Joseph Lang and Macroeconomics

Joseph Lang, an obscure German whose principal work was published in Russia in 1811, is the first real macroeconomic mathematical economist. Kröncke had, before him, defined national income and wealth2 and Isnard had presented a model of a closed exchange economy,3 but it was Lang who, not only followed Isnard's lead, but was also able for the first time to create a macroeconomic mathematical model where the problems of distribution, production, money and prices are viewed in their interdependence and the analysis is pursued with consistency and clarity to the ultimate limits the model will allow. His book bears the title Grundlinien der politischen Arithmetik,4 but his is an entirely novel conception of Political Arithmetic. It is the mathematical part of the Science of Economics5 and its aim is to search for the general relation of interdependence existing among economic quantities. “It abstracts from everything particular and given, and uses Algebra in order to find these general laws”.6 Lang must have known the work of Isnard, because his influence is obvious.7 Like him, he assumes that a portion of the commodity is held by the producer and that only the rest is offered for exchange.8 Like him, he examines what products each producer gets in exchange for his product. But Lang's model is much more sophisticated, for he has introduced two innovations, both necessary for his later treatment. The first is that, while Isnard had examined individual commodities, Lang distinguishes three broad classes of goods and introduces aggregation. These are primary products, manufactured goods and services to include those of land, of capital and of the states.9 According to the product which every individual helps to produce, he is classified in one of these three classes. We thus have the class of primary producers, the “ manufacturing class “ and the “ service class “. It must be stressed that the manufacturing class includes not the capitalists but industrial workers, engineers, management, etc. Any saving that the owner of quantity M wants to make has been taken care of, before arriving at a which is the quantity intended for exchange. The quantity of money circulating among the classes is given and does not change. There is no saving of money (hoarding), and no class withdraws any money from circulation. Each class “returns again to the circulation, i.e. to the other two classes, all money which it has received from the other two classes ”.2 No class can give out more money than that received. There are no debts between classes. If a sufficiently long period is taken, debts are cancelled out by repayments. Having established the equality between money receipts and money payments, Lang proceeds, on much similar lines to Isnard, to examine the interdependence of receipts and payments of the various classes, under a general ceteris paribus condition, which includes the composition of each class, the price-level, the quantity of money, etc.3 If x, y and z are the total money receipts of the primary producers, of the manufacturing class and of services respectively, we shall have: (1) x = a + b where a are the receipts from the manufacturing class, and b the receipts from services ; (2) y =c +d where c are the receipts from primary producers and d the receipts from services ; (3) z =e +f where e are the receipts from primary producers, and f the receipts from the manufacturing class. On the other hand, when x', y’ and z' are the respective payments by primary producers, the manufacturing class, and the service class, we shall have: (4) x'=c + e (5) y’ =a +f and (6) z’ =b +d As therefore payments of each class are equal to its receipts, it follows that (7) a + b = c + e (8) c + d = a (9) e + f = b + d Up to this point Lang had considered money as the medium of exchange; but to be able to calculate receipts or payments from the quantities of goods, which each class has available for sale or buys, one needs to know their exchange value in terms of a common measure. This unit of value or accounting unit may be, according to Lang, different from the medium of exchange, and it is in terms of such a unit that receipts and payments must be equal. Lang takes as the unit of exchange value “ that quantity of food and other products of nature, which a person belonging to the manufacturing class needs on the average for the satisfaction of his immediate personal wants per year “.1 This is the unit of value and is equal to one. If it is assumed that the total population of a country is made up of V persons belonging to the class of primary producers, X belonging to the manufacturing class, and that Y persons offer services, we shall have in total2 (10) A = V + X + Y The receipts of the primary producers consist of the value of what they sell to the other two classes. They will therefore consist of X units sold to the manufacturing class, as it is assumed that each member of this class needs a unit of food; of the value of raw materials sold to industry, equal to, say, mX, where m denotes the relation of the value of materials to that of food ; and of the value of food sold to the “ service class “ equal to, say, fY. As he assumes that each member of this last class consumes more than a member of the manufacturing class, he puts f>1. Equation (1) above is thus replaced by a new equation for the total receipts of the primary producers : (11) B = X + mX + fY The receipts of the “ service class “, D, are (12) D=gB+e (X +mX) where gB is what the members of this class receive from primary producers, and e (X +mX) is what they receive from the manufacturing class. The receipts of the manufacturing class are (13) C = (1−g) where (1−g) B denotes the receipts from primary producers and kB its receipts from the service class. In the same way Lang gives the equations for the payments B’, D' and C' by the primary producers, the service and the manufacturing classes respectively : (14) B’= (1-g)B+gB (15) D' = fY+kB (16) C' =(X+mX)+e (X+mX) The requirement is that B' = B, C' = C and D' = D. There is no need for the receipts of, say, primary producers from services to be equal to their payments. But if a class gives more money to one class, it will give less to the other.2 For Lang, B or the receipts of the primary producers is of first importance. It generally increases with the increase in the population of the industrial class or of the owners of services; or when the relation of the exchange value of materials to that of food increases, the population remaining steady, or when the owners of services need more food than they used to need.3 Given the values of m, f, g, e, and k, the receipts or payments of each class can be calculated. The gross national product is made up of the sum of the gross products of the three classes. The gross product of the primary producers is made up of: (a) the value of the product which is used for reproduction, like seeds, etc.; this is equal to, say, U; (b) the value of the product which primary producers keep for their own consumption ; as their needs are assumed to be the same as those of the industrial class, the value of their consumption is equal to V; and (c) the value B of their “ superfluous “ product which they exchange and which was calculated above. In the same way Lang calculates the total product of the industrial class and for the service class he takes as the value of their services their total receipts. From the gross national income he distinguishes the net national income, which is the remainder after allowance for the depreciation of capital and for double counting has been made.4 This net income is divided by the population of the country to find the net income per capita.5 Lang had up to this point treated the unit of value as being separate from the medium of exchange; but now he asks “ What is the money price of this unit of value ? “ To answer Lang seeks to determine the total value of the circulation of goods. This is made up of: (b) Intra-class circulation of goods. A portion of manufactured goods circulates among industrial workers and a portion of primary products circulates among primary producers; but Lang does not think that owners of services have any use for the services of one another.1 If the value of manufactures thus circulating is μN and that of primary products is πB, we shall have as the total value of goods circulating (17) P = (2+k) B+πB+μN If x is the money price of the unit of value, Z the quantity of money (coins and credit) which circulates and y is the average velocity of the circulation of money, we shall have2 “ What therefore an increase in the quantity of money or the velocity of circulation does, when the real value of goods is not increased simultaneously, is to cause an increased money price of the unit of value and an increase of all money prices, in so far as they are determined by the money price of the unit of value.”3 y (Z + ∆ Z) = P (x + ∆x), it follows that y∆Z = P∆x and (21) which is directly comparable with (19). This is the clearest possible formulation of the quantity theory. We have already seen that Lang had assumed that primary producers gave to “ services “ a portion g of the value of their “ superfluous products “ B, in payment of rent, interest and taxes. If the price of the unit of value is x, gB has a “ money value “ gBx. He now assumes that for some reason the contributions of producers to services increase in money terms by an amount a and seeks to examine what will happen on the assumption that B will remain unchanged.3 According to Lang there are three possibilities: (a) The money price x changes, while the contribution in real terms remains unchanged. Then (b) The price x may remain unchanged, and primary producers will have to make up for the increased contribution by increasing the portion g of their total amount of available goods B. Then (c) It is, however, more plausible that both the price x and g will change. Then and λ>x Δg, as by definition x increases together with g. It may be noticed immediately that the greater Δg becomes, the smaller Δx. When will be zero. On the other hand, when Δg =0, Δx becomes a maximum equal to , as in the first case. This is a very broad outline of Lang's contribution to economic analysis. He has also many interesting things to say about the effects of a change in the quantity of money on the receipts and payments of each of his classes, since such a change creates a disequilibrium which must be adjusted. He also examines the effects of a change in the population on the composition of his classes and on his system in general. Lang's work is entirely unknown. The only one to attempt even a very cursory review of his work is R. M. Robertson, who accuses him of insisting on classifying the population of a country illogically into those engaged in agriculture, those engaged in manufacture, and “ officials “.1

Economics · Keynesian economics · Macroeconomics · Economic Theory and Institutions

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