Is Walras s Theory So Different From Marshall s?

Transcription

1 Is Walras s Theory So Different Fro Marshall s? Ezra Davar (Independent Researcher) Anon VeTaar 4/1, Netanya 40, Israel E-ail: ezra.davar@gail.co Received: July 17, 014 Accepted: August 5, 014 Published: August 8, 014 doi:10.596/jsss.vi1.634 URL: Abstract This paper shows that Marshall s theory is generally equivalent to Walras s one. It shows that Walras used two types of deand functions: (1) the original (ordinary) deand curve (function); and () the derived (general) deand function. Marshall also used both types of deand curves (function); however he did so in a very siplified and vague anner. Walras used a coon ethod of equilibriu establishent and re-establishent of equilibriu for all four types of econoies. First, he discussed the proble of equilibriu establishent using initial basic data. Second, Walras starts the adjustent process by using a odel to describe the equilibriu state. He then describes the process of equilibriu establishent fro a position of disequilibriu, by the use of his faous algorith tâtonneent. Finally, Walras discussed the proble of the variation of prices, or the proble of the re-establishent of equilibriu, as a result of changes in the initial basic data for any individual or any group of individuals. Marshall also used the sae ethod, but in an incoplete for. Despite that, Marshall did not forulate the odel for individual econoies, he discussed the conditions of its optiality; and discussed the process of equilibriu establishent. Furtherore, despite the fact that Marshall described verbally the coplete odel for the whole (acro) econoy in a siilar way to Walras, he did not forulate atheatically that odel. Marshall also discussed the proble of the re-establishent of equilibriu, as a result of changes in the initial basic data. Therefore, Friedan s stateent that they are alternative theories is istaken. Keywords: Walras, Marshall, Friedan, Original and Derived Deand Curves (Functions) 64

2 1. Introduction Over 60 years ago, in his seinal paper The Marshallian Deand Curve, Friedan stated that there are two theories of deand: Marshall s and Walras s. Friedan also claied that Marshall s interpretation of the deand curve is, in his view, wrong. He concluded his paper with the words: The current interpretation of the deand curve is Walrasian; and so is current econoic theory in general (Friedan, 1953, p. 93). Therefore, according to Friedan these two types of deand curves are different and utually exclusive (Hirsch & de Marchi, 1990, p. 3; and pp ). Furtherore, Friedan stated that the Walras s deand function (curve) is the one which is generally used in odern econoic theory. Since that period in econoic literature these two theories have been separated and naed as either the Walrasian deand curve (function) or the Marshallian deand curve (function) without any explanation as to the differences between the. At the sae tie, there are econoists who clai that there are differences between Walras s theory and Marshall s theory (De Vroey, 009; Jaffe, 1971; Ingrao & Israel, 1990). The ain difference is that Marshall s theory considers only partial equilibriu and not a general equilibriu theory, whereas Walras s theory considers only a general equilibriu theory (Screpanti & Zaangi, 1993, p. 178; Dasgupta, 1990, p. 45; Donzelli, 008; Stigler, 1990, p. 5; Dardi, 003; De Vroey, 1999a, 1999b; Hayes, 006)). Such differentiation between Walras s theory and Marshall's theory is not only incorrect, as will be shown in this paper, but also negatively reflects on the developent of econoic science; and it ight cause serious har when it is applied for practical recoendation (see recently published book of Cardenete et al., 01, p. 101); and there are soe econoists asserting that acroeconoics does not require icro foundations; and conversely, that icroeconoics does not require acro connections. Moreover, there are econoists who state that We have concluded that icroeconoics does not provide knowledge that could not be obtained otherwise and that, as it is usually taught (or presented in textbooks), it encourages an erroneous way of thinking and In a word, to understand the real world, one has to forget icroeconoics (Benicourt & Guerrien, p. 317 and p. 3 respectively). Furtherore, the glooy situation of the econoic theory has had an influence on econoic education, which itself deepens the crisis of econoic theory, because that textbooks both icro and acroeconoics have been negatively influencing several generations of econoic students. At the sae tie, Negishi states that It cannot be denied, in any case, that Marshall s partial equilibriu analysis is an indispensable copleent to Walras general equilibriu analysis in foring the foundations of current ainstrea econoics (Negishi, 1989, p. 345; see also Hutchison, 1953, p. 74). It is necessary to stress that in the econoic literature there are econoists which notice the siilarity of their approaches (Hicks, 1934, p. 338; Schupeter, 1954, p. 837 and Whitaker, 1975, p ). On the other hand, there are authors who notice that Marshall s approach is ore coplex than Walras s one (Raffaelli, 003, p. 91). In this paper, however, it will be shown that Marshall s deand theory is essentially siilar 65

3 to Walras s one, albeit that Walras s deand theory is coprehensive, whereas Marshall s deand theory is not. This paper concerns itself only with these issues which are significant both fro the point view of the ethodology of econoic science and of course deand theory (Davar, 014). The paper consists of four sections. Following the introduction, in the first section, the first type of deand function (curve), naely, the original (ordinary) deand function is considered. In the second section, Walras s deterination of the second type of deand function, naely, the derived (general) deand function is discussed; firstly in detail for the exchange econoy, and then in brief, for other econoies. The third section describes the link between these two types of deand functions. The fourth section considers the attributes of the derived deand function in Marshall s approach. Finally, conclusions are presented.. Original (Ordinary) Deand Curve (Function) Let us start with Cournot s definition of the original (ordinary) deand curve (function): the sales or the deand generally, we say, increases when the price decreases (Cournot, 1738, p. 46) and the sales or the deand D is, for each article, a particular function F(p) of the price p of such article (ibid. p. 47). This definition describes the character of the deand curve for a certain coodity and for any large arket. It is clear, however that there ight be soe variations of the deand curve depending upon the character of the different coodities such as luxury and every-day consued coodities. Therefore the deand curve for each individual differs and they ay take on any for, ay be discontinued and even soeties inclined positively. However Marshall stated that There is then one general law of deand:- The greater the aount to be sold, the saller ust be the price at which it is offered in order to that it ay find purchasers, or in other words, the aount deanded increases with a fall in price, and diinishes with a rise in price. There will not be any unifor relation between the fall in price and the increase of deand (Marshall, 195, pp ). Marshall also stated that Thus the one universal rule to which the deand curve confors is that it is inclined negatively through the whole of its length (ibid. p. 99, note ; see also Marshall, 1930, p. 4). On the other hand, Walras as well as Marshal stated that Thus, the slope of deand curve, which can be very siply defined in ters of atheatics as the liit of the ratio of a decrease in deand to an increase in price, and Hence the quantity deanded y is too great for a price higher than p b. It follows therefore that the deand curve is negatively inclined (Walras, 1954, p.116 and p. 466, respectively). Walras assued that deand and offer curves for an individual ay be either continuous or discontinuous, whereas for total deand and total offer curves, they ust be always continuous (ibid. p. 95). Firstly, Walras deterined the effective supply and effective deand as a definite aount of a coodity at a definite price (ibid. p. 84 and p. 85). This eans that for both deand and supply, for a particular quantity, there is only one price, and vice versa. Secondly, Walras deterined the state of equilibriu by coparing the effective deand and the effective offer of a coodity: We have now to ake three suppositions according as the deand is equal to, greater than, or less than the offer. In the first case The arket is in a stationary state or in equilibriu, while in the second and third cases the arket is in disequilibriu (Walras, 1954, p. 85). 66

4 On the one hand, Marshall deterined what was efficient deand fro the equilibriu state His deand becoes efficient, only when the price which he is willing to offer reaches that at which others are willing to sell (Marshall, 195, p. 95). Yet, Marshall used siilar definition of equilibriu state but in inverse for, naely, the equilibriu is achieved when the deand price is equal to the supply price for the given quantity of coodity (vide infra). There are two additional arguents showing the siilarity of the deand theory of Walras and Marshall. Firstly, they both used a coon ethod of establishent and re-establishent of general equilibriu, i.e., they assued that the given basic data does not change during the process of equilibriu establishent and considered the proble of equilibriu re-establishent as a result of changes in the given basic data (Marshall, 195, p. 34; Walras, 1954, p. 4). So, Marshall frequently used the ter other things are being equal to point out the above stateent. Walras stressed this fact when the process of equilibriu establishent first begins for each econoy. Secondly, both authors state that fro the production econoy deand curves of services and supply curves of coodities are not used and therefore, they are absent. However, in the process of equilibriu establishent the deand quantity of services is deterined by the equation syste which is based on the deand quantities of coodities. Furtherore the supply quantities of coodities are deterined siultaneously with their deand quantities assuing that they are equal (vide infra). To su up we can conclude that Marshall s and Walras s definition of the original (ordinary) deand curve (function) for a certain coodity (service) are in principle siilar (Schultz, 1938, p. 9). 3. Walras s Deterination of the Derived (General) Deand Functions It is well-known that Walras was the first author who used the deand (supply) function which is different fro the original deand curve (function) where the quantity of a particular (certain) coodity depends not only on its price but also the prices of other coodities (Schultz, 1938, p. 9; Sauelson, 1947, p. 97). This fact was ephasised by ost odern authors and referred to as a Walrasian deand function (see for exaple Mas-Colell & others, 1995). However, they odified Walras s derived deand function, and noted that the quantity of a certain coodity not only depends upon prices but also upon the other paraeters of the initial endowent. In the following we will clarify this difference between Walras s and the odern authors definition of the derived deand function. Because in the ajority of odern econoic literature the proble of an individual econoy is presented in relation to the exchange econoy let us start our exaination of the various econoies fro that point. 3.1 Walras s Derived (General) Function for the Exchange Econoy Walras stated that the following is the necessary and sufficient data in order to establish equilibriu in an exchange econoy: (1) the traders utility or want equations for coodities, which can generally be represented by curves and () the initial quantities of the coodities in their possession (Walras, 1954, p. 173). This eans that each individual beforehand knows the holding quantities of coodities (q 1, q,..., q ), which he ight 67

5 exchange with other individuals and thus forulates utility functions for every coodity separately (Φ 1 (q 1 ), Φ (q ),..., Φ (q )). It is necessary to point out that this data does not change during the whole process of equilibriu establishent. In these conditions, the goal of each individual is the axiu satisfaction of wants by the exchange of coodities for their given prices (p 1, p,..., p ), i.e., by the deand of one coodity and by the offer of others. In addition Walras assued that every product ight be either offered or deanded depending on its holding quantity. However, product cannot be offered if individuals do not hold it. Therefore Walras assued that every coodity ight be either deanded (d i ) or offered (o i ), such that the suation value of deand ust be equal to the suation value of offer. This condition is known as the budget constraint for individuals. Now, let us forulate a odel in the exchange econoy for each individual using the odern ters: axiize Φ i (x i ), (3.1) 1 subject to x i - d i + o i = q i, (i =, 3,..., ), (3.) x 1 + d i p i - o i p i = q 1, (3.3) x 1, x i, d i and o i 0, (i =, 3,..., ), (3.4) where x i - is the quantity of coodity i which reains to the individual by the result of exchange and it is calculated as either (q i + d i ) or (q i - o i ); - conditions (3.) indicates that the offer of a certain coodity cannot be ore than its available quantity; - condition (3.3) is the budget constraint for an individual, which eans that either the offer of or deand for a coodity used as the nuéraire (the first, according to Walras s approach) depends on the balance between the total value of deand (expenditure) d i p i and the total value of offer (incoe) o i p i of the coodities not used as the nuéraire. If d i p i > o i p i then the oney coodity is offered in order to pay for the excess of the total value of deand and it is defined as o 1 = ( d i p i - o i p i ). Also the latter cannot be ore than its available quantity q 1. And, if d i p i < o i p i then the oney coodity is deanded in order to store (reserve) excess of the total value of supply and it is defined as d 1 = - ( d i p i - o i p i ). The solution of the syste (3.1)-(3.4), if it exists, deterines the deand and offer quantities of coodities, which guarantees axiu satisfaction for each individual by the additional conditions... that axiu satisfaction will be achieved by each trader when the ratios of 68

6 the raretés of the coodities not used as the nuerate to the rareté of the coodity so used equal the prices cried [Walras, 1954, p. 164]. This eans that φ i (x i ) = p i φ 1 (x 1 ), (,3,...,) (3.5) or r i = p i r 1, (,3,...,) (3.6) where r i = Φ i (x i )/ x i = φ i (x i ), (1,,3,...,) (3.7) and r i is known as the arginal utility (rareté) of coodity i for a certain individual. Fro the solution to equations (3.1)-(3.4) (assuing it exists and is unique), we obtain deand quantities for a part of the coodities and offer quantities for the rest. And, consequently, the final quantity of good (x i ) is defined. Because of that the latter does not take place in the process of equilibriu establishent is oitted in the following discussion. It follows fro the structure of the odel that if either o i or d i is positive, the other would equal zero; because both have the sae price and both influence the utility functions indirectly by the final endowent x i (Hiller & Lieberan, 1995, pp ). In other words, a certain coodity cannot be offered and deanded siultaneously by the sae individual. In addition, every coodity s offered quantities are bound by its available quantities (conditions (3.)) and its deand quantities are bound by the available quantities of all coodities, i.e., by the budget constraints (condition (3.3)). This eans that the derived (generally) deand (or offer) functions is a result of the solution of the odel of individual econoy, that is, it has pure theoretical nature. So: o i = f i (p 1,p, p 3,..., p ; q 1, q,..., q ; φ 1,, φ ); (,3,...,) (3.8) d i = f i (p 1,p, p 3,..., p ; q 1, q,..., q ; φ 1,, φ ); (,3,...,) (3.9) while the individual s deand or offer of the nuéraire (product (1)) is obtained by either the equation o 1 = ( d i p i - o i p i ) or d 1 = - ( d i p i - o i p i ), (3.10) where φ i is the paraeter of the utility function of product i. Equilibriu conditions (3.5) or (3.6) are identical with Walras s one (ibid. p. 165). But, definitions of deand function (.8) and offer function (3.9) differ fro Walras s definition, naely fro y 1 = f b,1 (p b, p c, p d ), z 1 = f c,1 (p b, p c, p d ), w 1 = f d,1 (p b, p c, p d ) (Walras, 1954, p. 165). The functions (3.8) and (3.9) are deterined on the basis of the solution of the atheatical odel (3.1)-(3.4). Hence, by the theory of atheatical (linear) prograing, unknowns of odels depend upon all the paraeters of the odel. In this particular case they depend upon prices (p), available quantities (q), and the paraeters of utility function of coodities (φ). What this eans is that Walras s deand and offer function is incoplete, i.e. is incorrect. However the question is why? Does Walras not know that such dependence is satisfied only by prices? The paraeters of Walras s individual odel ight be divided into two types: first, the internal paraeters i.e. the initial available quantities and the utility functions of goods, and 69

7 secondly, the external - prices of coodities, which are generally unknowns. However, it ust be pointed out, the prices becoe known for each iteration of adjustent process (tâtonneent) (vide infra). Consequently, Walras divided the process of equilibriu establishent into two stages. The first stage of the process is the establishent of equilibriu prices (external paraeters) for the given available quantities and utility function (internal paraeters). The second stage of the process is the analysis of the variation of prices (equilibriu re-establishent) when initial quantities and utility functions are changed. Thus, Walras's definition of derived (general) deand (supply) functions relates to the first stage. This eans that the deand (or offer) of a certain coodity depends only on the prices of all coodities until general equilibriu is established. When equilibriu is established during the second stage of the process, then deand and supply is also dependant on the internal paraeters (available quantity and utility of all goods) too. Walras used his faous tâtonneent for equilibriu establishent (vide infra). It is necessary to stress that Walras's followers have isunderstood his two stage approach ever since Pareto (J. van Daal & D. A. Walker, 1990; Walker, 1996, 006). They altered the first stage and though the second stage was used it was used in a different way fro Walras s approach. For exaple, Sauelson writes: That is to say, the quantity of each good is a function of all prices and incoe. These are the general deand functions. The Marshallian partial equilibriu deand functions for the first good would be, of course, x 1 = h 1 (p 1, p,..., p n, I) = D 1 (p 1 ), (1), where all other prices and incoe are held constant by ceteris paribus assuptions (Sauelson, 1947, pp ). It is iportant to note two things. First, Sauelson considers only two paraeters (prices and incoe) and the third paraeter of utility functions is issing. Second, Sauelson assues that the original deand function ight be identified with the derived deand function and that it is acceptable for each individual. Sauelson s deterination of the derived deand function was borrowed by the odern authors and called a Walrasian deand function : When x(p,w) is single-valued for all (p,w), we refer to it as the Walrasian (or ordinary or arket) deand function (Mas-Colell and others, 1995, p. 51) 1. There is an additional erroneous arguent ade against Walras s approach. This arguent is derived fro a isunderstanding of Walras s two stage definition of the derived deand (offer) function. Walras s followers write as if Walras did not discuss probles of coparative static in his general equilibriu theory (Hicks, 1946, p. 61). Therefore, this eans that in Walras s notations: o i = f i (p, p 3,..., p ); (,3,...,) (3.11) d i = f i (p, p 3,..., p ); (,3,...,) (3.1) while the individual s deand or offer of the nuéraire product (1) is obtained by the equation (.10). 3. Derived (General) Function for Another Three Econoies 3..1 Derived Function for Production Econoy In the production econoy Walras considered two distinct arkets. The first is the services arket, where owners of factors either sell various productive services, which are bought by entrepreneurs or other individuals for productive purposes or the services are bought by other 70

8 individuals for the purposes of consuption. The second arket is the products arket, where entrepreneurs sell their products and individuals buy the for the purposes of consuption. Here, as well as, in an exchange econoy, productive services and products are exchanged by the rule of free copetition. In addition, their prices (rent, wages, interest, and prices, respectively) are stated in ters of nuéraire. Moreover, the current (equilibriu) price of each service or each product is established in accordance with the law of supply and deand. In other words, by the relationship between effective deand and effective offered (between selling prices (deand prices) of coodities and their cost of production (supply prices)). Each individual, at this stage, exchanges his own capital services for the products and other individual services. Therefore, in addition to the previous Exchange Econoy, where utility functions of each product are given, here each individual has to define utility functions for every service separately (Φ j (y j )) and their available quantity. It is necessary to point out that in the production econoy Walras assued that individuals do not possess any quantities of products, and therefore, available quantities of products fro the previous econoy are absent; and in a state of equilibriu in production, entrepreneurs ake neither profit nor loss (Walras, 1954, p. 5). In this section we did not differ between types of services and assued that their total nuber is equal to n. Therefore the derived deand function for the production econoy is an extended version of the Exchange Econoy (see (3.8) and (3.9)). The coplete derived deand (supply) function of products (services) obtained on the basis of individual odels solution for the production econoy ust include prices of products and services, the available quantities of services and the paraeters of utility functions of products and services ust be included. Thus: d j = f j (p, p 3,..., p ; p 1, p,..., p n ; q 1, q,..., q n ; φ 1,, φ ; φ 1,, φ n ); (j=1,,3,...,n) (3.19) o j = f j (p, p 3,..., p ; p 1, p,..., p n; q 1, q,..., q n ; φ 1,, φ ; φ 1,, φ n ); (j=1,,3,...,n) (3.0) x i = f i (p, p 3,..., p ; p 1, p,..., p n ; q 1, q,..., q n ; φ 1,, φ ; φ 1,, φ n ); (,3,...,) (3.1) while the individual s deand of the nuéraire (product (1)) is obtained by the equation x 1 = - x i p i - d j p j + n j= 1 o j p j, (3.) n j= 1 Where x i, d j, and o j are the deand for products and services, and the offer of services respectively. Due to this Walras s version of the derived deand function for production econoy has to be also an extended version of the exchange econoy (see (3.10) and (3.11). This eans that d j = f j (p, p 3,..., p ; p 1, p,..., p n ;); (j=1,,3,...,n) (3.3) o j = f j (p, p 3,..., p ; p 1, p,..., p n; ); (j=1,,3,...,n) (3.4) x i = f i (p, p 3,..., p ; p 1, p,..., p n ;); (,3,...,) (3.5) x 1 = - x i p i - d j p j + n j= 1 o j p j, (3.6) n j= 1 71

9 However, in the equilibriu state, for the given available quantities and utility function nן the first stage of the equilibriu establishent process, there will always be agents (consuers and producers) which stay outside of the equilibriu state. The result is that they can change their given available quantity and utility function and therefore, the second stage of the equilibriu establishent process is required. 3.. Derived Function for Capital Foration and Credit Econoy Capital foration and credit econoy are extended by the production of new capital goods, which are required for two purposes. The first is the renewal of the old capital goods, which have been destroyed, in order to keep up the existing level of total production if it is required. The second purpose is to expand existing fixed capital. On the other hand, in order to deand (purchase) new capital goods there ust be individuals whose incoes exceed their purchase of consuers goods and services, so that the aggregate of the first is greater than the aggregate of the latter, i.e. there is a saving. In order to convert this new ter, a saving, to a ter which would be coprehensive, that is, one which would be siilar to other consuers goods, Walras introduced an abstract (ideal) coodity (E) consisting of perpetual net incoe with price p e = 1/i. This eans that each individual has a certain want of coodity (E) which is either deanded (d e ) or offered (o e ) as well as other capital services and quantity of which is obtained by the condition of axiu satisfaction by its function of utility Φ e (q e ). So, the derived deand function for the Capital Foration and Credit Econoy is an extended version of the Production Econoy (see (3.19) - (3.1)). The coplete derived deand (supply) function of products (services) obtained on the basis of an individual odel for Capital Foration and Credit Econoy ust include the following additional paraeters relating to the derived deand function of a Production Econoy: price (p e ) of a new coodity (E), its available quantity (q e ), and the paraeter of its utility function (φ e ). This is: d = f(p, p 3,..., p ; p 1, p,..., p n ; p k, p k ; p e ; q 1, q,..., q n ; q e : φ 1,, φ ; φ 1,, φ n ; φ e ); (3.6) Where, for siplicities sake we use d to express a coon notation for deand and supply functions for all kinds of coodities and services. Walras s version of a derived deand function for Capital Foration and Credit Econoy then has to be also an extended version of the Production econoy (see (3.3) - (3.5)). This eans that according to Walras s approach the derived deand function has the following for d = f(p, p 3,..., p ; p 1, p,..., p n ; p k, p k ; p e ); (3.7) In the capital foration and credit econoy alike the exchange econoy and production econoy, in the equilibriu state, for the given available quantities and utility function nן the first stage of the equilibriu establishent process, there will always be agents (consuers and producers) which stay outside of the equilibriu state. The result is that they can change their given available quantity and utility function and therefore, the second stage of the equilibriu establishent process is required Derived Function for a Circulation and Money Econoy Circulation and Money is Walras s final study of econoy. In this econoy Walras extended 7

10 three previous econoies (Exchange, Production, and Capital Foration and Credit econoies) by introducing the circulation of capital goods, oney, and raw aterials. So, the derived deand function for the Circulation and Money Econoy is an extended version of the Capital Foration and Credit Econoy (see (3.6) and (3.7)). The coplete derived deand (supply) function of products (services) obtained on the basis of an individual odel for the Circulation and Money Econoy ust include a nuber of additional paraeters relating to the derived deand function of Capital Foration and Credit. The following are the additional paraeters : the price (p u ) of a circulating oney s service, its available quantity (q u ); prices of the services of availability of products as circulating capital goods (p a ) and their available quantity (q a ) the paraeter of its utility function (φ a ); and raw aterials prices (p r ) in circulation and their available quantities of (q ); thus: d = f(p, p 3,..., p ; p 1, p,..., p n ; p k, p k ; p 1, p,..., p ; p r ; p u ; p e ; q 1, q,..., q n ; q 1, q,..., q ; q 1, q,..., q r ; q u ; q e : φ 1,, φ ; φ 1,, φ n ; φ 1,, φ ; φ e ); (3.8) Where, as in the previous econoy, for siplicities sake we use, d to express a coon notation for both deand and supply functions for all kinds of coodities and services. Walras s version of a derived deand function for Circulation and Money Econoy then has to be also an extended version of the Capital Foration and Credit Econoy (see (3.7)). This eans that according to Walras s approach the derived deand function has the following for d = f(p,p 3,..., p ; p 1, p,..., p n ; p k, p k ; p 1, p,..., p ; p r ; p u ; p e ); (3.9) 4. The Link between These Two Types of Deand Functions There are two types of deand (supply) functions: the original (ordinary) deand (supply) curve (function) and the derived (general) deand (supply) functions for coodities and factors. The original deand function eans that the quantity of the coodity in question depends only on its price and vice versa, the price of the coodity in question depends only on its quantity. This eans that the original deand function is an invertible function and it ight be drawn, i.e., there is original deand curve. The derived (general) deand function eans that the quantity of the coodity in question depends on the prices of all coodities and services including oney. The derived deand function is not invertible opposed to the original deand function 3. The proble which we ust now turn our attention to is what kind of relationship is between these functions, i.e., whether they are alternative, substitutable or whether they can co-exist and be used siultaneously. In order to answer this question it is necessary to consider the process of general equilibriu establishent for the exchange econoy in detail. Walras stated that in order to any rando prices to becoe equilibriu prices it is necessary for the total effective deand to equal the total effective supply for all coodities which obtained by the aggregation of the results of the solution of individuals econoy. Therefore, Walras forulated two equivalent types of equation systes describing the equilibriu state. First, the excess deand (offer) for all coodities ust equal zero. Second, the total deand ust equal the total offer for all coodities except the coodity used as nuéraire, where equilibriu would be consequently established. 73

11 Based upon one of the essential assuptions that total effective deand ust equal total effective supply, Walras (Walras, 1954, p. 168) forulated equation systes for the whole econoy for the deterination of current (equilibriu) prices, thus: D i (p,..., p ) = O i (p,..., p ), (,3,...,) (4.1) Walras also stated that since prices of coodities are by their nature positive, it is evident that, if the above equations are satisfied... we also have (Ibid. p.169). D 1 - O 1 = D i p i - O i p i = 0, (4.) It is necessary to point out that these systes of equations describe an equilibriu situation for the whole econoy in the Exchange Econoy. But the question is how Walras achieved this equilibriu situation. Generally, there ight be three situations for each coodity: 1) where its total deand is greater than its total offer; ) where its total offer is greater than its total deand; and 3) where its total deand equals its total offer: D i (p,..., p ) >=< O i (p,..., p ), (,3,...,) (4.3) This eans that there is a disequilibriu state, and in such situation, Walras used a characteristic of the original deand function in order to carry out the process of general equilibriu establishent. On the basis of these deand curves Walras stated that for the first situation, the price of the coodity will increase in order to decrease deand quantity. In the second situation the price will decrease in order to increase the deand quantity. Finally in the third situation the price will not change. Walras used these rules of change in prices in the real arket in his theoretical solution for the establishent of equilibriu (Walras, 1954, p. 170). This eans that in order to establish an equilibriu situation Walras used tâtonneent (iterative process), where the iteration consists of several stages of coparison between the total deand and the total offer for each coodity of which inequality exists. So that at each stage first a new price syste is deterined on the basis of the original deand curve according to whether there is an equilibriu or disequilibriu situation for each coodity. Then using this given price syste each individual deterines his own derived deand (offer) functions and by eans of these individual deand and offer quantities, the total deand and the total offer are deterined in order to establish whether there is equilibriu. In other words it is necessary to copile data to deterine a new price syste for the next stage and to deterine whether it would be necessary. The nuber of stages is equal to the nuber of coodities for which inequality exists. So, Walras used here the property of the original deand function. According to the rules of the real arket, he stated that, it is possible to establish partial equilibriu, i.e. equilibriu for a certain coodity if it exists at all (probles of existence of equilibriu will not be discussed here). Walras stated, therefore, that by continuing the sae way for the new price syste, the process oves closer and closer to a state of equilibriu. Walras forulated the law of the establishent of equilibriu prices for the exchange econoy for the given data (ibid): Given several coodities, which are exchanged for one another through the ediu of a nuéraire, for the arket to be in a state of equilibriu or for the price of each and every coodity in ters of the nuéraire to be stationary, it is necessary and sufficient that at these prices the effective deand for each coodity equal its effective offer. When this 74

12 equality absent, the attainent of equilibriu prices requires a rise in the prices of those coodities the effective deand for which is greater than effective offer, and fall in the prices of those coodities the effective offer of which is greater than the effective deand. This law allows us to conclude that Walras s original tâtonneent, the iterative process of equilibriu establishent, is a theoretical version of the equilibriu establishent process in a real arket. In addition, in this law Walras expressed directly that the quantity of deand of a certain coodity is changed according to the original deand function, naely in relation to its price only. This eans that in the process of equilibriu establishent Walras used both deand functions: original (ordinary) and derived (general). It is necessary to stress that Walras s original law differs fro Walras Law which is used in odern econoic literature (Davar, 01). After equilibriu establishent Walras discussed probles of the variation of prices when the given data, utility function and initial endowent of coodities, is changed for soe individual or a group of individuals. Without discussing Walras s original presentation of the proble it is still iportant to stress that Walras forulated the Law of Variation of Coodity prices in an Exchange Econoy (Walras, 1954, p. 180). 5. Attributes of the Derived Deand Functions in Marshall s Deand Theory Marshall did not define, unfortunately, the derived deand function obviously. However a studied look of the text and atheatical appendix of his Principles of Econoics, leads us to conclude that Marshall also used this function in his theory. The ain reason that Marshall did not clearly consider the derived deand function, in our opinion, is that not only did he not forulate any atheatical odel for an individual econoy (Dardi, 003, p. 1) but also he did not forulate a coplete odel for the whole (acro) econoy. Therefore, he could not discuss the adjustent process between an individual econoy and a acro econoy in the sae way that Walras did. This is also the reason, by our opinion, why ajority of econoists call Marshall s theory a partial equilibriu theory, and not a general equilibriu theory. However, Marshall deterined the condition of optiality for a odel of an individual s econoy and forulated fragents of a whole econoy in the sae way Walras did. This shows that he generally discussed a General Equilibriu Theory, as did Walras (vide infra). There are any attributes, but we will confine ourselves only to those which are relevant and central to the subject under discussion. 5.1 Attribute for the Individual Econoy in Marshall s Deand Theory Despite the fact that Marshall did not forulate and discuss a atheatical odel for an individual econoy, he deterined exactly the condition of optiality for an individual econoy. Marshall firstly forulated a general rule, stating that If a person has a thing which he can put to several uses, he will distribute it aong these uses in such a way that it has the sae arginal utility in all. For if it had a greater arginal utility in one use than another, he would gain by taking away soe of it fro the second use and applying it to the first (Marshall 195 pp ). Then he concretized this rule for oney stating that 75

13 But when coodities have becoe very nuerous and highly specialized, there is an urgent need for the free use of oney, or general purchasing power; for that alone can be applied easily in an unliited variety of purchases. And in a oney-econoy, good anageent is shown by so adjusting the argins of suspense on each line of expenditure that the arginal utility of a shilling s worth of goods on each line shall be the sae (ibid. p.118). It is worthy noting two points. Firstly, already at the level of the individual econoy Marshall considered nuerous nubers of coodities. Secondly, he discussed an aount of oney but not oney incoe (Sauelson, 1947, p. 100 and p.190, see note 6). Marshall stated that The larger the aount of a thing that a person has the less, other things being equal (i.e. the purchasing power of oney, and the aount of oney at his coand (our italics) being equal), will the price which he will pay for a little ore of it: or in other words his arginal deand price for it diinishes (Marshall, 195, p. 95). Regarding oney he concluded, that 'At one and the sae tie, a person s aterial resources being unchanged, the arginal utility of oney to hi is a fixed quantity, so that the prices he is just willing to pay for two coodities are to one another in the sae ratio as the utility of those two coodities (ibid. p. 95). This eans that the arginal utility of oney stood fixed until the initial given paraeters for individuals do not change and it is the sae to relations for all coodities. This is identical with Walras s approach. Marshall considered a atheatical expression of this condition of optiality for the individual econoy in Note II in his atheatical appendix (ibid. p. 838). He wrote: If is the aount of oney or general purchasing power at a person s disposal at any tie, and μ represents its total utility to hi, then dμ/d represents the arginal degree of utility of oney to hi. If p is the price which he is just willing to pay for an aount x of the coodity which gives hi a total pleasure u, then dμ/d Δp =Δu; and dμ/d dp/dx = du/dx. If we take into account the fact that by p Marshall notated the price paid for an aount of coodity, and therefore dp/dx is the price of the unit coodity, we can conclude that this last expression is identical with Walras s conditions of optiality for an individual econoy (see (3.5)). Naely, the axiu satisfaction for a person will be achieved when the ratios of the arginal utility of any coodity (which is not used as the nuéraire (oney coodity)) to the arginal utility of the oney coodity is equal to the price of coodity in question 4. Marshal continued (ibid.): If p is the price which he is just willing to pay for an aount x of another coodity, which affords hi a total pleasure u, then and therefore dμ/d dp /dx = du /dx 76

14 dp/dx : dp /dx = du/dx : du /dx. Journal of Social Science Studies The latter expression is an extended version of the above conditions of optiality for an individual econoy, which eans that the ratio of the arginal utility of two coodities is equal to the ratio of their prices. This stateent is identical to Walras s according stateent (Walras, 1954, pp ). To su up, we can conclude that the conditions of optiality for the individual econoy according to Marshall s approach are the sae conditions that Walras set. 5. Attributes for the Whole Econoy in Marshall s Theory In this section, despite the fact that Marshall did not forulate a coplete odel of the whole econoy and did not discuss the process of adjustent (equilibriu establishent) between the individuals econoy and the whole econoy, we will show that generally Marshall s approach is equivalent to Walras s one. Firstly, Marshall as well as Walras assued that there would be free copetition and unifor prices. He wrote: Thus we assue that the forces of deand and supply have free play; that there is no close cobination aong dealers on either side, but each acts for hiself, and there is uch free copetition; that is, buyers generally copete freely with buyers, and sellers copete freely with sellers (Marshall, 195, p. 341; and 1930, p. 1); and we assue that there is only one price in the arket at one and the sae tie (Marshall, 195, pp ). Secondly, Marshall stressed repeatedly that he forulated atheatically only fragents of the whole odel despite the fact that he depicted theoretically (verbally) the whole acro odel. For exaple, Marshall, firstly, stated that In the theory of Doestic values it is not necessary to consider at one tie the special circustances of ore than one coodity; (Marshall, 1930, p.), and then he discussed how equilibriu is established. Marshall started with the following definition: Definition. R (Fig. A) being a point on Ox, let OR easure the aount of coodity which would be produced in a year if the scale on which the production is carried on at a given tie were continued unifority. Then R is the Aount-index at that tie (Marshall, 1930, p. 10). This definition is siilar to Walras s deterination of effective deand and effective supply, but in inverse for. Naely, according to Walras s approach, the effective deand and the effective supply are deterined for a certain given price; while according to Marshall s approach the Aount-index deterines the deand price and the supply price for a certain given quantity. Marshall continued: With this definition we ay enunciate the fundaental Prop. XIX. Let a vertical straight line drawn through the Aount-index cut the deand curve in d, and the Supply curve in s. If d is above s the Aount-index will tend to ove to the right. If d is below s the Aount-index tend to ove to the left. If d coincides with s, the Aount-index will be in equilibriu, tending to ove neither to the right nor to the left (ibid.). This is also siilar to Walras s rule of the establishent of equilibriu, but also in inverse 77

15 for. Naely, according to Walras s approach, the price of the coodity, in a disequilibriu situation, changes depending on whether there is either excess deand or excess supply; in the first situation the price ust increase; in the latter situation, the price ust decrease (vide supra). Thus, according to Marshall s approach, the quantity of the coodity, in a disequilibriu situation, changes depending on either if the price of deand is greater than the price of supply (the excess deand price), or the price of supply is greater than the price of deand (the excess supply price). In the first case the quantity ust increase, while in the latter, it ust decrease. It ust pointed out, however, that Marshall did not use the ters excess deand price and excess supply price. Marshal illustrated his approach for a local corn arket (see Marshall, 195, pp ). Marshall finished by the defining the equilibriu state: Prop. XX. The Aount-index is in equilibriu whenever it is vertically below any point of intersection of the Deand and Supply curves (Marshall, 1930, p.11). In other words, the equilibriu is established when the deand price is equal to the supply price for the given quantity of coodity; which is also siilar to Walras s deterination of the equilibriu state, but in inverse for, naely, the equilibriu is established when the effective deand is equal to the effective supply for the given price of coodity. It ust be stressed that when several coodities are discussed, which ust be generally considered, the use of Marshall s ethod is probleatic, since in this case, the aggregate deand and supply are siultaneously defined for several coodities, and this is only possible when their prices are given, i.e., by Walras s ethod. Now let us to discuss Marshall s version of the theoretical (verbal) acro odel of the whole econoy. He wrote Marshall (195, Note XXI, p. 855): We ay now take a bird s-eye view of the probles of joint deand, coposite deand, joint supply and coposite supply when they are all arise together, with the object of aking sure that our abstract theory has just as any equations as it has unknowns, neither ore nor less. In a proble of joint deand we ay suppose that there are n coodities A 1, A, A n. Let A 1 have a 1 factors of production, let A have a factors, and so on, so that the total nuber of factors of production is a 1 +a +a a n ; let this =. First, suppose that all the factors are different, so that there is no coposite deand; that each factor has a separate process of production, so that there are no joint products; and lastly, that no two factors subserve the sae use, so that there is no coposite supply. We then have n+ unknowns, viz. the aounts and prices of n coodities and of factors; and to deterine the we have n+ equations, viz.-(i) n deand equations, each of which connects the price and aount of a coodity; (ii) n equations, each of which equates the supply price for any aount of a coodity to the su of the prices of corresponding aounts of its factors; (iii) supply equations, each of which connects the price of a factor with its aount; and lastly, (iv) equations, each of which states the aount of a factor is used in the production of a given aount of the coodity. 78

16 Marshall described here a general equilibriu odel for the Production econoy which is siilar to Walras s one, with inor differences (Walras, 1954, Lesson 0, pp. 37-4; see also Davar, 1994, pp.38-5). First of all, there is the equilibriu state, which is established by coparing between: (1) the deand price of a coodity (equations (i)) and its supply price (cost of production) (equations (ii)); and between () the supply quantities of factors (equations (iii)) and their deand quantities (equations (iv)). Secondly, Marshall, as well as Walras, used only the supply functions of the factors services and the deand functions for coodities fro the Production Econoy in order to establish equilibriu. Thirdly, if due to the change in prices and quantities in any of the above coparisons there is inequality and therefore disequilibriu the process of adjustent ust be continued until equilibriu is established if it exists at all. Let us present Marshall s illustration of deterination both of the cost of production and the derived deand quantities of factors. For his deterination of the cost of production Marshall stated that (Marshall, 195, p. 343): Let us suppose that a person well acquainted with the woollen trade sets hiself to inquire what would be the noral supply price of a certain nuber of illions of yards annually of a particular of cloth. He would have to reckon (i) the price of the wool, coal, and other aterials which would be used up in aking it, (ii) wear-tear and depreciation of the buildings, achinery and other fixed capital, (iii) interest and insurance on all the capital, (iv) the wages of those who work in the factories, and (v) the gross earnings of anageent (including insurance against loss), of those who undertake the risks, who engineer and superintend the working. This is a very coprehensive deterination of the cost of production for the woollen industry and is siilar to Walras s one. For the latter, naely for the derived deand quantities of services Marshall stated that The deand for raw aterials and other eans of production is indirect and is derived fro the direct deand for those directly serviceable products which they help to produce. there is a joint deand for the services which any of these things render to helping to produce a thing which satisfies wants directly and for which there is therefore a direct deand: the direct deand for the finished product is in effect spilt up into any derived deands for the things used in producing it (Marshall, 195, p. 381). This is also siilar to Walras s definition of the deand of the factors services (vide supra). Marshall continued that When therefore the aount produced (in a unit tie) is such that the deand price is greater than the supply price, then sellers receive ore than is sufficient to ake it worth their while to brings goods to arket to that aount; and there is at work an active force tending to increase the aount brought forward to sale. On the other hand, when the produced is such that the deand price is less than the supply price, sellers receive less than is sufficient to ake worth their while to bring goods to arket on that scale; so that those who were just on the argin of doubt as to whether to go on producing are decided not to do so, and there is an active force at work tending to diinish the aount brought forward 79

17 to sale. When deand price is equal to the supply price, the aount produced has no tendency either to be increased or to be diinished; it is in equilibriu (ibid. p. 345). So, Marshall, as well as Walras, considered equilibriu establishent as taking place siultaneously in two directions. First, when the deand price of a certain coodity is greater than its supply price (cost of production) then the aount of coodity produced tends to increase due to increased quantities of factors with accordingly their high prices and consequently enlarging supply prices. Furtherore in the opposite case, naely, when the deand prices of a certain coodity is less than its supply price then the aount of the coodity produced tend to decrease by using decreased quantities of factors with accordingly their lower prices and consequently their decreasing supply prices. In this case the adjustent process is carried out on basis of the original supply curves of factors. Second, when the supply quantity of a certain factor is greater than its derived deand quantity, then the quantity of a coodity deanded tends to increase. This consequently increases the used quantities of factors. Thus when the supply quantity of factor is less than their required quantity then the quantity of coodity deanded tends to decrease and decreases the used quantities of factors. Therefore in this case the adjustent process is carried out on the basis of the original deand curves of coodities. In other words, Marshall also used identically expressed Walras s excess deand (supply) for the sae purpose, but he did not define excess deand (supply) (see Marshall, 195, note 1, p. 346). Finally, Marshall, as well as Walras, stated that if there is any change in the initial given data for any individual of group of individuals then the new process of equilibriu establishent ust be carried out. This eans that equilibriu ust be re-established. Marshal stated that For indeed the deand and supply schedules do not in practice reain unchanged for a long tie together, but are constantly being changed; and every change in the alters equilibriu aount and equilibriu price, and thus gives new position to the centres about which the aount and the price tend to oscillate (Marshall, 195, pp ). At the sae tie, there are econoists which claiing that as if there is an iportant difference between Walras s and Marshall s deterination of cost of production. Naely, they asserted that Walras used coefficients of production (Walras, 1954, p. 39), this is, average technology, while Marshall used a representative fir. Indeed, Marshall stated that These results will be of great iportance when we coe to discuss the causes which govern the supply price of a coodity. We shall have to analyse carefully the noral cost of producing a coodity, relatively to a given aggregate volue of production; and for this purpose we shall have to study the expenses of a representative producer for that aggregate volue (Marshall, 195, p. 317). But question is how Marshall deterined a representative fir. Marshall stated that Thus a representative fir is in a sense an average fir. But there are any ways in which the ter average igth be interpreted in connection with a business. And a Representative fir is that particular sort of average fir, at which we need to look in order to see how far the econoies, internal and external, of production on a large scale have extended generally in the industry and country in question (ibid. p. 318). So, Marshall also used average 80