Recent studies have investigated the efficiencies of policies that use several policy instruments simultaneously (for example, a policy that uses a production subsidy combined with a production quota). Several studies of very specific cases find that optimal combination of two policy instruments is more efficient than optimal independent use of either. In this note we demonstrate using set theory and maximization theory, that all such specific results are examples of a more general result, which is that by combining m instruments efficiently, a government can always be at least as efficient as when using a subset of those m instruments. This result holds for any of the several definitions of "efficiency" in the literature.Agricultural and Food Policy,

Bullock, David S.

Salhofer, Klaus

English

Research Papers in Economics

A Note on the Efficiency of Income
Redistribution with Simple and
Combined Policies
David S. Bullock and Klaus Salhofer
Recent studies have investigated the efficiencies of policies that use several policy instruments
simultaneously (for example, a policy that uses a production subsidy combined with a
production quota). Several studies of very specific cases find that optimal combination of two
policy instruments is more efficient than optimal independent use of either. In this note we
demonstrate using set theory and maximization theory, that all such specific results are
examples of a more general result, which is that by combining m instruments efficiently, a
government can always be at least as efficient as when using a subset of those m instruments.
This result holds for any of the several definitions of “efficiency” in the literature.
Comparison of the efficiencies of alternative poli-
cies has been a main topic in the agricultural eco-
nomics literature since Nerlove (1958) and Wal-
lace (1962), Many studies in this field have con-
centrated on ranking what we will call simple
policies, which are those policies using single
policy instruments (for example, a policy that uses
a production subsidy only, or a policy that uses a
production quota only), More recent studies have
also investigated the efficiencies of combined poli-
cies, which we define as those using several instru-
ments simultaneously (for example, a policy that
uses a target price and a production quota). Several
of these latter studies find, for very specific cases,
that optimal combination of two policy instruments
is more efficient than using either of the instru-
ments independently. In this note we use set theory
and maximization theory to demonstrate that these
findings are examples of a more general result,
which is that making additional policy instruments
available to government allows for the attainment
of a more efficient policy. That is, a policy com-
bining m instruments efficiently will always be at
least as efficient as any policy using a subset of
those m instruments. This result holds for any of
the several definitions of “efficiency” commonly
used in the literature.
Once the question of the efficiency of combin-
ing policy instruments is viewed from our frame-
David S. Bullock is an associate professor, Department of Agricultural
and Consumer Economics, University of Illinois. Klaus Sathnfer is a
member of NAREA, Universitiit fur Bodenktdtur Wien, Department of
Economics, Politics, and Law, Vienna, Austria.
work using set theory and maximization theory,
this general result is not only intuitively appealing,
but rather obvious or even “trivial.” But perhaps
because the question at hand has not been ad-
dressed before using our framework, while so far
in the literature several specific examples of this
result have been presented, the generality of the
result has not been recognized or appreciated.
Thus, the contribution of our paper is not just the
general result presented, but the presentation of the
framework itself, which permits better understand-
ing of several issues in the current literature on the
efficiency of policies.
Studies of Combined and Simple Policies
In this section we briefly review several studies
that have compared the efficiencies of combined
policies and simple policies. These studies all
present specific examples of a policy combining
two instruments efficiently being superior to poli-
cies using either of the instruments independently.
Output Subsidies and Production Control
Just (1984) discussed the efficiencies of the simple
policies output subsidization (or equally, a target
priceldeficiency payments policy) and production
control, and of a combination of the two simple
policies. Just’s study used a stochastic setting (un-
certainty in producer and consumer prices). He
theoretically and empirically showed that “theBullock and Salhofer E@ciency of Income Redistribution 267
joint use of [target price/]deficiency payments and
production controls clearly dominates use of either
one individually” (p. 58) when government’s ob-
jective is either to maximize a weighted social wel-
fare function (SWF) or to maximize social welfare
subject to a given welfare (income) ratio between
producers and consumers/taxpayers,
Similarly, Innes and Rausser (1989) and Innes
(1990) proved in a different stochastic setting (un-
certainty in producer price and production), and
based on a weighted social welfare function, that
“production control is , , , an optimal complement
to a target price[/deficiency payments] program”
(Innes 1990, p. 53).
Alston and Hurd (1990) analyzed the effects of
the excess burden of taxation on the efficiency
ranking of alternative policies using the normative
criterion of’ ‘minimizing the total costs to consum-
ers and taxpayers of achieving a given increase in
producer surplus” (p, 150).1They noted that “it is
always inefficient to specialize in either a[n output]
subsidy or a production control for the case when
the [social] opportunity cost is one dollar per dollar
of government spending” (p. 150). They also
proved that, for the case in which there is an excess
burden of taxation, “the combined quota and out-
put subsidy policy remains superior to the output
subsidy alone” (p. 153),
Output Subsidies and Export Subsidies
Gardner (1988) found that, for a small country, a
combination of output subsidies (a policy that sets
a certain price to producers) and export subsidies
(a policy that sets a certain price to producers and
consumers) is preferable to either of the simple
policies alone if the government’s objective is to
maximize a weighted SWF with different weights
to producers, consumers, and taxpayers. A similar
result was derived by Alston, Carter, and Smith
(1993), who showed that when government at-
taches a higher weight to taxpayers than to con-
sumers because of the presence of excess burden of
general taxation, any amount of transfer to produc-
ers can be achieved more efficiently (i.e., at lower
social costs) by combining output subsidies and
export subsidies than by using output subsidies
alone.2 In addition Alston, Carter, and Smith
(1993) showed that in the large country case, using
a combination of output subsidies and export sub-
sidies may increase efficiency compared with us-
ing output subsidies alone.
Tartf and Production Control
Guyomard and Mahe (1994) showed, using a static
general equilibrium framework, that in the case of
a small country importer, “the level of [social]
utility under a production quota with a tariff is
greater than the level of [social] utility under a
simple tariff” (p. 34).
Price Support and Research Expenditures
De Gorter, Nielson, and Rausser (1992) used a
weighted social welfare function approach to show
that combining research expenditures and output
subsidies can improve social welfare compared
with levels achievable using research expenditures
alone (p. 34). Gardner (1992) confirmed this find-
ing for the case of a large country. He also showed
that this finding does not “depend upon farmers
being economic losers from technical progress”
(p. 14), as hypothesized by Tweeten and Coggins
(1992). Similarly, de Gorter and Swinnen (1992)
showed that joint use of research expenditures and
export subsidies increases social welfare subject to
a minimum producer welfare constraint.
The General Case: Increasing the Number of
Available Instruments Can Increase Efficiency
Letx= (xl,..., x~) be a vector of policy instru-
ment variables available to a government. A par-
ticular value of x is called a “policy,” Let u = (u,,
. . . . UJ describe welfare levels of n interest groups
affected by government policy. Groups’ welfare
levels are functions of government policy u = (ul,
. . . . u~) = (h/(x), . . . . h~ (x)) = h(x).
Let X be the set of feasible policies (where by
“feasible” we mean technically feasible, though
not necessarily politically feasible). Then F =
{u Iu = h(x), x l X} is the set of feasible policy
outcomes, Now let us examine the effects of one of
the m policy instruments of X being constrained to
a particular value: for example, let us constrain x~
to be fixed at some level x~, (This level may be a
level at which the instrument is not effective, such
as when production control is set at a very high
positive number, so that it never affects actual pro-
duction, or such as when a tax is set at zero. What
is the same, one can simply assume that x~ is not
available.) The new set of feasible policies may
then be defined as X’ = {x=x lxm=x~}.
Clearly X’ c X, the new set of feasible policies is
a subset of the original set of feasible policies.
Therefore it must be that the new set of feasible
policy outcomes is a subset of the original set of
feasible policy outcomes: F’ = {u I u = h(x),
xeX’}c F= {ulu=h(x), xeX}. That is, any
policy outcome achievable when only a subset of
the m original instruments is available is also268 October 1998 Agricultural and Resource Economics Review
achievable when all rn instruments are available.
(That is, a government could always choose not to
use some of the available instruments.) Con-
versely, there can be policy outcomes achievable
with all m instruments that are not achievable with
any subset of those m instruments. Therefore, no
matter the definition of “efficiency” (or “social
welfare”) used, making more policy instruments
available cannot decrease, and may increase, e&i-
ciency (or social welfare).
To examine the points made above in more
depth and to see how they relate to the literature,
let W u + R describe government’s objective
function (or a social welfare function, or some
function measuring “efficiency,” however de-
fined). Let con[h(x)] represent an optional con-
straint equation or inequality involving the welfare
of interest groups. Let government’s (or society’s)
decision problem be given by:
(1) ~~x {W(h(x)) s.t. con[h(x)]}.3
Hence the problem might be to maximize the sum
of welfare of producers, consumers, and taxpayers
subject to a given welfare ratio between producers
and consumers/taxpayers, as in Just (1984); or the
problem might be to maximize the welfare of con-
sumers and taxpayers subject to having producers
achieve some given welfare, as in Alston and Hurd
(1990); or the problem might be to maximize a
weighted linear social welfare function under no
constraint, as in de Gorter, Nielson, and Rausser
(1992).
Now let us examine the effects of one (or more)
of them policy instruments of X being constrained.
Again, we assume that x~ must be fixed at some
level xL. Then government’s problem is
(2) ~da~x {W(h(x)) s.t. conch]}.
A policy X* found by solving the maximization
problem (1) is said to be at least as efficient (or
politically desirable, or socially desirable, etc.) as
policy x*’ found by solving (2) if W(h(x*)) ~
W(h(x*‘)). Because the choice vector x in (2) must
be chosen from X’ c X, and the choice vector x in
(1) can be chosen from X itself, the maximization
problem (2) is more constrained than is the maxi-
mization problem in (1). It follows that for any
policy x*’ that solves (2), a policy x* can be found
that solves (1) such that W(h(x*)) 2 W(h(x*’)).
Therefore a government that can choose the levels
of m policy instruments must be able to attain
policy outcomes that are at least as efficient (so-
cially desirable, politically desirable, etc.) as those
it can attain if it has only a subset of those m policy
instruments available (or if one or more of the m
policy instruments are fixed at certain levels),
Dkcussion
Nothing in our analysis says that it will always be
optimal to use all policy instruments available. The
question of whether an additional available instrtt-
ment actually will be used in the optimal instru-
ment combination and hence will increase effi-
ciency is an empirical inquiry depending on market
conditions (e.g., demand and supply elasticities),
the government (social, political) objective func-
tion, implementation costs, the consideration of
multimarket effects, uncertainty, dynamic effects,
and so on. The results of the quoted papers are
interesting and important in showing that, given
some assumed conditions, the additional instru-
ment will actually improve efficiency. However,
our analysis does show that it never hurts to make
more instruments available for use. Though this
general result is rather obvious once viewed from
our framework, it has remained unrecognized in
the literature. The importance of our results is best
understood with the fact that some studies have
found results of combined policies being less effi-
cient than single policies. Our results make clear
that these studies have failed to consider optimal
policy instrument combinations.4
References
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Notes
1 Note that this is the same as maximizing the
welfare of consumers and taxpayers subject to a
given level of producer welfare.
2 In fact, Gardner (1988) discussed a combination
of deficiency payments and consumption tax, but
as shown by Alston, Carter, and Smith (1995), this
is consistent with what Alston, Carter, and Smith
(1993) called a combination of output subsidies
and export subsidies.
3 According to the reviewed articles and norma-
tive economics in general, government’s decision
problem is assumed to be welfaristic, i.e., it de-
pends solely on individuals’ (or groups’) welfare.
4 For example Gisser (1993) found that a combi-
nation of target price and acreage controls was
more efficient in the case of corn, wheat, rice, and
cotton, but less efficient in the case of feed grains.

Automatic Adjustment Rules for Agricultural Policy Controls. AEf Occasioned Papers,

Can Price Support Negate the Social Gains from Public Research Expenditures in Agriculture. Working Paper 94-06. Department of Agricultural, Resource,

Export Policy, Deficiency Payments, and a Consumption Tax.”

Is a Production Quota Pareto Superior to Price Support Only?”

Political Preference Functions and Agricultural Policy Reform:

Price Supports and Optimal Spending. Working Paper no.

Productive and Predatory public Policies: Research Expenditures and Producer Subsidies in Agriculture.”

Rationalizing Agricultural Export Subsidies: Reply.”

Rationalizing Agricultural Export Subsidies.

Some Neglected Social Costs of Government Spending in Farm Programs.”

The Dynamic of Supply,

Uncertainty, Incomplete Markets and Government Farm Programs.”

A NOTE ON THE EFFICIENCY OF INCOME REDISTRIBUTION WITH SIMPLE AND COMBINED POLICIES

A NOTE ON THE EFFICIENCY OF INCOME REDISTRIBUTION WITH SIMPLE AND COMBINED POLICIES

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