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5
Allocative Efficiency of Profit
Maximization: An Islamic
Perspective
*
Ruzita Mohd. Amin and Selamah Abdullah Yusof
Abstract: Profit maximization forms the basic assumption in the theory of
the firm. The application of profit maximization has been criticized as
inconsistent with Islamic behaviour. However, this paper contends that the
principle is valid for an Islamic economic framework, to achieve the desired
outcomes of an Islamic economy. In particular, it ensures allocative
efficiency, that is, the production of the ‘right’ goods in the ‘right’ amount.
This can be achieved if, in the valuation of its opportunity costs, the firm
takes into account the nature of the good to be produced, in accordance with
Islamic ethical values. A simple theoretical framework is presented to
support this proposition. The outcomes in the conventional and Islamic
frameworks are compared under both perfectly and imperfectly competitive
markets.
I. Introduction
In the Islamic perspective, man assumes the role of vicegerent of
Allah, accountable to Him for all his deeds, decisions and the
intentions behind them, including the conduct of his economic
activities. All resources are treated as a trust and rational decisions are
made with regard to their allocation in accordance with the guidelines
prescribed by Islam. As stated in the Qur’¥n, ‘O you who believe!
* This is a revision of a paper presented at the Western Economic Association
International 76th annual conference, San Francisco, July 6, 2001, in a session
organized by Zubair Hasan, International Islamic University, Malaysia. The authors
would like to thank Mustafa Omar Muhammad, Mohamed Aslam Haneef, and
Zubair Hasan for their comments and suggestions.
RuZITA MOHD. AMIN AND SELAMAH ABDULLAH YUSOF both are Associate Professors at
the Department of Economics, Kulliyyah of Economics and Management Sciences,
International Islamic University Malaysia.
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Betray not the trust of Allah and the Messenger, nor misappropriate
knowingly things entrusted to you’ (8:27).
The objective of man, who is also an economic agent in an
Islamic society, is to achieve well-being (fal¥^) in this world and the
hereafter and the approval of Allah (mar\a Allah). Many verses in the
Qur’¥n affirm this; for instance ‘But seek, with that [wealth] which
Allah has bestowed on you, the home of the hereafter, nor forget your
portion in this world: but do good as Allah has been good to you, and
do not seek mischief in the land: for Allah loves not those who do
mischief’ (28:77).
In addition, the Prophet Muhammad (peace be upon him) said:
‘All people are the dependents of Allah, and the most beloved among
them are those who are most benevolent to His dependents including
those who put His resources to proper use’ (Ibn Kathir, 1980: 287).
In an Islamic framework, it is accepted that a firm’s behaviour
must be guided by Islamic values and ethics, for that is what
distinguishes it as Islamic. Siddiqi (1992: 140), enunciates that the
firm should be in full compliance with the Islamic idea of justice and
its entrepreneurial decisions should be motivated by service of the
society. Production is viewed as a means not only to achieve material
satisfaction but also a means to attain goals in the hereafter (Kahf,
1992; Mannan, 1992).
In attempts to formalize the behaviour of an Islamic firm in a
theoretical framework, some authors have proposed maximizing
utility (rather than profit, as is usually assumed in conventional
economics) as the distinctly Islamic objective (for example Metwally,
1992; Bendjilali and Taher, 1990; and Hallaq, 1995). Broadly, they
state utility as a function of profit and charity/social welfare. The
approach varies, however, from one work to another. Metwally
(1992) deducts the amount of zak¥h1 paid by the firm from the profit
function, while he treats expenditure on charity as part of the cost
function. As a result, he argues that the Islamic firm in this model will
produce a higher level of output and at a higher price. Bendjilali and
Taher (1990) provide a relatively more elaborate theoretical
framework by deriving the condition for an Islamic monopolist to
produce a level of output higher than that of a profit-maximizing
conventional monopolist. In Hallaq’s model (1995) charity is
included to represent the social welfare variable in the utility function.
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However, the outcome for the Islamic firm here is no different from
the conventional firm in terms of price and output. In addition, there
are several flaws in the formulation and analysis of the model.
Other authors, for example Hassan (1983; 1992), have assumed
the same objective for the firm as in conventional economics, that is
profit maximization. They use this assumption to analyse the rewards
to the factors of production and how it affects the cost of production
of an Islamic firm. The resulting outcome is higher output with lower
prices, as compared to the conventional firm, mainly due to abolition
of interest. On the other hand, Siddiqi (1992) has argued that profit
could be maximized within Islamic tenets, stressing the attainment of
a ‘fair’ or ‘satisfactory’ level of profit.
Some of the works just mentioned are conceptual in nature
(Kahf, 1992; Mannan, 1992; and Siddiqi, 1992), while others have
attempted to provide models that illustrate the Islamic firm’s
behaviour. Unfortunately, however, there are inconsistencies in
Metwally (1992), Bendjilali and Taher (1990), and Hallaq (1995).2 In
addition, these works have implicitly assumed that higher output
must mean higher welfare to the society. This is rather simplistic in
that it maintains the conventional assumption that more is always
preferrable to less regardless of the type of good produced. Within an
Islamic framework that is not necessarily true, since the effect on
social welfare will depend on the nature of the good produced. In
addition, the pattern of production and allocation of resources must
incorporate the following guidelines as mentioned in Siddiqi (1992).
Some of these are:
i)
Prohibited goods and services are not be produced.
ii) The production of so-called ‘refinement’ goods is small, and
accordingly, fewer resources are allocated to their production.
iii) More resources are allocated to the production of so-called
‘necessity’ goods.
This paper will present a simple theoretical model that shows
how an Islamic firm will produce these outcomes while still
maintaining profit maximization. In this respect, the analysis will
focus on firms within an Islamic framework and compare outcomes
with those within the conventional framework. In addition, it will
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also analyse the behaviour of Islamic and conventional firms that coexist in the same economy. From the results, it will be shown that
there is an increase in social welfare in terms of meeting the needs of
the society if firms behave according to the principles of Islamic Law.
The next section (II) articulates some of the concepts that underlie the
analysis in this paper. Section III deals with the construction of a
theoretical model to formalize the issues discussed, and the last
section (IV) presents some policy implications of the model and the
conclusion.
II. Some Underlying Concepts
One of the main goals of an Islamic economy is to fulfil the basic
needs of food, clothing, shelter, medical care and education for all
human beings (Siddiqi, 1992: 4). The allocation of resources to
achieve this purpose is guided by the SharϢah, which promotes
Ma|¥li^ al-¢Ib¥d (the welfare of human beings). Ma|la^ah is that
which is beneficial or promotes welfare (Wehr, 1961: 522). According
to al-Ghaz¥lÏ and later al-Sh¥tibÏ, social welfare may be promoted
through a three-level hierarchy of activities or goods, namely, in
order, ‘necessities’ (dar‰rÏy¥t), ‘conveniences’ (^¥jiy¥t), and
‘refinements’ (ta^sÏniy¥t) (Ibn ¢®sh‰r, 1998: 210).
‘Necessities’ comprise all activities and goods that are essential to
the preservation of the five foundations of good individual and
collective life, according to Islam, namely religion (al-dÏn), life (alnafs), mind (al-¢aql), offspring (al-nasl) and wealth (al-m¥l).
‘Conveniences’ are all activities and goods that are not vital to the
preservation of the five foundations, but are needed to relieve or
remove impediments and difficulties in life. ‘Refinements’ include
activities and goods that go beyond the limit of conveniences, they
serve to brighten, complement or adorn life (Zarqa, 1989: 34-6). A
Muslim is religiously motivated to acquire or produce such goods and
services as have ma|la^ah. Some goods and services will have more,
others less, ma|la^ah, depending on their position in the hierarchy
(Khan, 1992: 73-4). Therefore, necessities will have higher ma|la^ah,
followed by conveniences and finally by refinements, assuming that
the necessities are not yet fully met.
In the Islamic framework, it is assumed that economic agents are
guided by Islamic values. Thus, an Islamic producer, being
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accountable to Allah, treats the resources at his command as a trust
and the production of goods as a duty, and he will base his production
decisions on the concept of ma|la^ah. He can still be profit-driven
but, being governed by the SharÏ¢ah, the Islamic producer’s valuation
of economic costs will be modified.
Costs exist because resources are scarce and have alternative
uses. For the Islamic producer, the opportunity cost of producing a
good (included in the calculation of economic costs), being measured
as its value or worth in its best alternative use (McConnell and Brue,
1999), must take into account the nature of the good produced
relative to the other alternative goods. Hence, the value of the best
alternative good will depend on its position in the hierarchy of goods
as stated earlier. For instance, in the production of a necessity good
which has a high ma|la^ah (giving high benefit or value to the
society), where its best alternative is to produce a refinement good
which has a relatively lower ma|la^ah (giving lower benefit or value
to the society), the opportunity cost of producing the necessity good
will be lower. Conversely, in the production of a refinement good of
which the next best alternative is a necessity, the opportunity cost of
producing the refinement good will be higher.4
Clearly, the goods considered here are only goods that are ^al¥l
(permissible). In the case of ^ar¥m (prohibited) goods, the
opportunity cost will be prohibitively high, which means that they
will never be produced by an Islamic firm. Thus, the valuation of
opportunity cost for a particular good will be different under the
Islamic framework than the conventional one. It will either be lower
or higher, depending on the nature of the good to be produced.
III. The Theoretical Model
Let us consider a firm in a conventional framework that sets its price
and output at the profit-maximizing level. Profit is usually defined as
economic profit, which is the difference between a firm’s total revenue
and total costs, including opportunity cost.
Thus, the profit function (π) is defined as follows:
π=π(q)=R(q)−C(q)
(1)
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where R is the total revenue, C is the total economic cost, and
q is the quantity of output produced and sold.
Total revenue (R) is given as:
R(q)=P(q).(q)
(2)
where P is the price, and total economic cost (C) is:
C=E(q)+Ic(q)
(3)
where E(q) is the explicit cost, and Ic(q) is the implicit/opportunity
cost.
The standard first-order condition for profit maximization
applies where marginal revenue is equal to marginal cost.
The above would also hold for a firm in an Islamic framework.
However, the calculation of opportunity cost would need to take into
consideration the nature of the good produced by the firm, relative to
other alternative goods. Thus, for simplification purposes, the
implicit/opportunity cost under the two frameworks will be as
follows:
Conventional implicit/opportunity cost:
Ic=Ic(q), where Ic(0)=0
(4)
Islamic implicit/opportunity cost:
Is=Is(q)=α(q)+Ic(q),
(5)
where α is the Islamic valuation of opportunity cost of the good based
on ma|la^ah, and α (0)=0.
For the production of a necessity good when the best alternative is a
refinement good, for α’(q)<0 for q>0 (since the higher is the
production of the necessity good, the higher the fulfilment of the
society’s needs, the smaller will be the opportunity cost associated
with its production).5 On the other hand, for the production of a
refinement good when the best alternative is a necessity good, α’(q)>0
for q>0 (since the higher the production of the refinement good, the
lower the fulfilment of the society’s needs, the higher will be the
opportunity cost associated with its production).6
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Thus, in the production of the necessity good, Is(q)<Ic(q), for all
q>0 and therefore, the total cost, average cost and marginal cost for
the good will be lower in an Islamic framework than in the
conventional framework. This is illustrated in Figure 1, for the case of
a firm operating in an imperfect market.
Price
MCC
C
AC (Conventional Framework)
MCS
PC
ACS (Islamic Framework)
PS
MR
*
qC
*
qS
AR=D
Quantity
Figure 1: Production of Necessity Goods under the Islamic and
Conventional Frameworks: The Case of Imperfect Markets
Assuming that the firm faces the same demand function7, its
profit-maximizing output level will be higher in an Islamic framework
(q *s ) compared to that in the conventional framework (q c*), and the
price level (Ps) will be lower. This means that, under the Islamic
framework in this model, more necessity goods will be produced at a
lower price which gives higher benefits to the society without the firm
having to deviate from its profit-maximizing decision.
For the production of a refinement good when the best
alternative is a necessity good, the opposite will hold since Is(q)>Ic(q),
for all q. The result will be lower output (q*s <q c*) and higher price
(Ps>Pc), under an Islamic framework, as shown in Figure 2. Again,
this implies higher benefit to the society since fewer will be allocated
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to the production of such goods, for refinements bring benefit only to
a relatively small group of individuals in the society.
Price
MCS
ACS (Islamic Framework)
MCC
PS
PC
MR
qS*
qC*
AR=D
Quantity
Figure 2: Production of Refinement (Luxury) Goods under the Islamic and
Conventional Frameworks: The Case of Imperfect Markets
This outcome can also be shown mathematically as follows. The
firm’s objective is to maximize profit, where the profit functions are
given below for firms operating within the Islamic and conventional
frameworks, respectively, based on equations (1), (2) and (3).
Islamic framework:
π(q)=R(q)−[E(q)+Ic(q)+α(q)]
(6)
Conventional framework:
π(q)=R(q)−[E(q)+Ic(q)]
(7)
The first-order conditions for profit maximization are:
R’(q*s)=E’(q*s)+I’c(q*s)+α’(q*s)
(8)
R’(qc*)=E’(qc*)+I’c(qc*)
(9)
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where q*s and qc* are the optimal outputs of the firm under the Islamic
and conventional frameworks, respectively.
It is assumed that marginal revenue is a decreasing function of q.
For the case of production of necessity goods, α’(q*s)<0. Therefore, for
the first-order conditions to hold, q*s>qc*. Alternatively, for refinement
goods, α’(q*s)>0 , thus q*s<qc*.
Similar results can also be obtained for both necessity and
refinement goods under competitive markets, as shown in Figures 3
and 4. As can be seen, for necessity goods, the total output produced
by the industry in the Islamic framework (Qs) is higher compared to
the conventional outcome (Qc), and price (Ps) is lower in the longrun. This is because more firms will be motivated to enter the industry
and produce the necessity goods due to its lower economic cost, and
as a result of this, the market supply of these goods in an Islamic
framework will be larger, hence pushing the market price lower than
in the conventional framework. Note that the individual firm’s output
may be the same as that of the conventional firm, as shown in
Figure 3.8 On the other hand, output for refinement goods will be
lower (Qs<Qc) and price higher (Ps>Pc) under the Islamic framework
compared to the conventional, due to lower market supply.9
Firm
Price
Market
MCC
SC
Price
ACC
MCS S
AC
SS
PC
MR C=AR C=DC
PC
PS
MR S=AR S=D S
PS
D
q*
Quantity
QC
QS
Quantity
Figure 3: Production of Necessity Goods under Islamic and Conventional
Frameworks: The Case of Competitive Markets
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Firm
Price
Market
MCS
SS
Price
SC
S
AC
MCC ACC
PS
MRS=ARS=DS
PS
PC
MRC=ARC=DC
PC
D
q*
Quantity
QS QC
Quantity
Figure 4: Production of Luxury Goods under Islamic and Conventional
Frameworks:The Case of Competitive Markets
Let us now consider a framework in which both Islamic and
conventional firms co-exist in the same economy, but one where the
Islamic firms are assumed to comply with Islamic values. For necessity
goods, if all firms face a market price of P as shown in Figure 5, the
Islamic firm will be able to obtain a positive economic profit (area
PABC), while the conventional firm will only obtain a normal profit.
In the long-run, the positive profits enjoyed by the Islamic firms will
attract other firms (most likely the Islamic ones) to enter the industry,
thus driving down the market price. In the final outcome, we will find
that more Islamic firms will produce necessity goods. Conversely, for
refinement goods, the opposite holds, that is, more conventional firms
will end up producing these goods, since the Islamic firms will not
find it profitable to enter the market (see Figure 6).
The outcome in Figures 5 and 6 can also be shown mathematically as follows. Since for necessities, the total cost, average cost and
marginal cost faced by the Islamic firm will be lower than that faced
by the conventional firm, at each level of positive output therefore
minACs<minACc, ACs and ACc are the average costs of the Islamic
and conventional firms, respectively. If P is the price level that would
give the conventional firm normal profit, then, minACc=P. Since the
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Price
MC C
ACC
MCS
AC S
A
P
MR=AR=D
Profit
C
B
qC*
Quantity
q*S
Figure 5: Production of Necessity Goods of Islamic and Conventional
Firms within the Same Competitive Markets
Price
MCS
AC S
MCC
D
AC
C
E
Loss
P
F
q*S
MR=AR=D
q*C
Quantity
Figure 6: Production of Luxury Goods of Islamic and Conventional Firms
within the Same Competitive Markets
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two firms coexist in the economy, and if P is the prevailing price in
the market in which the Islamic firm is also a price-taker, then,
minACs<P, and the Islamic firm will obtain positive economic profit.
On the other hand, for refinement goods, the total cost, average
cost and marginal cost faced by the Islamic firm will be higher than
that faced by the conventional firm, at each level of positive output
therefore, minACs>minACc. Similarly, if both firms coexist in the
same economy and if P is the prevailing price in the market in which
the Islamic firm is also a price-taker, then, minACs>P, and the Islamic
firm will obtain a negative economic profit.
From the above analyses, it can be seen that the profitmaximizing behaviour of firms under the Islamic framework ensures
a better allocation of resources with respect to the hierarchy of needs
of the society. Necessities will be produced at a much higher level
compared to refinement goods, and this will give greater benefit to the
society as a whole.
IV. Conclusion and Policy Implications
This paper demonstrates that profit maximization can still be applied
in an Islamic framework to achieve the desired outcomes of an Islamic
economy, provided that Islamic values are explicitly incorporated
particularly in the measurement of the cost of production of an
Islamic firm. In relation to this, taking ethical values into account in
the valuation of opportunity costs as part of the total cost of
production will help ensure the production of the ‘right’ goods and in
the ‘right’ amount, thus promoting allocative efficiency in the market.
This paper presents a simple theoretical model to support this
proposition for both perfect and imperfect markets by comparing the
outcomes under the Islamic and conventional frameworks. In
addition, we have also examined the outcomes for the case of both
conventional and Islamic firms co-existing in the same economy.
The analysis has focused essentially on the production side of
goods and services, assuming that the demand for such goods and
services in an Islamic framework does not differ from the
conventional framework. However, if consumers also behave
according to the Islamic values, we expect that the production of
necessity goods will rise in response to higher demand for these goods,
and the production of refinement goods will be lower under the
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condition that the economy has yet to fulfil the basic needs of the
society.
The economic environment and the values that economic agents
hold at present may not completely conform to the ideal Islamic
values. Hence, there is a need for the authorities to undertake certain
measures to achieve the outcomes that the model has presented. As
mentioned earlier in the paper, one of the goals of an Islamic economy
is to fulfil the basic needs of the society. If the market is left on its
own, it may not be able to achieve this. Thus, the government should
undertake the responsibility of ensuring that this goal is attained,
since in an Islamic economic system the government should coexist
with the market on a permanent and stable basis (Kahf, 1978: 48).
Among others, the government can choose to impose taxes on
the production of refinement goods or provide subsidies for the
production of necessities so that the social costs or benefits associated
with the type of good produced can be internalized within the cost
structure of the firm. In addition, other incentives to produce necessity
goods may take the form of providing physical infrastructure, training
and consulting services to producers. Furthermore, research and
development activities should put more emphasis on necessity goods.
With respect to the production of refinement goods, another
disincentive can be in the form of restriction of permits to produce
such goods. In the long-run, such measures combined with a sustained
effort to educate all economic agents and make them aware of the
proper Islamic values, and of the importance of placing a high priority
on fulfilling the needs of the society.
NOTES
1.
2.
Zak¥h is an obligatory financial levy on all surplus wealth and agricultural
income of Muslims. It is charged at varying rates and the objective is to provide
financial support to specified categories of people such as the poor and the needy
(Khan, 1994).
Hallaq (1995) argues that spending on charity increases average cost for the
Muslim firm, but the marginal cost remains the same as for the non-Muslim
firm. This argument is erroneous since spending on charity is a function of
profit, and therefore it must also depend on output. Hence, both the average and
marginal costs should be different for the Muslim firm. In Bendjilali and Taher
(1990), profit and output are treated as two independent variables, where one
can change while keeping the other constant. This is clearly incorrect since profit
is a function of output, and thus profit will change as output changes. In
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3.
4.
5.
6.
7.
8.
9.
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addition, they derive a general condition for a Muslim monopolist to produce
more than the profit-maximizing level, which they then apply to the CobbDouglas class of utility functions. However, the condition derived is not the
condition that permits production higher than the profit-maximizing level,
rather the parametric restriction is for the second order condition of utility
maximization. Metwally (1992) assumes that changes in expenditure on charity
δP
(G) will increase demand at given prices (P). However, this is stated as δG
> 0. In
addition, he defines profit as the difference between the firm’s revenue and its
production and charity costs. However, he subsequently treats both production
costs and charity costs as separate entities in the model. Furthermore, we found
errors in the derivation of the first order condition for utility maximization,
hence the conclusion he derives may not be valid.
It is recognized that the distinction between necessity, convenience and
refinement good is somewhat nebulous with respect to individuals and epoch.
However, for the purpose of analysis, this paper maintains the definitions given,
for a particular point in time.
As mentioned earlier, it is implicitly assumed here that the economy has yet to
fulfill the needs of the society. Therefore, higher amounts of necessity goods
produced is assumed to give higher benefit to the society as compared to
refinement goods.
In the analysis, the authors consider the best alternative to the production of a
necessity good is the production of a refinement good. The two contrasting
goods are deliberately chosen to provide a clear distinction between the two
kinds of goods so that the difference in the ma|la^ah can be easily distinguished.
However, it is not necessary to have such a restriction. The analysis and results
will still hold as long as the next best alternative good has a position lower in
the hierarchy of goods than the good in production.
A similar argument, as in preceding note (n. 5) applies to the production of a
refinement good. In this case, the analysis and results will still hold as long as
the next best alternative good has a position which is higher in the level of
hierarchy of goods than the good in production.
The authors disagree with Mannan (1992) who refuted the ‘given demand
hypothesis’. This is because the market demand curve is assumed to reflect
effective demand upon which the firm should base its decision.
This is one possible outcome, where a firm’s profit-maximizing output level is
the same under both the Islamic and conventional frameworks. It is also possible
to obtain the profit-maximizing output, for an individual firm in the Islamic
framework, at either a lower or higher level than the conventional outcome,
depending on where the marginal cost (MCs) intersects the price level (Ps). See
the Appendix for the mathematical demonstration of this. However, in all of
these cases, the final result will still hold, i.e., total output produced by the
industry in the Islamic framework will still be higher and the price level lower
than in the conventional framework in the long-run.
Again, the profit-maximizing output level of the firm in the Islamic framework
may be lower, higher or the same, as is the case for necessities. Similarly, the
final result will still hold, i.e., total output produced by the industry in the
Islamic framework will be lower and the price level higher than in the
conventional framework in the long-run. Again, see the Appendix for the
mathematical demonstration.
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19
APPENDIX
Conventional firm:
For the conventional firm, the cost function is given by:
C=E(q)+Ic(q),
where E(q) = explicit cost
Ic(q)= conventional implicit cost
The average cost of the firm will be: AC =
E( q ) I C ( q )
+
q
q
The minimum point of the AC curve is obtained at:
A C′ =
qE ′( q ) − E( q ) qI C′ ( q ) − I C ( q )
=0
+
q2
q2
Let the output level corresponding to this minimum AC be qc*.
Islamic firm:
For the Islamic firm, the cost function is given by:
C S = E( q ) + I C ( q ) + α ( q ) ,
where E(q) = explicit cost
Ic(q)= conventional implicit cost
α(q)= the Islamic valuation of opportunity cost of the good based on
ma|la^ah.
α(0)=(0),
α´(0)<0 for q>0, for the production of a necessity good in which the best
alternative is a refinement (luxury) good, and
α´(0)>0 for q>0, for the production of a luxury good in which the best
alternative is a necessity good.
The average cost of the firm will be: AC S = AC +
α ( q)
q
The minimum point of the AC curve is obtained at:
qα ' ( q) − α (q )
2
q
α ' ( q) α (q )
= AC ' ( q) +
− 2 =0
q
q
AC S' = AC ' (q ) +
Let the output level corresponding to this minimum AC be qs*.
For necessity goods, α(q)<0, α´(q)<0, for q>0.
Therefore:
If qα´(q)=α(q), then qs*=qc*.
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If |qα´(q)|>|α(q)|, then qs*>qc*.
If , |qα´(q)|<|α(q)|, then qs*<qc*.
For refinement (luxury) goods, α(q)>0, α’(q)>0, for q>0.
Therefore:
If qα´(q)=α(q), then qs*=qc*.
If |qα´(q)|>|α(q)|, then qs*>qc*.
If |qα´(q)|<|α(q)|, then qs*<qc*.
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