Enriching the Theory of Factor Pricing and Income Distribution in Islamic Perspective

The paper aims to elaborate the theory of factor pricing and income distribution in Islamic perspective. We place Sadeq’s thought as the benchmark and expand it. Using calculus differential, we construct factor pricing and income distribution under mudharabah scheme, which can describe the behavior of producer (mudhaarib) in making decision on business operation appropriately. The paper can prove mathematically that when Islamic principles are internalized, income distribution becomes more equal. This is expressed in parameters s, 1-s, and 1/1-s, as a share of profit goes to capital owner (shahibulmaal), entrepreneur (mudhaarib) and worker, respectively. The paper also proposes that wage level will be determined not only by perception or the mind set of capital owners and workers on the value of their assets, but also the standing moral of entrepreneurs and capital owners.


INTRODUCTION
Previously, manyeconomists wrote about the income distribution problem from various approaches. Kaldor (1995) viewed Ricardo's Principles of the law, which regulates distributive share,as the 'Principal Problem in Political Economy'. After this finding, Kaldor posed various theories of distributive share and attempted to classify it into four main strands of thought i.e:(1) Ricardian or Classical Theory, (2) Marxian, (3) Neo-Classical orMarginalist Theory, and (4) Keynesian. Kaldor (1955) reviewed the main strands of those thoughts. Kaldor saw that Ricardo's theory was based on two separate principles, namely marginal principle and surplus principle. The marginal principle serves to explain the share of rent and the 'surplus principle'the division of the residue between wages and profits.
Meanwhile, Stiglitz (1969) attempted to develop a theory of distribution of wealth and income among individuals. Stiglitzexamined the implication for distribution of alternative assumption in terms of the form of the consumption function, the heterogenity of labor skills, the inheritance policies, and the response of the reproduction rate to diferent levels of income. Ahmad (1984) investigated the distribution of income in an Islamic economy. The institutions of zakah, sadaqah, and the spending for the sake of God (infaq), all are redistributive in nature and are aimed at ameliorating the misery of the poor and needy. He developed a model in which Keynesian tools of analysis are employed and The KaldorPasinetti frame has been adopted. The result indicated that an Islamic economy possesses a strong redistributive instrument in the scheme of distribution.
In addition to Ahmad, Sadeq (1989) also proposed a tentative theory of income distribution in Islamic perspective. He pointed out that there are two general normative principles of factor pricing in Islam, i.e justice and scarcity. Then, he used the theory of marginal product as a theoritical framework to show how Islamic principles work and to determine wage level. He also illustrated how profit sharing under mudharabah dan musyarakah scheme works really well. Rapanos (2005)also examined the effects of a change in the minimum wage on income distribution and employment in the original Harris-Todaro model. His finding indicated that the increase in the urban minimum wage will have negative impact such as increase urban unemployment, decrease employment in the urban sector (manufacturing) and also the employment in the agricultural sector. Therefore the return to capital will fall, the return to land will fall, and the rural wage will rise. He stresses that the increase in the minimum wage will benefit labor and harm landowners and capitalists.
On the other hand, Meisami (2011) did empirical study and focused on human quality aspect. He examined the impact of the various components of human capital on income inequality and poverty in Islamic countries. Based on the result of this research, he proposed some policy recommendations, such as implementing programs designed to fight illiteracy, providing sufficient care for pregnant women, continuing to reduce the prevalence of child malnutrition, and reducing infant mortality from continuing to happen. In addition, economic growth and development in itself will lead to less poverty and may bring about an equal distribution of income in an Islamic economy. Furthermore, primary educational opportunities bring about a lessening of income inequality in Islamic countries.
The next researcher is Ekinci (2011). He achieved an integration of monetary and value theories along the Ricardian lines, extended to a monetary production economy as understood by Keynes. He introduced the circuit of fixed capital; this circuit is closed when the present value of prospective returns from employing it is equal to its supply price. In a steadygrowth, given the equilibrium between nominal wages and interest rates, the equation that closes the circuit of fixed capital can be solved for prices, implying a definitive income distribution.
According to the aforementioned literature, we can see that only Sadeq who explore of income distribution theory from factor pricing aspect and Islamic perspective. After him, we get difficulty to find new thinking about it, whereas there is big opportunity to elaborate Sadeq's tentative theory of factor pricing and income distribution. Finally we placedSadeq's thought as a benchmark to develop factor pricing and income distribution theory in Islamic perspective, with the following arguments: first, Shadeq constructed a tentative theory focused on factor pricing as a source of income distribution problem. Sadeq utilized the theory of value marginal product of input in conventional economic perspective as the theoritical framework for Islamic principles' internalization. Second, factor pricing concept as a study of functional income distribution is more relevant than personal income distribution to the context of Islamization, especially the market mechanism aspect. Third, Sadeq found a new concept, but it has not been proven mathematically. Fourth, even though long publication ago, Sadeq's paper is not mean outdated. Precisely, this indicate that factor pricing and income distribution is classic problem. Therefore, we are interested to continue Sadeq's thought and expand it.

METHODS
This research is basic/pure research which use Alqur'an and Hadits as basis data. Therefore focus of research methodology is content analysis on Alqur'an and Hadits. Content analysis is a way to elaborate the purpose of substance from a document, manuscript, law, etc(Babbie, 1980). Then will be used three methods simultaneously i.einductive, deductive and comparative method to find concept and theory of factor pricing both conventional and Islamic perspectives. By inductive method, we start from the facts, then looking for and understanding concept of factor pricing both conventional and Islamic perspectives. While by deductive method, we analyze factor pricing in both conventional and Islamic perspectives to find differential between them. Comparative method is used to compare between factor pricing in both conventional and Islamic perspectives. Inductive and deductive method is facilitated by focus group discussion and depth interview with several experts. N o v e m b e r 1 9 , 2 0 1 4 We also use calculus differential to construct factor pricing and income distribution under mudharabah scheme. This mathematic equation can describe the behavior of producer (mudhaarib) in making decisionon business operation appropriately and finally find proposition of factor pricing and income distribution. Sadeq (1989) started his paper with the definition of factors of production. He found that shariah provides that labor can be hired on a fixed wage and reusable physical assets on a fixed rent. He used traditional theory of factor pricing i.e marginal productivity theory as theoritical framework. According to this theory, a factor will be paid a price equal to its marginal product.

REVIEW OF FACTOR PRICING AND INCOME DISTRIBUTION IN ISLAMIC PERSPECTIVE: SADEQ'S THOUGHT
For labor case, he stressed that the general normative principles of factor pricing i.e justice and scarcity must be primary in pricing the human factor of production due to there is a humanity element. And market forces will be secondary in determining the price of labor. The principles ofjustice included brotherly employer-employee relationship in the overall behavior, the work load and working condition should be humanly acceptable, employers must guarantee basic needs (flood, clothing, medicare etc.) of their brother employees. Sadeq (1989) believed that since wage depends on both subjective (humanity) and objective (contribution and market forces ) factors, it will be more appropriate to define first a possible range of wages rather than a fixed one. The upper and lower limits of wage rates are VAP L and VMP L , which give the wage range VMP L ≤ W ≤ VAP L . The exact wage within this range will depend on the application of humanity principle, whose required roles may vary in time and space, and on the enterpreneur's average desired rate of profit.
This condition is illustrated in Figure 1 which are adopted from Sadeq and adapted by authors.

Figure 1. Determination of Wage in an Islamic Economy. Adopted from Sadeq(1989) and adapted by authors.
As we see, the minimum wage in the wage range will be W1 = VMPL which is given by the intersection of VMPL and SL, and the maximum wage W2 = VAPL is given by the intersection of VAPL and SL. If the effective demand curve combining both subjective and objective factors is DE, the equilibrium wage is OW3 which is within the wage range determined earlier. Here equilibrium wage is higher than the VMPL but lower than the VAPL, OW1 < OW3< OW2.
Different from the pricing of labor, Sadeq (1989) stated that the prices of physical assets may well be determined by market forces because the absence of the humanity principle. Sadeq (1989) pointed out that according to the Islamic shariah, a fixed price for the service of the physical assets is allowed, and it is called rent. The entrepreneur receives the transacted service, which causes depreciation of the asset, and hence its price must be paid. This analogy cannot be applied for financial assets because money does not depreciate because of its use.
For the income of capital ownership and entrepreneurship, Islam has a specific concept. In traditional economics, 'capital' generally refers to the mass of long-lived and reproducable implements of poduction such as roads, bridges, factories, machines, and houses. These are also called 'physical capital' (Maddala, 1989). The diverse types of capital equipment could convert into monetary and the rental price of capital is interest rate. Meanwhile, profit is payment for skill of entrepreneurship (Sukirno, 2002). Entrepreneurs devote their time to bring potential investors together, choosing plant location, hiring labor or executives, and financing the operation of the firm. In Islamic economics, on the other hand, Sadeq S L N o v e m b e r 1 9 , 2 0 1 4 (1989) stated that these two factors of production share in profit. It means that the price of capital and entrepreneurship are simultaneously determined. The sizes of these prices are post-determined, but the shares are pre-determined.
Islam propose syirkah as a form of partnerships to share in profit. Among the various types of syirkah, there are two major forms i.emudharabah and musyarakah. As Sadeq (1989) wrote that in the case of mudharabah, the entrepreneur does the business with the other's capital, whereas the partners share in capital in the case of musyarakah. Sadeq (1989) pointed out that in each of the forms, the general principles of factor pricing and income distribution will be applied in the ex-ante determination of the share of capital and entrepreneurship. In the case of mudharabah, these shares will be determined by the interaction of productivity-adjusted for and scarcity-adjusted supply of capital, Dk and Sk respectively, as is illustrated in Figure 2.
In Figure 2, we can see that the Dk and Sk intersect at T, which simultaneously determinesthe profit share of capital and entrepreneurship. It determines s % of the profit share of capital, so that the rest (1-s) % of the profit goes to entrepreneurship. Sadeq (1989) remind that this analysis will be applicable when any positive profit is made. If no profit is earned or if any losses are incurred, the risk of zero profit or losses will be borne by capital, and the entrepreneurship's service will go unrewarded.

RESULTS: PREPOSITION OF FACTOR PRICING AND INCOME DISTRIBUTION UNDER MUDHARABAH SCHEME
In this step, we try to develop a model in a mathematical term to show how factor pricing and income distribution in business practice, i.e mudharabah. We have two reasons: First, according to the above explanation, we see Sadeq discussing wage determination and business practice (mudharabah) partially. Meanwhile, wage determination process is conducted under business practice, which is embedded in producers' behavior. Second, Hasan (1986) in (Muqorobin, 2012) who providedan elaboration using a value-added model for production process at a macroeconomic level which ownership of a fraction of capital accumulated from retained earning of private sectors can be allocated through sharing in profit. Hasan used mathematical form to express this problem as:

VA = f(π,Wmin)
whereVA represents the net value-added, which is shared between profit (π) and minimum wage (Wmin). Profit, on the other hand, is shared between capital and labor, respectively, in the ratios of x and (1-x), which rewrites equation (1) as: From this equation, it is clear that xπ belongs to the capital owners, while the rest goes to the workers. Hasan make sure that the minimum wage, Wmin , is a fraction of wage paid to the workers regularly. In addition, policy on the issuance of (1x) π , which is a fraction of profit, belongs to the workers.

3)
Total revenue is the value of total product produced. It is assumed that all products can be sold. Equation (4)

. (3')
According to equation (3'), the cost of production involves material and workers' expenses. Meanwhile, the return for mudhaarib as a manager is represented in profit sharing. Equation (5) presents the identity of its production cost.

. (5)
Where w is wage level, and r is price of unit of material. The first term in the right part of equation (5) indicates expense for worker, and the second term indicates the expense for production material. Based on Islamic teaching, wage level is predetermined based on mutual agreement betweenmudhaarib and worker. Further, benefit-based and consideration of Islamic principles, such as justice, humanity and fulfillment basic need of worker. It seems very subjective at first glance, but in the next explanation we will know the size of the wage.
Implicitly, the structure of these costs is different from Sadeq's (1989), which is a modification of the classical approach. As a consequence of mudharabah scheme, profit sharing becomes the weighting in wage determination. If there is no profit sharing concerned, wage level is less than it should be. As an example, the agreement for wage is one million Indonesian Rupiahs, and the fraction of profit for mudhaarib (1s) is equal to 0.5, with the weighting in mudharabah scheme, the actual wage becomes 2 million Indonesian rupiahs (1/0.5*1 million = 2*1 million). Profit sharing gives additional income for worker. In this context, it can be argued that w is the wage level for the fullfilment of basic needs, and 1/(1s) is the parameter representing the subjective aspect for justice and humanity.
According to the discussion of revenue function and identity of cost, equation (3) can be expanded and presented as equation (3'). It is known that the fraction profit for mudhaarib is (1s) from equation (3), which refers to equation ( Then, economic mathematic method can be used to elaborate information behind the economic problem of mudhaarib. The first order from equation (6) to decision variables of mudharib involving L1, A, M1, dan is expressed in equation (7). The first order indicates mudhaarib's considerations for input determination, which includes the consideration of opportunity cost of worker, , and his/herself, .  Sadeq (1989), in this term is weighted by fraction of profit for mudhaarib, (1s). Intuitively, the size of its VMPL is under the VMPL in Sadeq's version (1989). But it is not so, due to the existence of the right hand equation presenting the income of worker as reversely weighted from fraction of profit for mudhaarib. Hence, in this stage parameter will be neutral at  In this figure is depicted the income of shahibulmaal, mudhaarib, and worker curves. Optimal worker lies on mudhaarib, referring to VAPL equal to the income of worker. Hence, the number of workers employed is OL1. The level of profit sharing will directly influence wage level in compliance with musyatarak contract. If shahibulmaal increases his/her share, s, the income of mudharib (1s) will decrease, but the income of worker will rise, with the assumption that shahibulmaal does not increase his/her valuation to capital,  0 .In fact, the size of VMPL is equal to value average product of labor, VAPL=  ............................................. (7.a") Equation (7.a") features a proposition that wage level that is under mudharabah' scheme wage is determined by the price of output (P), the value of capital (), and the time of worker (). Intuitively, equation (7.a") has several arguments as follows: (1) The higher the value of shahibulmaaltocapital, the lower the wage level,  w.
(2) An increasein the output price will raise wages, Pw. This condition gives a chance to addtime to work in this firm and decrease time to another work, L2 (compensation of income). (3) Workers have to valuate rightly the value of time. If the value is too much, it will decrease wages. (4) Wage determination can not be separated from subjective factors. Therefore, Sadeq (1989) argued that wage level rests on the standing moral of mudhaarib and shahibul maal, too. This argument is reflected in  and  symbols.
The proposition for raw material price can be elaborated from equation (7.b). The phenomenon behind this equation is identical with conventional economics that uses raw material when the price of unit of raw material is equal to value marginal product of asset (VMPA). However, in this equation it is adapted with profit share. Therefore, the unit price of raw material is not only determined by output price and contribution of material to output ,but also by profit share.

CONCLUSION
We have developed a theory of factor pricing and income distribution as an expansion of Sadeq's tentative theory in Islamic perspective. We found that income distribution becomes more equal when Islamic principles are internalized. This is expressed in parameters s, 1-s, and 1/1-s, as a share of profit goes to capital owner (shahibulmaal), entrepreneur (mudhaarib) and worker, respectively. From some of the propositions given, we concluded that wage level will be determined not only by perception or the mind set of capital owners and workers on the value of their assets, but also the standing moral of entrepreneurs and capital owners. To prove this proposition, we suggest that an empirical study be done in the future. Therefore, this finding will be examined and become a robust theory.