What did Thünen really maximize?

No one can deny the important contributions made by Johann Heinrich von Thunen (1783-1850), a pioneer of the marginal revolution in economics, as an independent discoverer of the marginal productivity theory and as the father of the economics of space. Commemorating the two hundredth anniversary of his birth, Samuelson (1983) analyzed these contributions beautifully and skillfully. Von Thunen is, however, also known by the formula of natural wage inscribed on his grave stone. Classical economists before the marginal revolution explained the wage as the subsistence wage, while modern economists after the revolution emphasized the importance of the labor productivity in their theory of wage. In between, Thunen demonstrated the natural wage as the geometric mean of the subsistence wage and the average product of a laborer. Samuelson, who evaluated Thunen's positivistic economics (the marginal productivity theory and the economics of space) very high, interpreted the natural wage of Thunen as the socially optimal wage from the point of view of the welfare economics, and criticized that it is a major felony and a crime against normative economics.In Negishi (1990), we defended Thunen against Samuelson. Following an interpretation suggested by Yamada (1934), a pioneering study of Thunen in Japan, the natural wage is derived as an equilibrium wage in a competitive stationary economy, which Thunen himself studied in his famous Der isolierte Staat. In other words, we defended the theory of natural wage as a positive theory against Samuelson's criticism which regarded it as a normative theory. To be more decisive, however, as a rejoinder to Samuelson's critical comment that Thunen maximized a strange, irrational social welfare function, we have to argue further that the so-called Thunen's social welfare function itself is a rational, reasonable function, given his own model of a competitive stationary economy. In other words, what Thunen did can be interpreted as an early, pioneering attempt to use the so-called Negishi method, Negishi approach, or Negishi theorem, which is now intensively used for the proof of the existence of a general equilibrium and the numerical calculation of a general equilibrium. See Negishi (1960), Kehoe (1991), Mas-Colell and Zame (1991) and Ginsburgh and Keyzer (1997).