On the Relative Stability and Optimality of Consumption in Aggregative Growth Models

This paper stems from the recent discussion in this Journal between J. C. Liu and K. Kubota [2] and J. K. Sengupta [4]. This discussion was based on part (a) of an earlier paper by Sengupta [3], and concerned certain mathematical manipulations that had been performed there.2 To avoid repetition, we assume that the reader is acquainted with problems, arguments, notation, etc., in the above papers. In what follows we concentrate mainly on part (a) of the Sengupta paper. We argue that the discussants have missed a fundamental point. When the planning horizon is infinite, optimal paths for the Sengupta model do not always exist. Furthermore, when they do exist, we have an analogous situation to that of a static maximization problem with the solution on the boundary of the feasible set. Explicitly, we show that for a> n there exists no optimal programme, irrespective of the level of the initial capital stock, denoted by Ko. Also for a =n and Ko> 0 there exist no optimal paths. For a = n and Ko = 0 an optimal programme does exist, but optimal K(t) = 0 for all t. For a 0, we have optimal K(t) > 0 for t E [0, T), and optimal K(t) = 0 for t > T, where the value of T is determined by certain properties of the optimal paths. Our results imply that calculations of asymptotic rates, comparisons, etc., are redundant, especially when no optimal paths exist. It is well known that when the utility integral, as welfare criterion, does not converge, it does not really make sense to require that its value be maximized. Hence in what follows we order alternative feasible consumption streams employing the Weizsacker-Atsumi (W-A) criterion.3 We shall say that a path is W-A optimal if it overtakes all other feasible paths. Sengupta also refers in [4] to the need of employing the overtaking criterion when the planning horizon is infinite, but he seems to expect that this supports his argument

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• On the Relative Stability and Optimality of Consumption in Aggregative Growth Models

  J C Liu, K Kubota•Economica•1971

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• On the Relative Stability and Optimality of Consumption in Aggregative Growth Models

  Jati K Sengupta•Economica•1964

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