Excess Burden

1
Excess Burden

• The First Fundamental Theorem of Welfare
  Economics says that, under ideal conditions, the
  behavior of producers and consumers will
  automatically lead to efficiency.
• Thus when taxes distort economic decisions, they
  reduce efficiency and create what is called the
  excess burden of the tax.
• This excess burden is a welfare loss beyond the
  tax revenue collected. It is also referred to as
  the welfare cost or deadweight loss.
• For example, if I stopped buying beer because of
  a tax on beer, no taxes would be collected but
  there would still be a welfare loss.

2
Tax Shifts Budget Constraint

• Initially, there are no economic distortions.
• Original budget constraint has a slope
  -(Px/Py)
• After a tax on x less x can be bought.
• The new budget constraint has a slope -(1
  t)Px/Py.

y
x
3
Measuring the Tax Payment

• For any level of x, the vertical distance
  between the two budget constraints shows the tax
  payment measured in terms of the good y.
• Set Py 1 or let y represent all other goods.
• For example, if we hold purchases of x fixed at
  x1 then purchases of y would have to fall from y1
  to y2 .

y
y1
y2
x1
x
4
A Decline in Utility

• The tax causes the utility-maximizing bundle of
  goods to switch from 1 to 2.
• Naturally, utility decreases.
• The tax revenue collected is equal to the
  distance between A B.
• Is the decrease in utility greater than the tax
  revenue collected?

y
A
x
5
Equivalent Variation

• Equivalent variation is the amount , if there
  were no tax, by which income would have to be
  reduced to yield an equivalent decline in
  utility.
• Such a reduction income is shown as a parallel
  shift of the budget constraint and is equal to
  the vertical distance between A and C.
• The distance between B C is the dead weight
  loss (DWL).
• DWL is the difference between what is paid in
  taxes and an equivalent (in terms of utility)
  reduction in income

A
x
6
Lump Sum Tax

• A lump sum tax is a tax that is paid regardless
  of a consumers behavior.
• Significantly it doesnt change relative prices.
  Rather, it simply decreases income by the amount
  of the tax.
• Note that reduction in income is identical to the
  tax collected. (The distance between A B.)
• There is no Deadweight Loss.

x
7
Why no Lump Sum Taxes?

• An example of such a tax is a head tax.
• Such taxes are regressive.
• If everybody has to pay 100, this is much more
  of a burden to a poor person than it is to a
  billionaire.
• Margaret Thatcher replaced property taxes with a
  head tax and was subsequently booted out of
  office.

8
Wherefore Excess Burden?

• Remember, allocative efficiency requires that
  MRSxy MRTxy
• However, after the tax, the consumer faces a new
  budget constraint such that utility is maximized
  where MRSxy (1 tx)Px/Py.
• For producers, the important thing is price net
  of taxes. Thus, profit-maximizing producers will
  still set MRTxy Px/Py.
• Since tx gt 0, MRSxy gt MRTxy. That is, the
  necessary condition for allocative efficiency is
  not satisfied.

9
Intuitive Explanation

• As long as consumers are willing to cover the
  economic costs of producing a good, then economic
  efficiency dictates that the good should be
  produced.
• However when a tax, rather than production
  costs, pushes a good beyond a consumers price
  range, then too few resources will be
  dedicated to the production of a good for which
  consumers would have been willing to pay.
• Basically economists want decisions to reflect
  opportunity costs rather than the tax structure.

10
Does Quantity Have to Change for There to be
Inefficiency?

• Before and after the tax on x, the consumption of
  x is x1.
• The excess burden is equal to BC.
• Equivalent Variation equals E1S
• Tax Revenues equal E1E2.
• E2S is the excess burden
• A lump sum tax resulting in the same reduction in
  utility would raise more revenue. (IC runs
  tangent to both new BCs)
• Tax did change consumption of Y alter the
  relative mix of X Y!

11
Substitution and Income Effects

• The move from our initial equilibrium (1) to our
  new equilibrium (2) can be divided into two
  parts
• The move from 1 to 3 is the income effect.
• The move from 3 to 2 is the substitution effect.

12
SE causes DWL

• Excess burden is caused when a tax changes
  relative prices and the consumers MRS--this is
  exactly what the substitution effect is.
• The income effect can offset or mask the
  substitution effect.
• While there is no perceived change in quantity
  demanded, there is still a deadweight loss.

• s