Thunen’s Achievements

In the introduction to the second edition in 1842 of The Isolated State (Part I) Thunen states that his theoretical-cum-empirical “method of analysis has illuminated - and solved - so many problems in my life, and appears to me to be capable of such wide­spread application, that I regard it as the most important matter contained in all my work”.

Thunen’s basic analytical workhorse is the model of a closed economy on a flat plane with homogenous soil and a city in the centre as an idealized economic space, and a long­term steady state as an idealized situation with respect to time. Production techniques in agriculture, the price of grain in the city, the real wage and the interest rate are constants in Part I of The Isolated State. The model determines the prices of agricultural products, the location of their production, production intensities and the land rent. The model in Part II comprises his theory of marginal productivity and of capital formation, enabling the calculation of steady state wages and interest rates. In his posthumously published works and his unpublished manuscripts he discusses different scenarios with respect to the extension and structure of the Isolated State and the resulting functional income dis­tribution (different populations, replacement of the monocentric by a polycentric model, formation of capital by workers and capitalists).

Thunen defines self-interest in terms of objective functions, that is, the maximization of rents by the proprietors of land and renewable resources, of capitalists’ pure profits and of a “surplus wage rent” of the capital accumulating workers (as “marginal” produc­ers of capital).

Thunen’s spatial models of agricultural production and prices as well as his marginal productivity theory are the first static equilibrium models. The core elements of his models are the following:

1. Diminishing returns to factor inputs, including capital: “Every additional capital, additionally invested in an enterprise or trade, brings less return than capital previously invested” (Thunen 1850: 98, original emphasis).

2. Marginal products equal factor prices: “The return which capital as a whole gives when lent out is determined by the return of the last unit of the capital” (ibid.: 100). “The value of the labour of the last worker employed is also his wage” (ibid.: 182, origi­nal emphases).

3. Factor prices and factor substitution:

By producing one and the same product, p, a part of the capital can be substituted by increased labour; and again, a part of labour can be substituted by increased capital; in this way capital is like a coworker that competes with the wage earner... The entrepreneur who knows and follows his own interest will increase his relative capital, q, until the cost of the work of the capital and the cost of the work of a human being are in the same proportion as their efficiency in production. (Ibid.: 123)

4. Income distribution:

The significance of capital we have measured by the increase in the product of labour of a man which results from an increase in the capital with which he works. Here labour is a constant, capital a varying magnitude. When on the other hand we consider capital as remaining con­stant and the number of workers as varying, we realize in a large business, that the significance of labour and the share of labour in the product is determined by the increase in the product which results from another labourer. (Ibid.: 190)

5. Dynamic equilibrium condition. With respect to the relation between the value of stocks and the flows resulting from these stocks he states: “As wages of labour are related to the amount of revenue which the same amount of labour produces if that labour is used for the production of capital, so are capital and interest related” (ibid.: 92).

As these conditions are taken to hold with regard to every good, and as market forces equalize interest rates and wages as well as the prices of each good (in the same location), Thunen develops equations that are reminiscent of the production equations of Sraffa (1960) in order to calculate the relative prices of produce in circumstances in which there are no rents of land, using labour as the numeraire (see Nellinger 2014c). These equations are also used in passages on trade theory in his unpublished manuscripts, the stock-flow problem in the economy of natural resources (Boventer, 1984: 142) and in his monetary theory. To simplify matters, Thunen variously used simple interest, although compound interest would have been appropriate. As Kurz (1995) observed, Thunen wrongly thought that his findings in a model with a single capital good produced by unassisted labour carry over to a system in which heterogeneous capital goods are produced by means of themselves.

Thunen did not demonstrate that the dynamic process converges to a steady state, he simply assumed that the system was stable. He expected, but did not prove, that devia­tions from the long-term steady state path would be corrected smoothly.

While the demand side in Thunen’s analysis is rather primitive, he may be said to have adopted ideas of the German “Gebrauchswertschule” (useful value school). However, a paternalistic proprietor of an estate and a member of the educated classes (“Bildungsburger”), he could not fully endorse utilitarian ideas.

For a long time, economists saw a contradiction between Thunen’s marginal produc­tivity concept of the wage rate and his tombstone formula wage. According to Thunen this wage should obtain if land is freely available (for example, in North America at his times) and population is constant. Yet Dorfman (1986), Samuelson (1986) and van Suntum (1988) have clarified that Thunen’s correctly derived natural wage equals the marginal productivity of labour at an optimal capital-labour ratio.

In his unpublished manuscripts Thunen also investigates the actual wage in central Europe, which according to his empirical analysis was somewhat higher than the subsist­ence wage. Thunen deplored the fact that workers typically spent the difference to raise more children rather than investing it in a better education for their children or on capital goods.

Thunen then introduced human capital in the production function to theoretically explain the low wages of workers in Europe and to demonstrate how to improve them (see Nellinger 2014c). Real capital formation, whether physical or human, has to yield a uniform interest rate, considering that the upbringing and education of children is an investment as any other investment. The investment in workers’ human capital - by own savings or public schooling and apprenticeship - will increase the product of their labour and, a fortiori, their wages. The resulting Vap-wage will always be higher than the subsistence wage, unless the population relative to the available natural resources increases greatly - which Thunen believes depends on the labourers’ reproduction behaviour. Capital formation by capitalists and workers or technical progress may defer the limitations of individual well-being. At this point Thunen merges the contemporary ideal of a well-educated citizen, perfecting his mind and controlling his sexual drives, with his pure economic analysis based on rational behaviour.

Part III of The Isolated State is titled “Principles for the Determination of Rent, the Most Advantageous Rotation Period and the Value of Stands of Varying Age in Pinewoods” and contains Thunen’s work on forestry optimization under different tech­nical conditions and factor scarcities. It is superior to, and far more detailed than, many subsequently published works, but inferior to the so-called Faustmann approach (see Faustmann 1849).

Johann Heinrich von Thunen’s contributions to the problem of the commons - hidden in an 1831 article about urban agriculture (Thunen 1831b) and in an unpub­lished manuscript (see Nellinger 2014b) - have been totally neglected until now. It deserves to be mentioned that he published his ideas about the core problem of the commons two years earlier than William Forster Lloyd. He not only presented the correct allocation criteria for the open access and the regulated scenario but addition­ally developed a framework on (1) how to obtain the maximal resource rent through an auction system - drafting the first demand table; (2) how to redistribute the gains to the communal property owners - developing an adequate compensation mechanism; and (3) how to establish this institutional innovation democratically - thereby anticipat­ing important elements of Elinor Ostrom’s common property rights framework (1990: 182).

A 60-page manuscript on monetary questions written by Thunen (1823-50: 35-95) has been discovered recently (see Nellinger 2014a). It contains an algebraic equation of exchange, analyses the interaction between the monetary interest rate and the rate of return on real capital and provides a synthesis of an extended quantity theory and the production cost theory of money. Thunen’s monetary theory includes important elements foreshadowing the development in monetary economics in the late nineteenth and the early twentieth century mainly influenced by contributions of Irving Fisher, Knut Wicksell and John Maynard Keynes.