Fairness and Goodness in the Allocation of Resources: Evidence from Nigeria
Adenaike, Abayomi S.
Department of Economics
Olabisi Onabanjo University, Ago-Iwoye
yomisamsonass@yahoo.com, 08038240190
Sennuga, Mabayoje A.
Department of Economics,
Tai Solarin College of Education, Omu-Ijebu
albert_sennuga@yahoo.com, 08038835912
&
Adekoya, Esther O.
Department of Accounting, Banking and Finance
Olabisi Onabanjo University, Ago-Iwoye
bolagoodleaf@yahoo.co.uk, 08038253744
Abstract
This paper examines the different dimensions of fairness and goodness in resource allocation,
and their impact on the economy. Difficult choices are involved when resources are scarce.
There are several alternatives and the option of proceeding with a programme is set against
some theoretical alternative uses of funds. Governments are often forced to finance new
programmes at the expense of existing ones. Regardless of who makes the decision, the
principles to be used are the same; what varies is level of investment in analysis justified by the
resources at stake. The framework employs in this paper is based on game theory and
information economics which explores principal-agent problem under moral hazard. Finally,
this paper suggests that optimal resource allocation for implementing high revenue effort
involves allocating more revenue to the agent with higher tax effort. The paper then concludes
that lump-sum revenue allocation unrelated effort is inefficient from the perspective of
incentivizing the sharing mechanism. Governments are expected to address resource inequity
and fiscal imbalances using transfers to induce states to internalize social and economic
externalities through the adoption of socio-economic programmes as well as matching grant as a
corrective measure to the mismanagement of the public fund.
Keywords: Resource allocation, fairness, choice and efficiency
1.0 Introduction
The literature on welfare economics and resources allocation has grown rapidly in recent
years. The utilitarians were the first to talk of welfare in terms of the formula, the greatest
happiness of the greatest number. Vilfredo Pareto considered the question of maximizing social
welfare in allocation of resources on the basis of general optimum conditions. Marshall (1920)
and Pigou (1951) concentrated on particular section of the economics system in their postulates
of welfare economics. It was Robbins’ (1932) ethical neutrality view about economics that led to
the development of welfare economics as an important field of economics studies. Kaldor
(1939), Hicks (1939) and Scitovsky (1951) have laid the foundation of the new welfare
economics with the help of the compensation principles’ avoiding all value judgments and also
explained social welfare in Paretian sense. On the other hand, Bergson (1938), Samuelson
(1948), Tintner and Arrow (1951) have developed the concept of the social welfare function. In
this study, we shall refer to certain basic concepts of welfare economics and then pass on the
Pareto’s welfare conditions for an understanding of modern analysis of welfare economics and
resources allocation.
The current resources allocation formula in Nigeria produces inefficient fiscal and
economic outcomes. Economic analysis of fiscal federalism has a long tradition in the literature
(Oates, 1993; Jha, 1998). The efficiency and equity gains from federalism are well documented.
However, suffice to identify the following important positive effects of federalism: risk pooling;
economies of scale in the provision of public goods; inter-jurisdictional externalities and tax
harmonization, revenue sharing becomes an important characteristic of fiscal federalism. They
are expected to address resource distribution inequity and associated fiscal imbalances in such
environment. Also, the federal government may use transfer to induce some sub-national units to
internalize social and economic externalities through the adoption of certain socio-economic
programmes, for example, the Millennium Development Goals, education, health, environment
quality and infrastructures. Thus, there are problems associated with revenue sharing that
generated significant Pareto inferior revenues distribution with consideration impact on political
and economic stability (Iwayemi, 2009).
According to Iwayemi (2009), revenue sharing mechanisms in most federal system are
politically determined. They often emerged from bargaining processes among parties with
different political, social and economic preferences. The balance of power determines the weight
of factors that underlie the sharing formula. Most of the times, the party or group with the
dominant power determines the outcome to the dissatisfaction of other groups or parties in the
revenue sharing game. Pareto inefficient outcome emerges from revenue sharing giving the
underlying distribution of power. The failure to implement Pareto-improving revenue allocation
policy is underpinned by the distributive politics of such an environment. Three problems have
been identified in the literature for the pervasive occurrence of revenue sharing inefficiency and
inequity in most federal systems, namely, information asymmetry, time inconsistency and
transaction costs (Dixit, 1996; Dixit and Londregan, 1995; and Coate and Morris, 1995). For
efficient and equity reasons, the free-rider and opportunistic behaviour of states should be
minimised in order to address the disparities in the inter-state social and economic situations and
support weak fiscal bases that cannot produce Pareto-efficient fiscal and economic outcomes.
The broad aim of this paper is to provide a framework for the design of an efficient resource
allocation that would ensure fairness, goodness and economic justice in Nigeria.
The rest of the paper is structured as follows: section two is based on the issues of
fairness and goodness in the resources allocation using Pareto conditions for economic efficiency
in allocation of resources. Section three examines the external effects in consumption and
production of public goods, and the attainment of the Pareto conditions through the use of
taxation and subsidies as well as social welfare conditions for efficient, fairness and goodness
in the allocation of resources. The subject of section four is the challenges of fiscal federalism in
Nigeria and other issues and emerging problems from intergovernmental transfer system. This
section also reviews the theoretical framework based on recent research in game theory and
economics of information which explores how to tackle the incentive problems associated with
inter-governmental fiscal relations structured as a principal-agent problem. While section five
describes principle of social welfare, choice and economic justice and section six concludes the
study with policy recommendations and suggestions for further research.
2.0 Pareto Optimality in Resource Allocation
Pareto optimality provides a definition of the economic efficiency of allocation that
serves as the basis for much of the welfare economics (Henderson and Quandt, 2003). An
allocation is Pareto-optimal or Pareto-efficient if production and distribution cannot be
reorganized to increase the utility of one or more individuals without decreasing the utility of
others. Alternatively, an allocation is Pareto-nonoptimal if someone’s utility can be increased
without harming anyone else. And an allocation is said to be Pareto-superior to another if the
utility of at least one individual is higher and the utility of none is lower, even though the
allocation may not be Pareto-optimal.
However, the analyses of Pareto-optimality usually stop short of value judgments and
interpersonal comparisons of utility levels. Therefore, change which improves the positions of
some individuals but cause deterioration in those of others cannot be evaluated in terms of
efficiency; the net effects of the moves may or may not be beneficial. Hence, welfare can be said
to increase (diminish) if at least one person’s position improves (deteriorates) with no change in
the positions of other. Thus, no situation can be optimal unless all possible improvements of this
variety have been made. The abstraction from distributional considerations limits the number of
questions that may be answered with the Pareto apparatus. Our discussion here is not limited to
static efficiency; we also pay attention to the welfare aspects of resource allocation over time and
the time path of welfare (Henderson and Quandt, 2003).
2.1 Pareto Optimality for Consumption and Production
In this section, we describe resource allocation by specific consumption levels for each
individual and specific input and output levels for each producer. A distribution of consumer
goods (including leisure and other withheld primary factors) is Pareto-optimal if every possible
reallocation of goods that increases the utility of one or more consumers would result in a utility
reduction for at least one other consumer. Pareto Optimality will be achieved if each consumer’s
utility is a maximum given the utility level of all other consumers. For instance, assuming that
there are two consumers denoted by the first subscripts 1 and 2 and only two goods, Q1 and Q2.
The utility functions of the consumers are U1(q11, q12 ) and U2(q21, q22 ) where q11 + q21 = q01
and q12 + q22 = q02 , Now assume that consumer II enjoys the level of satisfaction U20 =
constant. In order to maximize the utility of consumer I subject to this constraint, form the
function
U*1 = U1(q11, q12) + λ [U2 (q10 - q11, q20 - q12) – U20]
............ 2.1.1
where λ is a Lagrange multiplier, and set its partial derivatives equal to zero, we have
δU*1 = δU1 - λ δU2 = 0
δq11
δ q11
δ q21
δU*1 = δU1 - λ δU2 = 0
δq12
δ q12
δ q22
δU*1 = U2 (q01 – q11, q20 – q12) - U20 = 0
δλ
δU1/ δq11
δU1/ δq12
=
δU2/ δq21
δU2/ δq22
………… 2.1.2
The left-hand side of the equation above is consumer I’s Rate of Commodity Substitution
(RCS), and the right-hand side is consumer II’s. The RCSs of the consumers must be equal to
achieve Pareto optimality in consumption assuming that the second-order conditions are fulfilled.
If the equations were not satisfied, it would be possible to redistribute the goods in such a way as
to increase I’s utility without reducing II’s, the argument is symmetric. The equations (2.1.2)
show from maximization of II’s utility given a fixed level of I’s. Thus, if the equations were not
satisfied, it would also be possible to increase II’s utility without reducing I’s. The mathematical
analysis for the two consumer case is easily generalized for any number of consumers. Hence,
within the present framework, the evaluation of alternative positions after the redistribution of I
and II, would involve interpersonal comparison of utilities which is not possible under this
condition. Once the conditions above are satisfied, it is not possible to improve further the
position of either consumer without deterioration in the position of the other.
For Pareto optimality for production however, we assume that consumers are not satiated
and that each individual’s utility level is independent of the quantities consumed by others, an
increment in the quantity of any consumer good without a decrement in the quantity of any other
consumer good can lead to a utility increment for at least one consumer without utility decrement
for others. Therefore, Pareto optimality among producers requires that the output level of each
consumer goods be at a maximum given the output levels of all other consumer goods. Assume
that there are two producers using two inputs to produce two goods with the production
functions: q1 = f1 (x11, x12) and q2 = f2(x21, x22), where x11 + x21 = x10 and x12 + x22 = x20 are the
available input quantities and q1 and q2 are the output levels. Maximize the output of good I
subject to the constraint that the output of II is at the predetermined level q20, form the function:
L = f1 (x11, x12) + λ [(f2 (x10 - x11, x20 - x12) - q20]
……….2.1.3
and set its partial derivatives equal to zero, we have
δL = δf1 - λ δf2 = 0
δx11 δ x11
δ x21
δL = δf1 - λ δf2 = 0
δx12 δ x12
δ x22
δL = f2 (x1 – x11 x20 – x12) - q20 = 0
δλ
δf1/ δx11
δf1/ δx12
=
δf2/ δx21
δf2/ δx22
……… 2.1.4
The left-hand side of the equations 2.1.4 above is I’s Rate of Technical Substitution
(RTS) for X1 and X2, and the right-hand side is II’s. Therefore, the RTSs of producers must be
equal to achieve Pareto optimally in production. If the equations were not satisfied, it would be
possible to increase the output of one good without decreasing the output of the other.
3.0 External Effects in Consumption and Production of Public Goods
Market imperfections are externalities where its offers no price for service or disservice.
However, these externalities lead to misallocation of resources and cause consumption or
production to fall short of an optimum level, thus, they do not lead to maximum social welfare of
the citizens in the society (Jhingan, 2001). A different type of externality in consumption occurs
when goods are consumed collectively. Each member of society gains satisfaction from the total
outputs of a public good. Public good according to Baumol (1965) is one whose consumption by
one individual does not reduce its utility to any other individual. The consumption of public
goods is joint and equal. The services provided by the government are public goods such as free
education, good healthcare, public safety, national defence, court for the administration of
justice, disease control, etc.
The benefits of public goods are indivisible. They are available to everybody whether a
person pays for them or not. Thus, they are not subject to the exclusion principle. Their benefits
also are provided at zero marginal cost. That is, their benefits can also be provided to an
additional user without any additional cost. For instance, the cost of providing justice doesn’t rise
when one additional person seeks justice from the courts. Therefore, no one’s satisfaction is
diminished by the satisfaction gained by others, and it is not possible for anyone to appropriate a
public good for her own personal use, as is the case with private goods.
Therefore, the purpose of this section is to evaluate the social desirability of alternative
allocation of resources. In the absence of elaborate value judgments concerning the desirability
of alternative income distributions, a simple value judgment is to consider a reallocation to
represent an improvement in welfare if it makes at least one person better off without making
anybody worse-off. Thus, if it is not possible to reallocate resources without making at least one
person worse-off, the existing allocation is Pareto-optimal. Hence, the first-order conditions for
Pareto-optimal must be modified in the presence of external effects in consumption or
production. So, price (P) must equal social marginal cost (SMC) rather than private marginal cost
if there are external effects in production.
3.1 Taxes and Subsidies
Pigou (1953) opined that the use of taxes or subsidies to bridge the gap between private
and social costs and benefits. Hence, the state can impose taxes in all cases of external
diseconomies in consumption and production. Research has shown that market economies
deviate from the marginal conditions necessary for Pareto optimality. These economies usually
can be led to Pareto-optimality through the imposition of appropriate taxes and subsides. Per unit
taxes (subsidies) will decrease (increase) the levels of consumption and production activities by
increasing (decreasing) their marginal costs if marginal costs are increasing. Accompanying
lump-sum taxes and subsidies, which do not affect activity levels, may be used to distribute the
gain from a movement to a Pareto-optimal allocation. It is then demonstrated that positive net tax
revenues provide social dividend that can be used to increase the utility of one or more members
of society.
Also, in order to bring about equality, we favoured state interference rather than selfinterest, and suggested the use of social control measures to close the gap between private and
social costs and benefits arising from externalities. The social control measures include:
relocating smoke emitting industries out of the residential area by providing appropriate sites and
facilities; provision of free education and massive funding; provision of good healthcare service
delivery; public safety through security of life and properties; and tax concessions and subsidies
to consumers and producers among others. From the forgoing, it is pertinent to say that the
Nigeria’s governments over the years have given concessions and subsidies to the industrialists
and private businessmen and neglect the educational and health sectors which the majority of the
poor masses can benefit. This anomaly is evidenced in the recent and ongoing strike actions of
Academic Staff Union of Universities over poor funding of education and their counterpart in
health sector over non-implementation of agreements.
3.2 Social Welfare Conditions for Efficient and Fairness in Resource Allocation
Economic welfare connotes the welfare of a group or society comprising all individuals.
It means the summation of individual welfares. But unlike an individual, a society has no mind
or consciousness. In a society, every person thinks and acts differently from each other. Hence,
no social choice-expansion index can reflect social welfare. Thus, social welfare implies the
aggregation of the satisfactions or utilities of all individuals in a society (Jhingan, 2001).
According to Pigou (1951), an individual welfare resides in his state of mind or consciousness
which is made up of his satisfactions or utilities.
But modern economists explain it in terms of given scale of preferences that an
individual’s welfare is said to have increased when he is better-off, that is, when he himself
believes that his welfare has increased as a hypothesis. But it is not possible to ask every
individual whether his welfare has increased or not. Mishan (1960), suggests a choice expansion
index. So, whenever an individual’s choice index of hitherto unavailable goods expands his
welfare is said to have increased, provided his tastes remain unchanged.
The concept of social welfare function was first introduced by Bergson (1938) and later
on developed by Samuelson (1948), Tintner and Arrow (1954). They posited that no meaningful
propositions can be made in welfare economics without introducing value judgments. It is an
attempt to provide a scientifically normative study of welfare economics. A social welfare
function shows the factors on which the welfare of a society is supposed to depend. Bergson
defines it ‘as a function either of the welfare of each member of the society or of the quantities of
product consumed and services rendered by each member of the society’. Also, it can be
regarded ‘as a function of each individual’s welfare, which in turn depends both on his personal
well-being and on his appraisal of the distribution of welfare among all members of the society’.
Thus, the social welfare function is an ordinal index of society’s welfare and is a function of
individual utilities. It is expressed as: W = F ( u1, u2, … , un). Where W is the social economics
welfare, F is for function, and U1, U2,…, Un are the levels of utilities’ of 1, 2, … , n individuals.
W is an increasing function of these utilities.
The general properties of the social welfare function are similar to those of an individual
utility function. In particular, the value of the welfare index increases whenever the utility level
of one individual is increased without lowering that of other individual. Thus, the welfare
function is consistent with the Pareto optimality criterion, but it goes much further, since it
assigns a value to every economics state. Therefore, the existence of a social welfare function
implies a comparison of the welfare position of the individual members of society.
4.0 The Challenges of Fiscal Federalism in Nigeria
According to Iwayemi (2009), the major challenges with incentives implications are
identified with the Nigerian fiscal system. Firstly, there is lack of fiscal correspondence between
revenue generation and expenditure especially at the sub-national levels. The high degree of
fiscal imbalance creates the classic common pool problem with its characteristic free rider
behaviour for some of the three tiers of government. Internally generated revenues effort
becomes a back burner issues. Local tax effort becomes a side issue. Since public spending is not
connected in any significant way to internally generated revenues based on local tax effort, the
lack of fiscal correspondence encourages most state and local governments to believe they do not
face a hard budget constraint.
Secondly, the perverse inter-temporal fiscal behaviour that common pool revenue sharing
encourages fiscal behaviour at the sub-national level is highly pro-cyclical and is determined in
most states and local governments by tax revenues sharing. The sharing of Excess Crude Oil
Revenues and the bi-monthly sharing of revenues from the Federation Account continues to pose
significant monetary policy challenges for the Central Bank of Nigeria whose key mandate is to
keep inflation in check.
Thirdly, there is fiscal inefficiency when the sub-national units do not have to bother
about the efficiency of public expenditure or even be accountable for such expenditures since
their revenues are not based on local tax efforts. Under this condition, the issues of optimal mix
of taxation at the sub-national unit, greater efficiency in expenditure and procurement becomes
unimportant for these governments, when bulk of the revenues for a tier of government comes
from transfer from other tiers, fiscal efficiency will be of low priority.
Fourthly, there is the lack of equity, fairness and inefficiency associated with politically
redistributed revenues when the formula is loaded with factors which reflect the preference of
those states with weak tax efforts. Genuine redistribution has conformed to the distributive
politics of Nigeria as determined by the politically dominant region in the country. On average,
revenue sharing has favoured the non-oil producing states and local governments. The factors
that are used in sharing revenues from the Federation Accounts has entrenched this imbalance.
Cheap oil revenues from the Federation Account have encouraged poor tax compliance, weak tax
base and weak tax administration. This has served as a disincentive to fiscal prudence and
sustainability.
Finally, intergovernmental fiscal transfer has and continues to generate highly
contentious fiscal games at different fora. These games and the strategic responses of the diverse
players in the fiscal games have created significant political and economical tensions in the
country. Against the foregoing inefficiencies and lack of equity in the current inter-governmental
revenues sharing game, it is important to explore how some of these emerging problems can be
addressed. The discussion that follows provides some insight in this direction.
4.1
Inter-governmental Fiscal Transfer System: Principal-Agent Paradigm under
Moral Hazard Conditions
However, the political economy literature has thrown light on the issue of fairness and
goodness in the resource allocation. Pareto inefficient outcome will emerge from revenue sharing
giving the underlying distribution of power. The failure to implement Pareto improving revenue
allocation policy is underpinned by the distributive policies of such an environment. Three
problems have been identified in the literature for the pervasive occurrence of revenue sharing
inefficiency and inequity in most federal systems, namely information asymmetry, time
inconsistency and transaction costs.
The sharing of federally collected revenue has always involved strategic contest between
the resources rich and other less economcailly advantageous states. This game has been played at
different fora, political, economic, environmental, social and legal. The revenue sharing problem
can be reformulated as a classic principal-agent paradigm under moral hazard conditions. Since
the seminal contributions of Arrow (1970) and Spence and Zeckhauser (1971), the
characterization of many economic problems exhibiting information asymmetry in virtually all
spheres of economics in principal-agent model framework, has almost become conventional
wisdom (Bolton and Dewatripont, 2005; Holmstrom and Milgrom, 1987; Laffont, 1988; Laffont
and Tirole, 1988; and Mas-Colell, Whinston and Green, 1995).
Notably, incentives are at the heart of economic theory and it is central to the principalagent problem. Both theoretical and empirical researches have investigated the principal-agent
problem under a variety of conditions. The focus of this section is the insight that game theory
and the information economics offer in dealing with some aspects of the contentious issue of
revenue allocation mechanism in Nigeria.
The evidence in Nigeria over the years shows that over dependence on sharing oil
revenues by government at all levels to the neglect of internally generated revenues creates a free
rider problem, which is counterproductive to stronger fiscal base. Structurally, we design the
revenue redistribution problem as a principal-agent problem. However, the scope of information
asymmetry in the problem of government revenue collection across the three tiers of government
in Nigeria complicates the design of an incentive mechanism to drive revenue allocation among
the different tiers of government. Hence, the discussion that follows draws from Laffont (1988)
and Iwayemi (2009).
4.1.1 Principal-Agent Problem Model
In this section, we show that any state that produces good outcomes in terms of their
independent non-oil revenue generation efforts are positively rewarded to serve as an incentive
to making the sharing system more incentive compatible. Also, we sketch a framework within
which we factor in tax effort as a mechanism for incorporating incentive effects in the design of
a new revenue allocation formula that will serve as a basis for a more robust intergovernmental
fiscal transfer system.
For this purpose, the revenue sharing is characterized as a type of an economic game,
between the three tiers; federal, state and local government on the one hand and the Revenue
Mobilization Allocation and Fiscal Commission (RMAFC) on the other. The problem is
characterized as a multi-agent principal problem with the principal being the RMAFC and the
three tiers of government as the agents. Analytically, we classify broadly the tiers of government
into two agents, natural resource rich and non-natural resource rich states. Putting i index the
state categorization, i, (i = 1, 2). Denote revenue collection effort of state i by ei ≥ 0. The amount
of revenue generation by state i is denoted by Xi (expressed in monetary units). The revenue
collected in each state is not only a factor of the tax effort but also depends on nature, domestic
and world economic trends, which cannot be predicted with any degree of accuracy.
Moreover, we make the conventional assumptions that Xi the revenue collected (the
performance outcome) is an independently distributed random variable defined by a continuous
distribution function F ( . , ei ) with density function, f ( . , ei ),∀ei ≥ 0, ƒ ( . , si ( Xi ) ei ) ˃ 0 onǀ0,
+ ∞).f(. , ei) is twice continuously differentiable in ei and Fe(. , .) ≤ 0 implying first order
stochastic dominance. The following notations are useful:
U(t, e) = agent’s utility function in wealth
V(x,t) = principal’s utility function in wealth
e = agent’s revenue collection effort
ψ(.) = cost of effort
x = outcome of revenue collection effort
t(.) = the revenue transfer function to the agents as allocated revenue
f (.,ei)
= Probability distribution of x given e.
However, the timing of the game is as follows:
1. RMAFC offers a revenue allocation contract (e, t1, t2)
2. The agents accept or reject the offer. If it rejects, its payoff amounts to his reservation
utility.
3. If contract accepted, the agent chooses the level of revenue collection effort e.
4. Nature determines the outcome, the revenue collected, x, according to the probability
distribution f ( . , ei).
5. The outcome is observed by both principal and the agent and the payoffs are made.
Now, suppose state i receives a monetary transfer ti from RMAFC as federally distributed
revenues. The Von Neumann Morgenstern (VNM) utility function for state I is represented by
u(ti) – ψ(ei)
………(4.1.1)
We make the usual monotonocity and convexity assumptions:
u' > 0; u´’<0; ψ’ >0; ψ” > 0
………(4.1.2)
Each state is assumed to be risk averse. The principal (RMAFC) observes only total
revenue generation, X1 + X2. The RMAFC as the principal is assumed to be risk neutral. Suppose
the preferences of the RMAFC can be represented by the utility function V, ti is the revenue
transfer to the agents. RMAFC income is federal revenue less the transfers to the agents, the tiers
of government.
V = X1 + X2 - t1 – t2
……….(4.1.3)
v’ > 0; v” < 0, v(0) = 0
The participation (individual rationality) constraints for the state governments can be
written as follows:
u(ti) – ψ(ei) ≥ π
i = 1, 2
………(4.1.4)
Therefore, in order to incentivize the revenue generation, let ti (Xi) denote the transfer
from the federation account but contingent on the outcome of tax revenue effort in each
governmental level. It is a reward function, providing the incentive for greater revenue
generation effort in each state/local government. We assume that t is private information to the
agents, e is not verifiable. Given t(.), each tier of government chooses the effort level, e, by
maximizing her expected utility. This implies solving the optimization problem:
∞
Max ∫0 [𝑢(𝑡(𝑥)) − 𝜓(𝑒))]𝑓 (𝑥, 𝑒)𝑑𝑥
………(4.1.5)
Differentiating equation (4.1.5) yields the first-order conditions for state i which is:
∞
∫0 [𝑢(𝑡(𝑥)) − 𝜓(𝑒))]ƒe (xi, ei) dxi – ψ’(ei) = 0
for i=1,2
……….(4.1.6)
Where fe is the derivative of the density function with respect to e. Equation (4.1.6) is the
incentive compatibility constraints for each state. The problem that the RMAFC will solve is to
maximize its net income subject to the incentive and participation constraints of the states. The
principal wants the agents to put in high rather than low revenue collection effort through an
incentive mechanism. The principal’s maximization problem involves equations, thus:
∞
∞
Max ∫0 ( x1 – t(x1)) ƒ (x1, e1) dx1 + ∫0 ( x2 – t(x2)) ƒ (x2, e2) dx2
………(4.1.7)
Such as:
∞
∫0 ( u(t(xi)) ƒe (xi, ei) dxi - ψ’(ei) = 0
∞
∫0 ( u(t(x)) ƒ (xi, ei) dxi - ψ(ei) ≥ π
for i=1,2
(Incentive Constraint)
………(4.1.8)
for i=1,2
(Participation Constraint)
………(4.1.9)
Here, the analysis examines optimal incentive contracts under moral hazard. Thus, we
set-up Lagrangean function and δi and λi as the respective Lagrangean multipliers for equations
(4.1.8) and (4.1.9), the first-order condition for maximization yields the equilibrium conditions:
1
𝑢′ (𝑡( 𝑥𝑖 ))
= 𝜆𝑖 + 𝛿𝑖
ƒ𝑒 (𝑥𝑖 ,𝑒𝑖 )
ƒ (𝑥𝑖 ,𝑒𝑖 )
i = 1, 2
.……(4.1.10)
i = 1, 2
……….(4.1.11)
Solving equation (4.1.10) for t yield
t(xi) = (𝑢, )-1 [ 1/ { 𝜆𝑖 + 𝛿𝑖
where
ƒ𝑒 (𝑥𝑖 ,𝑒𝑖 )
ƒ (𝑥𝑖 ,𝑒𝑖 )
ƒ𝑒 (𝑥𝑖 ,𝑒𝑖 )
ƒ (𝑥𝑖 ,𝑒𝑖 )
}]
is likelihood ratio, when it is increasing in revenue outcome x for given level of
effort, e, the agent’s transfer will also be increasing in total revenue outcome. Equation (4.1.11)
depicts that States are made to bear some risk in revenue sharing to induce a good level of effort
at revenue generation when both λi and δi > 0 at the optimal solution. This establishes the result
that optimal revenue scheme for implementing high revenue effort involves allocating more
revenue to the agent with higher tax effort. This is consistence with Laffont (1988) and Iwayemi
(2009). Thus, this result shows that lump-sum revenue allocation unrelated effort is inefficient
from the perspective of incentivizing the sharing mechanism.
5.0 Social Welfare, Choice and Economic Justice
Maximization of social welfare combines the Pareto optimality conditions with the social
welfare function to provide a determinate and unique solution to the challenges of social welfare,
choice and economic justice (Bator, 1957; and Jhingan, 2001). View broadly; our goal in this
section is to study means of obtaining a consistent ranking of different social situation or “social
state”, starting from well-defined and explicit ethical premises.
From the social point of view, can we judge some situations to be “better “or worse than
others in well defined and meaningful ways? To answer question like this, our focus must shift
from the purely positive to the essentially normative. Normative judgment invariable motivates
and judge economic policy in matters ranging from taxation to the regulation of firms and
industries. When government intervenes to change the laissez - failure market outcome, different
agents will often be affected very differently. Typically, some will “win” while other will “lose”.
When the welfare of the individual agent is important in formulating social policy, there are
really two sorts of issues involved. Firstly, we have to ask the possible question: How will the
proposed policy affect the welfare of the individual? Secondly, we have to ask the much more
difficult normative question: How should we weigh the different effects on different individuals
together and arrive at a judgment of “society’s interest”? (Mas-Colell, Whinston and Green,
1995).
On the first issue, it is the case that the effect of a new government policy essentially
reduces to a change in prices that consumers face. Taxes and subsidies are used to perform this
kind of analysis in order to know how the policy measures affect a person’s welfare. This is the
essence of the partial equilibrium approach. The second issue is based on social and economic
justice. In the ethical system proposed by Rawls (1971), the welfare of society’s worse-off
member should guide society decision making. In order to conclude on the level of generality, a
social choice can be just about anything: the election of a particular candidate to a political
office, particular way of dividing a pie among a group of people, adoption of a market oriented
form of organizing society, or a particular way of distributing society’s resources among
members. A social choice problem arises whenever any group of individuals must make
collective choice from among a set of alternatives before them. The social choice challenge
involved is easy to state. But which of the possible alternative actions is best for society?
Although easy to state, the question is hard to answer. However trying to make any trade-off
among the alternatives, we need to ask this question, does intensity of preference matter? If we
think it does, other questions enter the picture. Can intensity of preference be known? Can
people tell us how strongly they feel about different alternatives? Can different people’s intense
desires be compared so that a balancing of gains and losses is achieved?
Blake (1948) has shown that majority voting satisfies the rest of Arrow conditions,
provided that the number of individuals is odd! Another approach has proceeded along different
lines and has yielded some very interesting results. Rather than argue with Arrow’s requirements
on the social relations, or his requirements on the information assumed to be converged by
individuals’ preferences. In Arrow’s (1951) framework, utility is assumed to be only ordinally
measurable and completely non comparable across individuals. If these restrictions are relaxed,
and utility is assumed to be measurable in certain ways and interpersonally comparable to certain
extents, interesting social welfare possibilities emerge, particularly when various “equity”
requirements are placed on the social relations. The basic references for this line of work include
Hammond (1976), d’Aspremont and Gevers (1977), Roberts (1980), Sen (1984) and Mas-Colell,
Whinston and Green (1995).
5.1 Social Choice and Economic Justice
In this section we shift our focus from ‘prediction’ to ‘assessment’ and ask a different
sort of questions, beyond the technical question of what must be assumed in the way of
measurability and comparability of utility to sensibly apply a given social welfare function, there
is the basic reality that the choice among such functions is effectively a choice between
alternative sets of ethical values. On this ground, matters of opinion really are involved. They
rightfully belong in the very first stage if any analysis aimed at assessing the social significance
of economic policies or institutions, when the choice of social welfare function is made (MasColell, Whinston and Green, 1995).
The literature in economics and philosophy - one and the same in the days before Adam
Smith – have combined again more recently to jointly consider the more character of the choice
that must be made. Guidance has been sought by appeal to axiomatic theories of justice that
accept the social welfare approach to social decision making. Two broad historical traditions on
these questions can be distinguished. One, the utilitarian tradition associated with Hume, Smith,
Bentham, and Mill. The other is the “contractarian” tradition, associated with Locke, Rousseau,
and Kant. More recently, the two traditions have been refined and articulated through the work
of Harsanyi (1953, 1955, and 1975) and Rawls (1971), respectively.
Both Harsanyi and Rawls accept the notion that a “just” criterion of social welfare must
be one that a rational person would choose if she were “fair–minded”. To help ensure that the
choice be fair-minded, each imagines an “original position,” behind what Rawls calls a “veil of
ignorance”, in which the individual contemplates this choice without knowing what his or her
personal situation and circumstance in society actually will be. Thus, each imagines the kind of
choice to be made as a choice under uncertainty over who you will end up having to be in the
society you prescribe. The two differ, however, in what they see as the appropriate decision rule
to guide the choice in the original position.
Harsanyi’s approach is remarkably straightforward. First, he accepts the Very Neumann
Morgenstern (1947) axiomatic description of rationality under conditions of uncertainty. Thus, a
person’s preferences can be represented by a VNM utility function over social states, u i(x),
which is unique up to positive affine transforms. By the principle of insufficient reason, he then
suggests that a rational person in the original position must assign an equal probability to the
prospect of being in any other person’s shoes within the society. If there are N people in society,
there is therefore a probability 1/N that i will end up in the circumstances of any other persons j.
Person i therefore must imagine those circumstances and imagine what her preferences, u j(x),
would be. Because a person might end up with any of N possible “identities”, a “rational”
evaluation of social state x then would be made according to its expected utility:
N
∑
𝑖=1
1
(N) ui (x)
……..(1)
In a social choice between x and y, the one with the higher expected utility in eq.(1) must
be preferred. But this is equivalent to saying that x is socially preferred to y if and only if
𝑁
𝑁
∑𝑖=1 ui (x) > ∑𝑖=1 ui (y)
……..(2)
a purely utilitarian criterion.
Rawls rejects Harsanyi’s utilitarian rule for several reasons. Among them, he objects to
the assignment of any probability to the prospect of being any particular individual because in
the original position, there can be no empirical basis for assigning such probabilities, whether
equal or not. Thus, the very notion of choice guided by expected utility is rejected by Rawls.
Instead, he views the choice problem in the original position as one under complete ignorance.
Assuming people are risk averse, he argues that in total ignorance, a rational person would order
social states according to how he or she would view them were they to end up as societies’
worst–off member. Thus, x will be preferred to y as
min[u1(x),…,uN(x)] > min[u1(y),…,uN(y)].
……………….(3)
a purely maximum criterion.
Ultimately, then, Rawls’ own argument for the maximin over the utilitarian rests on the
view that people are risk averse. But this cannot be a wholly persuasive argument, as Arrow
(1973) has pointed out. For one, the VNM utility functions in Harsanyi’s framework, nothing
precludes individuals from being risk averse in the original position. Moreover, one need not
reject the expected utility rule as a basis for choice to arrive at Rawls’ criterion.
To see this, take only utility function ui(x) over social states with certainty. These same
preferences, of course, can be represented equally well by the positive monotonic transform
v’(x) ≡ -u’(x)-a, where a>0. Now suppose v’(x) is i’s VNM utility function over uncertain
prospects. It is easy to convince yourself that the degree of risk aversion displayed by v(x) is
increasing in the parameter a. Now suppose, as Harsanyi does, (1) equal probabilities of having
any identity, (2) an ordering or social states according to their expected utility, and so (3) a
social welfare function.
N
𝑁
W =∑𝑖=1 v i (x) ≡ -∑𝑖=1 ui (x)-a
(4)
Because the ordering of states given by (4) has only ordinal significance, it will be
exactly the same under the positive monotonic transform of W given by
𝑁
W* = (-W)-1/a ≡(∑𝑖=1 ui (x)-a )-1/a
(5)
For p ≡ -a < 0. We’ve already noted that as p → -∞ (a→ ∞), this approaches the maxin
criterion (3) as a limiting case. Thus Rawls’ maximin criterion- far from being incompatible
with Harsanyi’s utilitarianism –instead can be seen as a very special case of it, namely, the one
that arises when individuals are infinitely risk averse.
On reflection, this makes a good deal of sense. Maximin decision rules are appealing in
strategic situations where the interests of some rational and fully informed opponent are
dramatically opposed to your own. In the kind of thought experiment required in the original
position, there is little obvious justification for adopting such a decision rule, unless, of course,
you are extremely (irrationally?) pessimistic. Once again, your choice of social welfare function
is a choice of distributional values and, therefore, a choice of ethical system. The choice is yours.
6.0 Conclusion and Suggestions for Further Research
Fairness is economic justice. Fairness promotes peace and progress, whereas injustice
breeds crisis and stagnation. Those who plan to oppress others preach chaos; they cannot at the
same time lament why those they have oppressed for decades agree to die rather than live as
slaves (Ogbimi, 2008). Human beings have feelings, they think and react to situation, so, they
cannot be treated like domestic animals. Whenever some human beings are treated like animals
who cannot think, a reaction must be expected because they would rise one day to claim their
rights as living beings. Therefore, economic justice and good governance is demanded for
Nigerians for fairness and goodness to prevail in the resources allocation.
From the forgoing, it is pertinent to say that the Nigeria’s governments over the years
have given priority, concessions and subsidies to the industrialists and private businessmen
belonging to just a sector of the economy and neglect the education and health sectors which the
majority of the poor masses do benefits. This anomaly is evidenced in the recent and ongoing
strike actions of Academic Staff Union of Universities over poor funding of education and their
counterpart in health sector over non-implementation of agreements.
Furthermore, an important aspect of the oil question in Nigeria concerns how to share the
economic surplus from oil in the context of intergovernmental fiscal relations. This paper has
shown that it is Pareto-optimal for the revenue allocation formula to provide incentives for the
three tiers of government to exert more tax effort to generate more revenues in their specific
areas of jurisdiction rather than being a free rider as is currently the case. Overhauling Nigeria’s
fractious revenue sharing arrangement to minimize the anomalies identified in the system and
more importantly, properly designing an intergovernmental transfer system that compensates
federating units for tax efforts are sine –qua- non for both long term political and economic
stability. The bearing of such an approach to fiscal transfer on fiscal prudence, sustainability and
political stability of the federation and social harmony should be evident enough of opportunity
fiscal behavior otherwise the ultimate economic and social outcomes may be against the long
term of the federation.
In conclusion, the application of economics even to an imperfect world such as Nigeria is
not only challenging but also stimulating analytically and policy wise. What this paper has done
is to kick start the application of modern economic theory to an important issue in fiscal
federalism in Nigeria. However, there are several areas of research in Sub-Saharan African that
would benefit immensely from the application of game theory and economics of information.
The pervasiveness of incomplete information and information asymmetry in the region suggests
that wide ranging and fruitful research can be carried out in all areas of economics from political
economy to public sector economics, development, industrial, financial, international,
environmental, monetary, microeconomics and macroeconomics.
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Biography
A short biography of the authors is as follows:
1. Abayomi S. Adenaike: A Lecturer in the Department of Economics, Olabisi Onabanjo
University, Ago-Iwoye. A holder of higher degree of Master of Science (M.Sc.
Economics) from the University of Ibadan, Ibadan, Nigeria and an Associate Chartered
Accountant (ACA) of the Institute of Chartered Accountants of Nigeria.
2. Maboyoje A. Sennuga: A Lecturer in the Department of Economics, Tai Solarin College
of Education, Omu-Ijebu. A holder of higher degree of Master of Science (M.Sc.
Economics) from the University of Ibadan, Ibadan, Nigeria.
3. Esther O. Adekoya: A Lecturer in the Department of Accounting, Banking and Finance,
Olabisi Onabanjo University, Ago-Iwoye. She holds a higher degree of Master of Science
(M.Sc. Business and Applied Economics) from the same Institution.