Will the true Francesco Ferrara please stand up?

Abstract

This note suggests that Fazio's re-interpretation of Ferrara's discussion of distribution as a bilateral monopoly is incorrect. A more natural formalization of the work by Ferrara is proposed.

Keywords:

• Cost of reproduction
• distribution
• bilateral monopoly
• Ferrara
• Fazio

Acknowledgements

The author wishes to thank two unknown referees for their comments.

Notes

1 For Ferrara's life and his contribution to economics, see the bibliography reported by Fazio. Here it will be sufficient to point out that Ferrara was the inventor of the cost of reproduction doctrine, an interpretation of the theory of value at one time popular in Italy.

2 Notice that the assumptions made by Fazio on technology are different from those made by Ferrara, who, quite reasonably, does not claim that returns to scale are constant in farming.

3 Here and below it is assumed that all the conditions required to obtain meaningful solutions are met.

4 The first formula after (9) in the article by Fazio is stated incorrectly. It should read: f_K(L, C) −[f(L, C)/(L+C)] = 0.

5 Fazio (2009: 260–1) recalls a statement by Ferrara about the existence of ‘… two causes, like two rigid bars, … fixed around the [sic!] capital and confine it inside specific borders. On one side, it is not possible to ask from the worker more than he can produce by himself … On the other side, it would not possible, even at the right price, to offer him more than it would be tolerable so that his natural ability to produce would improve …’ and then ‘Introducing this reasoning, Ferrara precedes the main elements and analytical solutions adopted by Edgeworth … and Bowley …’. All this is irrelevant. The first ‘bar’ does not even exist in a setting in which the production function for farming has been specialized, as Fazio has done. The second requirement makes sense only in a model in which quantities rather than prices are emphasized.

Again according to Fazio, ‘… Ferrara ignores completely the computation of multipliers, although these can be calculated very easily’ (2009: 256). A multiplier is defined as the derivative of a reduced form with respect to one of the exogenous variables. Since L is a constant rather than an exogenous variable, the computation of multipliers is impossible since in the system under consideration there are no exogenous variables.

6 There are two definitions of bilateral monopoly (see Hicks 1935: 16–18). Fazio compares his model that meets one definition with the model by Cournot that meets the other.

7 The translation from Italian is mine (A.G.).

8 It should pointed out, but it is rather obvious, that it is possible to derive Z _L and Z _C from the model by Fazio and to derive R and W from Equations (7) –(10).