Transcript Efficient and Equitable Taxation

Chapter 14:
Efficient and Equitable
Taxation
Econ 330: Public Finance
Dr. Reyadh Faras
Dr. Reyadh Faras
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Optimal Commodity Taxation
 One economic policy question: At what rates should
various goods and services be taxed?
 The theory of optimal commodity taxation provides a
framework for answering this question.
 Knowing the right set of taxes depends on the
government’s goal.
 We assume that the only goal is to finance public
expenditures with minimum excess burden and without
using any lump sum taxes.
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Example
 A person consumes 2 goods (X&Y) and leisure (l).
 The prices are PX, PY and w, respectively.
 The maximum number of hours for work is fixed at T,
per year.
 Assuming the person consumes all of its income, its
budget constraint is: w (T-l) = PX X + PY Y
 The LHS gives total earnings, and the RHS shows
how the earnings are spent.
 The equation may be rewritten as:
wT = PX X + PY Y+ wl
 The LHS is the value of time endowment.
 Assume that it is possible to tax X, Y and l by the same
Ad Valorem rate, t.
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 The after tax budget constraint becomes:
wT = (1+t) PX X + (1+t) PY Y+ (1+t) wl
(14.3)
 Dividing both sides by (1+t), we have:
(1/(1+t)) wT = PX X + PY Y+ wl
(14.4)
 Comparison between (14.3) and (14.4) shows that: A
tax on all commodities including leisure is equivalent to
reducing the value of time endowment from wT to
(1/(1+t)) wT
 Because w and T are fixed, wT is also fixed.
 Therefore, a proportional tax on time endowment is a
lump tax, which has no excess burden.
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 Conclusion: a tax at the same rate on all goods
including leisure is equivalent to a lump sum tax and
has no excess burden.
 It sounds good, but putting a tax on leisure time is
impossible.
 The only available tax instruments are taxes on
commodities X and Y.
 Therefore, some excess burden is inevitable.
 The goal of the OCT is to select tax rates on X and Y
in a way that minimizes the excess burden of raising tax
revenues.
 It might be appropriate to tax X and Y at the same
rate, so called neutral taxation.
 This will be shown laterDr. to
be inefficient.
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The Ramsey Rule
 To minimize overall excess burden, the marginal
excess burden of the last dollar of revenue raised from
each commodity must be the same.
 Otherwise, it would be possible to lower overall excess
burden by raising the rate on the commodity with the
smaller marginal excess burden, and vice versa.
 Assume X and Y are unrelated to each other, meaning
that a change in the price of either commodity affects
its own demand only.
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Figure 14.1
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 Suppose a unit tax (ux) is levied on X, followed by a
tax of 1, the total price becomes P0 + (ux + 1)
 Quantity demanded falls by Δx to X2 and the
associated excess burden is ½ Δx [ux + (ux +1)]
 With some algebra, the marginal excess burden is ΔX
and the marginal tax revenue as X1 - ΔX
 The marginal excess burden per last dollar of tax
revenue is ΔX/(X1 - ΔX)
 The condition for minimizing overall excess burden is
that the marginal excess burden per last dollar of
revenue be the same for each commodity, we must set
ΔX/(X1 - ΔX) = ΔY/(Y1 - ΔY)
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 This implies ΔX/X1 = ΔY/Y1
(14.7)
 Equation (14.7) says that to minimize total excess
burden, tax rates should be set so that the percentage
reduction in the quantity demanded of each commodity
is the same.
 This result is called the Ramsey Rule.
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A Reinterpretation of the Ramsey Rule
 It is useful to explore the relationship between the
Ramsey Rule and demand elasticities.
 Let ηx be the elasticity of demand for X, and tx be
the tax rate on X expressed as Ad Valorem tax.
 By definition of A.V. tax, tx is the percentage
increase in price induced by the tax.
 Hence, txηx is the percentage reduction in demand
for X induced by the tax (same applies for Y).
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 The Ramsey Rule says that to minimize excess
burden, the percentage of change for X and Y must
be equal: txηx = tyηy
 Now divide both sides by tyηx to obtain:
(tx/ty) = (ηy / ηx)
(14.9)
 Equation (14.9) is the inverse elasticity rule:
“As long as goods are unrelated in consumption,
tax rates should be inversely proportional to
elasticities”.
 That is, the higher is ηy relative to ηx, the lower
should be ty relative totx .
 Efficiency doesn’t require all rates be set uniformly
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The Corlett-Hague Rule
 Corlett and Hague proved an interesting
implication of the Ramsey Rule: When there are
two commodities, efficient taxation requires taxing
the commodity that is complementary to leisure at
a relatively high rate.
 Since taxing leisure results in no excess burden,
but because it is impossible to tax leisure, taxing
goods used jointly with leisure, could lower the
demand for leisure.
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Equity Considerations
 The efficient tax theory may seem to have
unpleasant policy implication, as it relates tax
rates negatively with demand elasticities.
 Efficiency is one criterion to evaluate a tax system;
fairness is important as well.
 Tax system should have vertical equity:
 It should distribute burdens fairly across people
with different abilities to pay.
 The Ramsey Rule has been modified to account
for the distributional consequences of taxation.
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Example
 If the poor spend high share of income on X than
the Rich, and vice versa for Y.
 Suppose the social welfare function puts more
weight on the utilities of the poor than the rich.
 Then even though demand for X is less elastic,
optimal taxation may require higher tax rate on Y.
 It is true this will create larger excess burden, but
it redistributes income toward the poor.
 Society may be willing to accept higher burden in
return for a more equal distribution of income.
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In general, the optimal departure from the Ramsey
Rule depends on two factors:
 How much society cares about equality.
 The extent to which consumption patterns differ
between the rich and the poor.
Summary
 If lump taxes were available, taxes could be raised
without any excess burden.
 Since lump sum taxes not available, minimizing the
excess burden requires setting taxes in a way that
reduces demand for all goods in same proportion.
 For unrelated goods, set tax rates inversely with
demand elasticities. An exception to this rule is if
equity is an issue.
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Optimal User Fees
 A user fee is the price paid by users of a good or
service provided by the government.
 Government production may be appropriate if there
are economies of scale; greater output reduces AC.
 In this case a single firm can supply the entire market.
 This phenomenon is called natural monopoly.
 A private firm may produce the commodity, while in
some cases produced by the public sector.
 Private monopolies often regulated by governments.
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Figure 14.3
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Monopolist
 Decreasing AC often leads to public sector
production, or regulated private sector production.
 Unregulated monopolist seeking profit produces
where MR=MC at quantity (Zm), price (Pm), and
making profit.
 Is this efficient?
 According to welfare economics, efficiency requires
MC=P.
 But at (Zm) price is greater than MC, hence (Zm) is
inefficient.
 Efficiency and existence of monopoly profits provide a
possible justification for government taking over the
production of (Z).
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 In this case the government should produce up to the
point where P=MC at output (Z*) and price (P*).
 Problem: in this case P<AC, the firm incurs a loss.
 How should the government confront this dilemma?
 Several solutions have been proposed.
1) Average Cost Pricing
 When P=AC, the firm breaks even.
 It produces (ZA) and charges price (PA).
 Note that (ZA) < (Z*), meaning that AC pricing fall
short of the efficient amount of output.
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2) Marginal Cost Pricing with Lump Sum Taxes
 Charge P=MC, and fill the gap with a lump sum tax.
 This price ensures efficiency in the market, while
lump sum taxes guarantees no new inefficiencies.
 However, there are two problems:
 1st: Lumps sum taxes are generally unavailable. Only
distorting taxes are available, which may outweigh
market efficiency from P=MC pricing.
 2nd: Fairness requires consumers of publicly provided
services to pay for it “benefits-received principle”.
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3) A Ramsey Solution
 Suppose the government runs several enterprises,
who as group cannot lose money, but any individual
one can.
 Suppose the government wants the financing to come
from users of each service enterprise.
 By how much should the user fee for each service
exceed its MC?
 This is similar to the optimal tax problem.
 The difference between the MC and the user fee is
just the tax that the government levies on the good.
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 The government has to raise certain amount of
revenue enough for the group to break even.
 The Ramsey Rule gives the answer: set the user fees
so that demands for each commodity are reduced
proportionately.
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