The American Journal of Islamic Social Sciences h l .  7, No. 1, 1990 219 

A Zero Efficiency Loss Monopolist: 
An Islamic Perspective 

Boualem Bendjilali and Farid B. Taher 

Abstract 

In an blamic environment, the behavior of a single seller is different 
from that of a pure monopolist. His ultimate objective is not to maximize 
profit but b please Allah. Profit is only one of his motives. Therefore, he 
is expected to be ready to sacrifice part of his profits for the social good 
if and when the social priorities so require. This brief study seeks first to 
formulate this problem in its deterministic setting and to derive the optimaUy 
necessary conditions. s;eCond,*it examines the case of a family of utilities 
of the Cobb-aO@as form. 

Introduction" 

The tern monopoly has commonly been used in m i c m o m i c  literatwe 
to describe she market condition of a slngle seller (the only supplier) who 
behaves in such a way as to maximize profits. As a profit maximizer, the 
fm produces less and charges higher prices than would be the case under 
perfect competition. Such behavior by the profit maximizing firm has several 
adverse impacts: first, it imposes a social-welfare loss (or efficiency loss) 
by producing a P3MC; second, it redistributes income from consumers to 
shareholders of the monopolist fm; third, it misallocates resources through 
the restrktkm of output. Inaddition, one may thinle of social costs of resources 
used by a monopofist firm for the pktection and u t e n a n c e  of its market 
power through nonprice competition practices, such a i  defensive advertising 
and non-necessary prdduct differentiation. 

In d i t y ,  the existence of such social costs calls for government 

Boualem Bendjilali and Farid B. %her are P m h r s  of Economics at King Saud University, 
College of Bplsiness and Ekmomics, Unayzah, Saudi Arabia. 
*We are to acknowledge conversations with Dr. N. N. Ibrahihn and Dr. Y. Zamel. 



220 The American Journal of Islamic Social Sciences b l .  7, No. 1, 1990 

interference through a set of alternative government pricing regulations. 
Unhrtunately, however, gavenunent interfexnce by itself destmys the market, 
and may generate an even greater efficiency loss to the society. 

In an Islamic economy, monopoly as a market condition may prevail; 
in other words, the firm might be the only seller in the market. Nevertheless, 
the behavior of a Muslim firm is expected to differ from that of a non-Muslim 
monopolist because of the differences in their objectives. As a single seller, 
a Muslim producer is not expected to behave as a profit maximher. The 
firm's decision-maker (manager, owner, shareholders) believes that restricting 
output in order to raise the price of a necessary good is a bad deed. According 
to the traditions of the Prophet (+S), it is reported that he said: 

"Whoever takes the advantage of a monopoly condition to raise 
the price to Muslims is a sinner," 

and that he also said: 

"monopoly of food in Makkah is atheism." 

In Islam, the utility function of an individual depends on the welfare of other 
members of the society. This distinctive characteristic was best described 
by the Prophet (SPAS), when he said: 

"Muslims in their mercy and compassion are among themselves 
like one body; if one organ is sick other organs would show 
symptoms of sickness, too." 

Muslims also believe that they should earn righteously, and that trade 
transactions should be arranged on a fair basis. For Allah says: 

"0 ye who believe, eat not up your property among yourselves 
in Vanities, but let the= be amongst you traffic and trade by mutual 
goodwill, nor kill (or destroy) yourselves for Allah has been to 
you most Merciful." (4:29.) 

Thus, a Muslim producer (single seller) is expected to be concerned 
about the welfare of the society, and therehre willing to partially sacrifice 
his or her own profits in order to avoid any loss in the welfare of the Muslim 
society in accordance with the pxachmg of the Messenger (&US), as he said: 

"whoever is not concerned about Muslims' affairs is not a Muslim." 



Bendjildi/lfiber Zero Efficiency Lass Monopolist b l .  7, No. 2, 1990 221 

This behavioral approach of sacrificing profits for the benefit of society 
when it is needed has been mentioned by Siddiqi (lo), who says: 

“In an Islamic society behaviour of all economic agents is expected 
to be socially oriented, ready to sacrifice profits for the social 
good, if and when the social priorities so require.” 

This paper is an attempt to formulate the objective function of a single 
seller in an Islamic economy. The paper will also assess the w e k e  implications 
of the expected outcomes, in comparison with those of the conventional 
monopolist case. 

The paper is organized as follows: Section 1 will briefly present the 
w e l k  loss associated with the p d i t  maxifniziDg monopolist, and will discuss 
the effectiveness of government intervention. Section 2, the main core of 
this study, provides the formulation of the suggested Islamic model and the 
derivation of the necessary optimal conditions with application to the class 
of Cobb-Douglas utility functions. Section 3 is devoted to the conclusion. 

1. Profit Maximizing Monopolist 

Social Costs of Monopoly: 

A pure monopolist in Figure (1) maximizes profit by producing (XJ 
(where MC = MR), and charging (PJ. However, if the monopolist in this 
market is replaced by a large number of perfectly competitive firms, assuming 
no changes in cost functions, the aggregate marginal cost curve 

would coincide with the monopolist’s (MCJ curve and would 
&me the market supply curve 2 m, =M% = s . Equilibrium would 
be attained at (XJ and (PJ, which’&resent the society’s efficient outcome 
because P, = MC at this point. 

2 MC, 



222 The American Journal of Islamic Social Sciences Vol. 7, No. 1, 1990 

Fig. 1 

The welfare cost of monopoly can be defined as the net gain in social 
welfare attainable by moving from (X,,,) to (XJ. Net gains may be measured 
by aggregating social benefits (area under the demand curve) and social costs 
(area under the marginal cost curve) between (X,,,) and (Xc), or the area 
AbC. 

Government Interference 

Governments inte&re in monopoly situations to protect the public interest 
by imposing regulated prices. Such prices are assumed to induce production 
by the monopolist who tries to compensate for the reduction in price by 
increasing sales. 

Unfortunately, however, regulating a monopoly may not be feasible at 
all times. Government officials frequently lack precise informaton concerning 
demand and cost functions of the monopolist f m .  Apart from the information 
problem, regulation can only be enforced at some real cost. While eliminating 
the inefficiency associated with monopoly, government intervention would 
lead to inefficiencies in resource allocations by drawing resources away from 
otherwise efficient uses. That is why government interference has always 
been rejprded as second best. 



BendjilaWTaher Zero Efficiency Loss Monopolist W. 7, No. 2, 1990 223 

In the Islamic economy, a single seller is expected to be concerned about 
the social welfare and therefore to be willing to partially sacrifice his profits 
in order to attain efficiency and minimize social welfare loss. Such behavior 
would lead to the best solution under monopoly conditions. This point is 
the focus of the following section. 

2. The Model 

A. Assumptions 

Let us assume a firm that produces a necessary good and assume that 
this h is the only one in the market. Assume also that the firm is represented 
by its manager whose utility index depends on both profit and society’s welfare. 
This dependence on profit and society’s welfare in an Islamic environment 
comes from the fact that a Muslim economic agent has two main obligations: 
one toward self and family, and the second toward the society as a whole. 
Indeed, the Qur’an stresses the unity and caring among the individuals of 
the society. Moreover, the sayings of the Prophet (SAAS) point out this 
dependence between the individual Muslim (e.g., the firm’s manager) and 
the society as a whole. If we let W and T denote the society’s welfare gain 
as shown in Section 1 and the fm’s profits respectively, the entrepreneur’s 
utility U can then be written as: 

(1) u = u ( T ,  w) 
However, one knows that the welfare gain W is a function of the fm’s output 
Q. Therefore, equation (1) can be written as: 

since W is a function of Q. 

Let Q, and Q, denote respectively the output levels corresponding to the 
maximum profit and the efficiency level of output, that is, to the quantity 
at which marginal cost equals price, as shown in Fig. 2. 



224 The American Journal of Islamic Social Sciences Vol. 7, No. 2, 1990 

Fig. 2 

In the case that the entrepreneur cares only about maximizing profit, he or 
she will produce at the level Q, with a corresponding society’s welfare loss 
equal to W,, where W, has been defined in the fmt section. However, in 
the case that the entrepreneur cares about the society’s welfare in addition 
to profit, the output produced will be between Q, and Q,. Indeed, the 
more the entrepreneur cares about the society’s welfare the more he or she 
moves from the point M toward the efficiency point E. That is, the quantity 
produced moves from Q ,  toward the level of output Q,. At the efficiency 
point E, the society’s welfare loss will be equal to zero. 

The following properties of the entrepreneur’s utility function U are 
aSSUmed. 

H.l The marginal utilities of U with respect to both arguments are positive. 
In other mds 3- > 0 and a u 
H.2 The second partial derivatives it2U and 
negative. an 2 

> 0. -- U an a Q  

a2u are positive. 
and B 8 w -  

a 2U 
a Q n  

H 3  The cmss partial derivatives 

Assumptions H.1 and H.2 together mean that for a fixed level of output (for 
a fmed level of profit), the entrepreneur‘s utility fuIlction increases with a 
decreasing rate as profit (as output Q) increases. Assumption H.3 indicates 



Zero Efficiency Loss Monopolist Vol. 7, No. 2, 1990 225 

that for a fixed level of profit (for fixed level of output), the entrepreneur's 
utility curve will rotate around the origins as a pivot as indicated in Fig. 
3, as output increases (as profit increases). 

In addition to the first three assumptions, we assume a given total cost 
function W(Q) and a given total revenue function TR(Q), Accordingly, we 
have a given profit function (Q). The general objective function of the 
entrepreneur is to maximize the utility function subject to the profit-output 
transformation curve. 

U 

Fig. 3 

Where Qo < Qi < Qz. 

The profit-output transformation curve can be written as: 

(3) = TR (Q) - WQ) 

where TR.Q = p(Q).Q 

B. Specific Formulation of the Decision Problem and Optimal Conditions 

The utility maximization as perceived by the entrepreneur is: 

(4) Max U = M a x  U (T, Q) subject to 

T = TR (Q) - TC (Q) 



226 The American Journal of Islamic Social Sciences Vol. 7, No. 2, 1990 

The current-value Lagrangian is equal to: 

( 5 )  L = U (a, Q) - [a - TR (Q) + ‘K (Q)1 

The necessary conditions for maximizing the entrepreneur utility function are: 

r O  

(8) - 3L = TR(Q) - TC(Q) - n 
3A 

- 0  

From equations (6) and (7) we get: 

The left-hand side of equation (9) is the marginal rate of substitution between 
the level of output Q and the level of profit that is the MRSQa. Namely, 
equation (9) can then be rewritten as: 

Equations (10) and (11) represent the necessary conditions for maximization. 
We notice from equation (10) that in the case of MRSaa = 0, this will 
imply that MC = MR and therefore we are in the case of a pure monopolist. 
On the other hand, in the case where Q = Q, we have MC = p and hence 
the necessary condition (10) becomes: 

That is: 

See Fig. 4 and Fig. 5 for more geometric clarifications. Therefore, in order 
for the firm to prcxiuce a level of output between Q- and Q, the necessary 
condition becomes: 



226 The American Journal of Islamic Social Sciences Vol. 7, No. 2, 1990 

The current-value Lagrangian is equal to: 

The necessary conditions for maximizing the entrepreneur utility W o n  are: 

= o  

= o  (8) - a L  = TR(Q) - TC(Q) - II 
3.A 

From equations (6) and (7) we get: 

uQ = M C  .. MR ; 
(9) -q A > o  

The left-hand side of equation (9) is the marginal rate of substitution between 
the level of output Q and the level of profit that is the MRSQT. Namely, 
equation (9) can then be rewritten as: 

Equations (10) and (11) represent the necessary conditions for maximbation. 
We notice from equation (10) that in the case of MRSQT = 0, this will 
imply that MC = MR and therefore we are in the case of a pure monopolist. 
On the other hand, in the case where Q = Q, we have MC = p and hence 
the necessary condition (10) becomes: 

That is: 

See Fig. 4 and Fig. 5 for more geometric clarifications. Therefore, in order 
for the firm to produce a level of output between and Qe, the necessary 
condition becomes: 



Bendjilali/'hher Zero Efficiency Loss Monopolist Vol. 7, No. 2, 1990 227 

Fig. 4 Fig. 5 

Next, we would like to check the second order for maximization. By 
differentiating the first order conditions with respect to X and Q we get: 

4 -  

0 

-1 

-1 Am-MC 

Urn U a Q  

MR-MC 0 UQQ-X (MC'-MR') 
Q4l 

where MC' and MR' denote the derivatives of the marginal cost and marginal 
revenue with respect to output Q. The second order conditiofls for maximization 
must satisfy A1 < 0 and A2 > where: 

0 

-1 

-1 

"nn 

= - 1  < 0 

v 

and after a simple computatiop we get: 
4. 



228 The American Journal of Islamic Social Sciences Vol. 7, No. 2, 1990 

I Unn (MR-MC) 
= % (MC'-MR')-Uw- 2(MR-MC) U1 Q-Um (MR-MC) 2 

2 

Using assumptions Hl-H3 and the properties of the marginal revenue and 
marginal cost, we deduce that 4 is positive and hence the second order 
conditions are satisfied. 

C. Application to the Cobb-Douglas Class of Utilities 

Let us next consider the class of utilities represented in the form of Cobb- 
Douglas. That is, 

insert equation here 

We notice first that MRS,, # 0 since Uq # 0, since 6 0 and ?r and q 
are strictly positive. Moreover, U is strictly quasi concave. This is easily 
shown by looking at the following minor determinants. 

U 
n 

a -  U 8 -  
q 

a P  U 
nQ 
- 8 , ( B - l )  U 

7 
Then the minors 

and 

We are interested in what follows in looking at the restrictions that must 
be imposed a and f l  in order to get the level of output and level of profit 



BendjW'hher Zen, Efficiency Loss Monopolist Wl. 7, No. 2, 1990 

H I  

229 

0 

-1 

MR-MC 

that maximize the utility function of the entrepreneur, other than the case 
of a pure monopolist. Given the total revenue and total cost function, let 
the profit function be given by: 

The problem becomes: 

max U = 7ru qo subject to 

T = pq - Tc (q) 
The current value Lagrangian becomes: 

(17) L = P 48 - X [T - pq + Tc (q)] 
A simple computation gives the necessary conditions: 

The second order conditions are derived from the following minors of the 
following Hessian. 

Let 

-1 

w If 
= B  u 

MR - MC 

$($ -1) .I u-x ( M C W R ~ )  
Q 



230 The American Journal of Islamic Social Sciences Vol. 7, No. 2, 1990 
$ 

We know from the first order conditions that we must have the following 
minors H, and H, as follows: 

H, < 0 and H, > 0 

we get 

"1 = 

0 

-1 

-1 

a (a -1)U 
2 

R 

= - 1  < o  

Moreover, using equation (18) we get by a simple computation 

we know that 

Hence 

(20) MC' - MR' 

a U  and 1 m- 
n 

Using this last information H, becomes 

The second order conditions impose that H, must be positive and hence, 
from equation (21) we must have (Ma) > 0, that is, 

(21) 0 < (I! < l/4 

Equation (21) gives the optimal conditions that permit production between 
Q- and Q,. In other words, the elasticity of the utility with respect to profit 
is restricted to be between 0 and 1/4 for the class of utilities of the Cobb- 
Douglas form, in order for the entrepreneur to maximize utility and produce 
an outp'ut between the quantity Q ,  corresponding to the level of output 
produced in the case of a pure monopolist and the efficient level of output. 



Bendjilali/'Tgher Zero Efficiency Loss Monopolist 

3. Conclusion 

Vol. 7, No. 2, 1990 231 

In an Islamic economy, monopoly (single seller) as a market condition 
may prevail, however, the behavior of a Muslim is different ' h m  that of 
a non-Muslim, simply because their objectives and motives are difkrent. 
A Muslim single seller is expected to sacrifice part of his profit (according 
to the degree of faith he possesses) for the benefit of the welfare of the poor 
and the needy of the society that is, for the benefit of the social welfare of 
the society. This paper has been an attempt toward achieving this goal. It 
formulated the objective function of a single seller in an Islamic economy. 
It also derived the necessary and sufficient optimality conditions for 
maximization. The last section examined the case of a family of utilities of 
the Cobb-Douglas form. This study has examined this problem in its 
deterministic setting as well as in its static form. Ibo potentially interesting 
issues that m do not address here am the possibility of examining this problem 
in its dynamic form and the other in its probabilistic approach. These two 
issues will be part of our future research. 

REFERENCES 

Ahmad, S.M., "Economics of Islam," Sh. Muhammad Ashraf, Lahore, 1964. 
Ansari, M . F., "The Qur'i7nic Foundations and Structure of Muslim Society," 

Vols. 1 and 2, Sh. Muhammad Ashraf, Lahore, 1965. 
Averch, Harvey, and b l a n d  L.' Johnson, "Behavior of the Firm Under 

Regulatory Constraint," American Ecoomic Review 52, 1962. 
Zubair, Hasan, "rheory of Profit: The Islamic Viewpoint: Jountal ofReseurch 

in Islamic Ecoomics, International Centre for Research in Islamic 
Economics, King Abdulaziz University, Jeddah, b l .  1, 1983. . 

Cohen, K.J. and Cyert, R.M., nteory of the Arm, Resource Allocation in 
a Market &owmy, Englewood Cliffs, N.J.: Prentice Hall, Inc., 1965. 

Cyert, R.M., Feigenbaum, E.A., and March, J.G., "Models in a Behavioural 
Theory of the Firm," &hawurn1 Science, Vol. 4, April, 1959. 

Cyert, R.M., and March J.G., A &hvioltd ?heory ofthe Arm, Englewood 
Cliffs, N.J.: h n t i c e  Hall, Inc., 1963. 

Lerner, Abba P., "The Concept of Monopoly and the Measurement of 
Monopoly Power," Review of & o m ' c  Studies, 1943. 

MacMup, E ,  "Theories of the Firm: Marginalist, Behavioral, Managerial," 
Americun Economic Review, Vol. 9, 1%7. 



232 The American Journal of Islamic Social Sciences Vol. 7, No. 2, 1990 

Metwally, M.M., A Behaviouml Model @ a n  Islamic Ann, International 
Centre for Research in Islamic Economics, Discussion Paper No. 5, King 
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Siddiqi, M.N., “Economics of Profit-Sharing,” in Fiscal Policy and Resource 
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Siddiqi, M.N., Ekonom*cs Enterprise in Islam, Lahore: Islamic Publications, 
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Simon, H.A., “New Developments in the Theory of the Firm,” American 
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7. & . ... 

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