces the return from work effort,
  making work less remunerative.
• The substitution effect represents a potential
  loss of output of goods and services due to the
  reduction in the incentive to work.
• An income effect also results from the tax
  induced decline in the net wage.
• The income effect tends to be favorable to
  work effort, provided at leisure is a normal
• The income tax reduces income at all levels
  of work.
• The reduction in real income results in a
  decrease in the consumption of all normal
• Since leisure is a normal good, its
  consumption is likely to decrease as well.
• Decreases in leisure time imply that work
  effort increases.
• The actual effect of the tax on work effort
  depends on the relative magnitudes of the
  income and substitution effect.
Income     I

                         E1                      Effect
                0   L1        L2 L'
                                            Leisure Hours
Labor Market Analysis of
   Income Taxation
• The impact of taxes on labor income, market
  wages, net wages, and efficiency depends on
  the responsiveness of workers to tax induced
  wage declines
Perfectly Inelastic Labor Supply
• The total excess burden of the
  comprehensive income tax on labor income
  depends on the substitution effect of the tax
  induced net wage declined in the tax rate.
• All taxes, including lump sum taxes,
  resulting income effects that, other things
  being equal, make taxpayers worse off.
• Thus, the tax induced distortion in the work-
  leisure choice used to measure the excess
  burden of the tax must be based only on the
  change in work hours due to the substitution
  effect caused by the tax
Compensated Labor Supply
• A curve that shows how hours worked per day very
  with wages when the income effect of wage
  changes is removed is called a compensated labor
  supply curve.
• Such a curve reflects only the substitution effects of
  wage changes.
• Points on such supply curves can be used to
  measure the excess burden of attacks on labor
• Even if the regular, or uncompensated, market
  supply curve of labor is perfectly elastic, the excess
  burden of the tax will not be zero.
• In the figure, the regular markets supply curve of
  labor is assumed to be perfectly inelastic.
• The demand curve is based on the gross wage that
  the employer must pay to attract any given number
  of labor hours per year.
• The impact of the tax on labor income is to reduce
  the wages received by workers for any amount of
  labor supplied.
• Because the market supply of labor is perfectly
  inelastic, the tax induced reduction in wages
  received by workers does not result in any
  reduction in the quantity of labor hours supply.
• No change occurs in the initial market wage.
• Net wages received by workers therefore fall by
  the full amount of the tax per hour of labor.
• Under these circumstances, the income taxes
  borne entirely by workers in the form of a
  reduction in wages.
• This indicates that the substitution effect is
  exactly offset by an equal and opposite income
  effect, assuming that leisure is a normal good.
• Removing the income effect changes the market
  supply curve to an upward sloping compensated
  labor supply curve.
• Note that the tax induced decline in net wages
  received by workers is tW*G when the market
  supply curve is perfectly inelastic.
• This decline in wages received results in a
  substitution effect of –DQSL.
• The excess burden of tax equals .5(tW*G ) DQSL.
• One study has concluded that the excess burden
  per dollar of taxes on labor income based on the
  tax structure prevailing in the United States in the
  mid 1970’s would have been 8.1 cents even if the
  market, or uncompensated , elasticity of supply of
  labor were zero.
                   S   Regular Labor
                       supply Curve
       Wages                                               S
                                                           Com pensat ed
                                                           Labor Supply
         W*G                                               Curve

W N = W* G (1-t)
                                D = WG
                             W N = W G (1-t)

               0                               0   -DQSL       Labor
The Elasticity of Supply of Labor
        Exceeding Zero
• Suppose that the market supply curve of
  labor is upward sloping.
• In the diagram, the pretax equilibrium is at
  point A.
• The tax reduces the net wage for any number
  of our work per year.
• The new equilibrium is at point B.
• The number of hours worked declines.
• The gross, or market, wage increases.
• Net wages received by workers decline.
• In this case, a portion of the tax is shifted to
• Wages do not decline by the full amount of
  tax .
• The increase in wages reduces the profits of
  employers or or results in higher market
  prices of goods and services, as marginal cost
  of production increase.
• This results in some shifting of the tax burden
  to groups other than workers.
• The excess burden is noted at point B or W*N
  by the difference in labor hours between the
  compensated supply curve and the regular
  supply curve.
Wages                                       SC

        W*G                C

 { }


                                                 D = WG

             0          Q3 Q2 Q1

Empirical Evidence on Labor
• Empirical evidence on labor supply suggests that
  for males between the ages of 25 and 55, the
  income effect of wage changes is roughly equal to
  the substitution effect.
• The observed responsiveness of males in this age
  range to changes in tax rates is therefore quite low
  because the overall wage elasticity of labor supply
  with respect to the wage is close to zero.
• A zero overall elasticity of labor supply suggest
  that the incidence of a comprehensive income tax
  on labor income is borne by workers as a reduction
  in net wages.
• Empirical evidence indicates that the efficiency
  loss ratio of taxes on labor income in the United
  States in the 1970’s was in the range of five to
  $0.30 on revenues collected.
• For example one study concluded that in the tax
  system of the 1970’s, the efficiency loss ratio for
  the average married male was 22%.
• This implies that taxes on married males in 1970
  the United States cause distortions in resource use
  resulting in excess burden of $0.22 for each dollar
  of revenue collected two
• More recent estimates based on the income
  tax laws prevailing in 1988 suggest that the
  efficiency loss ratio for income taxes and
  United State’s had fallen to 13.5%.
• Analysis of the economic effects of the tax
  rate reduction of the Tax Reform Act of 1986
  suggest that there was very little increase in
  labor supply as a result of the tax declines.
• There was only modest increases in hours
  worked in response to reductions in marginal
  tax rates that averaged about 8 percent.
• The general conclusion of the analysis of the
  effects of the Tax Reform Act of 1986 on the
  labor supply is that such effects were not
Incidence of a Payroll Tax
     Economic Effects of a Payroll

•WWho bears the burden of the Payroll Tax

•S       Start with a no tax situation
Rate             S

10.00 = w


            L1           Labor
             S represents the minimum wage labor will take
             to supply a given quantity of labor -- based on
Wage         utility maximization -- consumption vs leisure choice

 10.00 = w

D represents the maximum wage the employer
will pay for a given quantity of labor -- based on       D
                                    L1                       Labor
Suppose Employers have to Pay a Payroll
Tax Equal to $ 2 Per Hour of Labor
Rate                           S

10.00 = w


              L2   L1                  Labor
Wage               Effective Cost of   S
Rate               Labor

                                 Actual Wage to
10.00 = w

              L2     L1                        Labor
Suppose Employees have to Pay a Payroll
Tax Equal to $ 2 Per Hour of Labor
Rate                               S


10.00 = w


              L2   L1                      Labor
• Note the real effects of the tax are exactly the
  same whether the tax is collected from employers
  or employees.
• Note also that in the previous example workers did
  not bear the full burden of the $2 payroll tax.
  Wages fell from $10 to $8.50. The reduction in the
  wage was $1.50.
• The distribution of the burden of the payroll tax
  depends on the elasticity of the labor supply and
  demand functions.
Perfect Inelastic Supply of Labor




                               D -T
 Relatively Elastic Supply of Labor

$11.50                            SL



                                D -T
           L2   L1
              Relatively Inelastic Demand for Labor
Rate                                            S


10.00 = w


                                 L1                   Labor
Taxation of Interest Income and
     Its Effect on Savings
• The taxation of interest income results in both
  income and substitution effects.
• Taxation of interest income lowers the return to
  savings but can either increase or decrease the
  amount of savings observed.
• The impact of the tax on interest income on
  choices can be understood with a simple
  entered temporal analysis of consumption in
  two periods.
• The allocation of a given amount of income
  over the two periods depends both on individual
  tastes an interest rate that a saver can earn.
• By saving a person for those present
  consumption in exchange for more future
• The marginal rate of time preference
  (MRTP) is the slope of an indifference curve
  for present and future consumption
  multiplied by minus one.
• It is a measure of the willingness of savers to
  forgo current consumption in exchange for
  future consumption.
• Future consumption is equal to

     C 2  (1  r ) S
     S  I C
     C 2  (1  r )( I  C )
     Slope  (1  r )
     In equilibrium,
     MRTP  (1  r )
• The introduction of a tax on interest income
  reduces the net return obtained from saving.
• If the taxes levied at a rate t , than after
  payment of the tax becomes r(1-t).
• This reduces the slope of the transformation
  line and it swivels downward.
• The new equilibrium is at E2.
• At this equilibrium, current consumption
  increases and as a consequent there is a
  reduction in savings.
• The actual impact on saving for any
  individual represents the combined income
  and substitution effects of the tax induced
  reduction in the net interest rate.
• The income effect of the reduction in the
  interest rate savers receive from r to r(1-t)
  provides incentive to reduce consumption of
  all normal goods in the current period and in
  the future.
• This implies a an increase in saving.
• The substitution effect of the decrease in the
  net return to savings cause by the tax
  increases current consumption and therefore
  results in less savings.
• There is a reduction in the opportunity cost
  of current consumption.
• Insofar as the savers seek to save specific
  amounts, or target levels, of savings, the
  income effect of the tax dominates, and
  savers actually may increase the rates of
  savings to offset the effect of the tax on their
  net return.
Future            E

                  F   E1
              0       C1 C’1         Present
Market Analysis of Taxation on Interest
       and Investment Income
• The initial equilibrium is at point A, at an
  interest rate of r1 which results in an
  efficient allocation of resources by equated
  the marginal social cost of savings with the
  marginal social benefit of investment.
• The imposition of the tax inserts a which
  between the interest received by savers and
  paid by investors and other borrowers,
  causing a loss and efficiency.
• Investment and saving fall from their
  equilibrium level, the S1 , to a reduced level,
• The tax lowers the return to savings at all
  levels from rG to rG(1-t) resulting in curve rN.
• The consequent reduction in the quantity of
  saving raises the market interest rate to r*G
  but leaves the net interest received by savers
  below the initial level, r1.
• The excess burden of the tax is measured by
  the triangle ABC if the income effect of a tax
  induced interest rate change is negligible.
• The excess burden depends on the specific
  tax rate and the interest elasticity of the
  supply of savings.
                  Supply of

r1            A

r*N   C

                                   D = rG

      S2 S1
                  Supply of

r1            A

r*N   C

                                   D = rG

      S2 S1
• Most studies find little response of savings
  supply to changes in tax rates.
• Studies of the tax rate reductions of the Tax
  Reform Act of 1986 were unable to detect
  any significant increase in savings
  attributable to the tax rate declines.
• The changes in the tax law at that time had
  only a mixed effect on the incentives to save
  and did not reverse the long-term decline in
  the personal savings rate that began in the
• There is, however, evidence of significant
  effects of taxation of capital on incentives to
• Taxes on investment income increase the cost
  of capital.
• Recent studies suggest that these taxes due
  reduce invest.

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