Giuseppe Freni

On the Mitra-Wan Forest Management Problem in Continuous Time

The paper provides a continuous-time version of the discrete-time Mitra-Wan model of optimal forest management, where trees are harvested to maximize the utility of timber flow over an infinite time horizon. The available trees and the other parameters of the problem vary continuously with respect to both time and age of the trees, so that the system is ruled by a partial differential equation. The behavior of optimal or maximal couple is classified in the cases of linear, concave or strictly concave utility, and positive or null discount rate. All sets of data share the common feature that optimal controls need to be more general than functions, i.e. positive measures. Formulas are provided for golden-rule configurations (uniform density functions with cutting at the ages that solve a Faustmann problem) and for Faustmann policies, and their optimality/maximality is discussed. The results do not always confirm the corresponding ones in discrete time.

A Ricardian Model of Forestry

This paper provides a continuous-time �Ricardian� model of forestry, where, in response to an increase in timber demand, forest cultivation is progressively intensified on the most fertile lands and/or extended to less fertile qualities of lands. It is shown that, at a given level of the rate of interest, a set of �break-through timber prices� gives the order of fertility (i.e., the order in which the different qualities of land are taken into cultivation) and that, for each land, prices of standing trees are positive above a �threshold timber price�. Since, for each land, the break-through price is higher than the threshold price, Ricardo is shown to be right: a higher demand for timber could simply raise those components of the landlord compensation which are not rent.

The Construction of Long-Run Market Supply Curves: Some Notes on Sraffa’s Critique of Partial Equilibrium Analysis

The 1925 paper by Piero Sraffa, ‘On the relations between cost and quantity produced’, originally published in Italian in Annali di Economia as ‘Sulle relazioni fra costo e quantita prodotta’, proposes a thorough and devastating criticism of Marshallian economics based on the method of partial equilibrium analysis of competitive prices. Just five years later Sraffa has no hesitation in concluding his contribution to the 1930 Economic Journal Symposium on Increasing Returns and the Representative Firm with the advice that Marshall’s Theory ‘should be discarded’ (Sraffa, 1930, p. 93). Note that Sraffa will never reconsider this issue, at least in published contributions, with the notable exception of a very brief hint in the Preface of his 1960 book, Production of Commodities by Means of Commodities.