Capital, Time and Transitional Dynamics

Harald Hagemann, Roberto Scazzieri

• Publisher: Routledge
• Year: 2009
• Print ISBN: 9780415588638
• eBook ISBN: 9781134158027
• Edition: 1
• Topic: Business
• Subtopic: Business General
• Index: Business

In the words of Robert M. Solow traverse analysis "is the easiest part of skiing, but the hardest part of economics". The aim of this volume is to assess the state and scope of modern traverse analysis as it had been initiated by John Hicks in his pioneering contribution Capital and Time (1973). The analysis of an economy which originally had been in a growth equilibrium which was disturbed by technical progress is one of the most challenging problems in economics. This book takes Hicks' work as the point of departure for theoretical work on the macroeconomic theory of capital dynamics along transition non-steady state paths

The original contributions in this volume explore the manifold theoretical roots of traverse analysis in classical and post-classical literature, its features as a specific method of economic dynamics, and its applications in a variety of fields from monetary economics to development and international economics. The essays thereby focus on the ways ahead from Capital and Time that have been suggested and actively pursued by a number of scholars in recent years. Its central theme is the role of capital structures as critical factors in determining the actual dynamics of any given economic system. This volume is inspired by the belief that this state of affairs is not a satisfactory one, and outlines a new agenda for capital theory. Contributors include Edwin Burmeister, Jean-Luc Gaffard and Heinz Kurz.

1 A retrospective view of Hicks’s Capital and Time: A Neo-Austrian Theory

Edwin Burmeister ¹

1 Introduction

In 1973 Sir John Hicks published Capital and Time: A Neo-Austrian Theory. This was his third book with the word ‘Capital’ in its title, the first being his classic Value and Capital (1939) and the second being Capital and Growth (1965). It departed significantly from his earlier work by assuming that the technology of an economy consisted of a set of neo-Austrian production processes in which a time sequence of inputs {a_t} produces a time sequence of outputs {b_t}.

In June 1974, I published a review article in the Journal of Economic Literature entitled ‘Synthesizing the neo-Austrian and alternative approaches to capital theory: A survey’, using Hicks’s book as a filter to select a list of topics for discussion.² Now, with almost 30 years of hindsight, I will revisit some of the problems that, in my view, remain both unsolved and important.

First, however, I will point out that reading Hicks in 2007 is as much a delight as it was in 1973. His style is refreshingly old-fashioned, and focused on answering economic questions with mathematics used only as a means of achieving those answers. For example, Hicks’s view of the von Neumann model is that it is logically elegant, but that ‘[…] the categories with which it works are not very recognizable as economic categories; so to make economic sense of its propositions translation is required. One has got so far away from the regular economic concepts that the translation is not at all an easy matter’ (Hicks, 1973, p. 6).

But, as I shall argue below, this bias in favour of regular economic concepts comes at the cost of generality. As a result the primary contributions of Capital and Time: A Neo-Austrian Theory are pedagogical. Hicks’s elegant examination of simple problems serves to deepen our economic understanding of many capital theory principles such as, for example, the duality between the factor-price frontier and the optimal transformation frontier. Yet one is left with a sense of unease that treacherous territory may lie just beyond these simple examples.

2 The Hicks neo-Austrian technology and truncation

The Hicks technology is based on the Austrian tradition of Böhm-Bawerk, Wicksell, and Hayek in which a flow of inputs over time produces output at a later point in time. Hicks generalizes this idea so that a production process consists of a time sequence of inputs {a_t} that produces an associated time sequence of outputs {b_t}. The Hicks neo-Austrian technology is the set of all such feasible production processes.

It is assumed that homogeneous labor is the only input and that there is only one type of homogeneous output, which Hicks identifies simply as goods, although I prefer to interpret output as the quantity of a single type of consumption goods (ibid., p. 37). Using this single consumption goods as the numeraire, b_t measures both the physical quantity and the value of output. Then letting w_t denote the real wage rate (in terms of consumption goods) during period t, a production process yields a net output stream given by

(1.1)

More than one production process may be used during any time period, and over time the economy may or may not converge to a steady-state equilibrium in which one most profitable production process is employed.

Hicks also assumes that a_t > 0 and b_t = 0 for t = 0, 1, …, m − 1. He then defines the construction period as the m time periods t = 0, 1, …, m − 1 during which labor inputs are employed, but there is no output of consumption goods (ibid., p. 15). It suffices here to point out the obvious fact that this technology is extraordinarily simple; see Burmeister (1974) for some details. However, it does enable Hicks to focus on some of the economic questions that arise from the pure role of time, without, for example, having to deal with the complications of heterogeneous inputs and outputs.

There is often some ambiguity in discrete-time models because the end of one time period coincides with the beginning of the next. To avoid inconsistencies in the Hicks neo-Austrian model, one can interpret labor input for a production process as the number of workers employed at the beginning of period t, who then work for the whole period and are paid a real wage rate at the end of period t. The output of consumption goods, on the other hand, is realized only at the end of period t. The reasons for these timing conventions are explained elsewhere (ibid., pp. 417–18) and need not concern us here.

Now assume that the real-wage rate is constant, w_t = w, and also that there is a constant per period (Hicks uses weeks) real rate of interest (in terms of consumption goods) denoted by r. Then the capital value of the process at the beginning of period 0 as

(1.2)

where the interest rate factor is R ≡ 1 + r. Note that k₀ is simply the present discounted value of the production process. Hicks assumes that capital markets are in equilibrium so that k₀ = 0 (ibid., p. 32).³ Note that k₀ = 0 is equivalent to a zero-profit condition when all inputs and outputs are measured in terms of discounted prices.

More generally, the capital value of the process at the beginning of any time period t is

(1.3)

so that

(1.4)

Thus the capital value of the p...

Table of contents

• Cover Page
• Title Page
• Copyright Page
• List of Figures
• List of Tables
• List of Contributors
• Preface and Acknowledgements
• Capital structure and economic transitions: An introductory essay
• 1 A retrospective view of Hicks’s Capital and Time: A Neo-Austrian theory
• 2 Hicks’s neo-Austrian theory and Böhm-Bawerk’s Austrian theory of capital
• 3 Traverse analysis and methods of economic dynamics
• 4 Hicks’s traverse analysis: From Capital and Growth to Capital and Time
• 5 Technical change, vertical and horizontal rigidities: A neo-Austrian approach
• 6 Simulation of the full employment traverse of Capital and Time
• 7 Traverse, division of labor and emerging structures
• 8 Hicks’s traverse in a small open economy
• 9 From traverse to out-of-equilibrium processes of change