Nicholas Kaldor on Adam Smith and Allyn Young

ABSTRACT

Nicholas Kaldor was much influenced by the Smith-Young view of increasing returns. The objective of this paper is to critically examine Kaldor’s interpretation of Smith and Young. In particular, five questions are addressed: (1) Does Smith’s Wealth of Nations have nothing much to contribute in terms of disequilibrium theory or increasing returns after the middle of chapter four? (2) Did Smith and Young have a sectoral view of increasing returns in the sense that they saw increasing returns being confined to manufacturing only? (3) Does the Youngian growth mechanism need to be supplemented with Keynesian aggregate demand so that growth does not fizzle out? (4) What are the important policy differences between Kaldor and the Smith-Young analysis of increasing returns? (5) Finally, what explains Kaldor’s interventionist bent of mind and his dirigiste approach to policy making?     

Welfare,competition, specialization and growth

In this paper we consider a model of horizontal differentiation with a quite general production function and derive the closed form solutions for the level of the variables in the decentralized economy and in the social planner case. This enables us to analyze how consumers’ welfare varies in terms of the degree of competition and the degree of returns to specialization. We find that welfare is increasing in the degree of returns to specialization both in the market economy and in the centralized economy and the decentralized economy's welfare is a bell-shaped function of the degree of competition.     

Can sustained economic growth and declining population coexist?

Most of the developed countries have been experiencing sub-replacement fertility. This leads to worries over the sustainability of economic growth in these countries. Given this concern, we ask the following questions: Is there a force that would allow economic growth and declining population to coexist? Is there a mechanism that could reverse the decline in fertility? We argue that returns to human capital in production provide the key to understanding this relation. Our theoretical framework predicts that, when the degree of increasing returns to human capital in traditional production technologies falls, advanced economies switch their productive efforts from labor-oriented technologies that require a constant creation of young workforce toward human capital-oriented technologies that support an ageing population. We call this shift the “endogenous efficiency-augmenting mechanism”. This suggests that sustained economic growth and a declining population can coexist in the long run. Finally, we compare our model against the data and find: (i) The degree of increasing returns to human capital has been falling over time throughout the world along with population growth rates. (ii) Increasing returns to human capital and population growth rates are positively correlated. (iii) Predictions of our model are consistent with what the data reveal.     

Regulated Competition under Increasing Returns to Scale

In the classical models of regulation economics, a mechanism that secures truthful revelation involves paying a subsidy to the firm. In this paper, we investigate whether it is possible to create a regulatory mechanism under a no‐subsidy constraint that induces the firm to report its private information truthfully. We consider a number of firms operating under regulated competition and with increasing returns to scale technology. It is shown that in equilibrium each firm chooses to report truthfully without receiving any subsidy. The use of competition may give rise to an efficiency loss due to the increasing returns to scale. However, we show that our mechanism may still be better, from a social welfare point of view, than the case of monopoly regulation that involves no subsidy.     

Economies of scale in Norwegian electricity distribution: a quantile regression approach

In this article, we investigate scale economies in Norwegian electricity distribution companies using a quantile regression approach. To the best of our knowledge, this is the first attempt to apply this estimation technique when analysing scale economies. We estimate the cost elasticities of the two output components: network length and number of customers, to calculate returns to scale. Our results show large potential of scale economies, particularly for the smallest companies. We also find that returns to scale is increasing over time. These findings have important implications for policymakers when they are deciding the structure of the industry in the future.     

Asset price volatility in a nonconvex general equilibrium model

Summary. Asset prices and returns are known to vary significantly more than␣output or aggregate consumption growth, and an order of magnitude in excess of what is justified by innovations to fundamentals. We study excess price volatility in a lifecycle economy with two assets (claims on capital and␣a public debt bubble), heterogeneous agents, and increasing returns to financial intermediation. We show that a relatively modest nonconvexity generates a set valued equilibrium correspondence in asset prices, with two␣stable branches. Price volatility is the outcome of an equilibrium selection mechanism, which mixes adaptive learning with “noise”, and alternates stochastically between the two stable branches of the price correspondence. Received: March 19, 1998; revised version: June 2, 1998     

Malmquist and Törnqvist productivity indexes: returns to scale and technical progress with imperfect competition

Caves, Christensen and Diewert proposed a method for estimating a theoretical productivity index for a firm using Törnqvist input and output indexes, augmented by exogenous estimates of local returns to scale. However, in order to implement their method, they assumed that the firm maximized revenue in each period, conditional on the observed input vector in each period, taking output prices as fixed. This assumption is not warranted when there are increasing returns to scale. Thus in the present paper, it is assumed that the firm solves a monopolistic profit maximization problem when there are increasing returns to scale and the results of Caves, Christensen and Diewert are modified in accordance with this assumption.     

Production Function Geometry With "Knightian" Total Product

Abstract: Authors of principles and price theory textbooks generally illustrate short-run production using a total product curve that displays first increasing and then diminishing marginal returns to employment of the variable input(s). Although it seems reasonable that a temporary range of increasing returns to variable inputs will likely occur as variable inputs are added to a set of fixed ones. This proposition implies an isoquant diagram that is not a familiar one in text-books. The authors examine a linearly homogeneous production function conforming to the textbook case and construct its isoquant diagram. They then use a geometrical proof attributable to Geoffrey Jehle (2002) to demonstrate that, in general, isoquants must have, outside the traditional ridge lines, a range where they are convex toward those (MP = 0) ridge lines and another range where they are concave toward them if there are short-run increasing, then diminishing, marginal returns. The authors suggest how this issue might be presented to students.     

Elementary results on solutions to the bellman equation of dynamic programming: existence,uniqueness, and convergence

We establish some elementary results on solutions to the Bellman equation without introducing any topological assumption. Under a small number of conditions, we show that the Bellman equation has a unique solution in a certain set, that this solution is the value function, and that the value function can be computed by value iteration with an appropriate initial condition. In addition, we show that the value function can be computed by the same procedure under alternative conditions. We apply our results to two optimal growth models: one with a discontinuous production function and the other with “roughly increasing” returns.     

Increasing returns and unsynchronized wage adjustment in sunspot models of the business cycle

A challenge to models of equilibrium indeterminacy based on increasing returns is that required increasing returns for generating indeterminacy can be implausibly large and rise quickly with the relative risk aversion in labor. We show that unsynchronized wage adjustment via a relative wage effect can both lower the required degree of increasing returns for indeterminacy to a plausible level and make it invariant to the relative risk aversion in labor. Consequently, indeterminacy and sunspot-driven fluctuations can emerge for plausible increasing returns regardless of the relative risk aversion in labor. Our model generates reasonable dynamics in terms of matching the business cycle, and sunspot shocks become more important with labor market friction.     

Increasing returns to scale and productive systems

We consider an economy in which some producers may have nonconvex technologies, in particular they may operate under increasing returns to scale. These producers constitute the I-part of the economy. The prices of all goods and the target supply of the I-part are supposed to be given. Each producer in the I-part produces a certain output in a cost-minimizing way. There is a planning board which has to find decentralizing (gross) output levels for the producers in the I-part such that the net output equals target supply. The existence of such output levels is proven under a productivity assumption which includes the case of strongly increasing returns to scale as well as productive Leontief systems.     

Increasing Returns,Learning-By-Doing And Neural Networks ∗

In this paper we draw an analogy between the process of learning-bydoing and the learning process which develops in a neural network context. The bridging tool we refer to is a dynamic production function whose only variable input is labour. By concentrating on the ‘neural network production function’ we show that the learning process can lead to increasing returns. The simulations show that when learning is characterized by an upper limit. returns are increasing for some time, while in the long run they go back to the level where they are constant.     

Economies of scale in the Australian tourism industry

The measurement of economies of scale in the tourism industry has not been done to this point, as tourism is not a specific industry according to international statistical standards. Among many industries related to tourism, four sectors (accommodation, transport, retail trade and recreational services) across six states and two territories from 1997 to 2007 are studied as they contribute nearly 70% of tourism output in Australia. By comparing regression results from the Cobb–Douglas (C–D) production function and the translog production function, we find that there is evidence of increasing returns in transport, retail trade and recreational services at the industry level. However, accommodation is characterized by constant returns to scale at the industry level. As accommodation is responsible for the biggest share of tourism output, this suggests that overall the tourism sector is not characterized by increasing returns. We also find that the degrees of returns to scale from the C–D and translog production functions are different and that the imposition of input share also influences the empirical results. Both of these factors stress the importance of model specification to the measurement of economies of scale.     

Existence of solutions in continuous-time optimal growth models

This paper studies the existence of solutions in continuous time optimization problems. It provides a theorem whose conditions can be easily checked in most models of the optimal growth theory, including those with increasing returns and multi-sector economies.      

Increasing returns to scale and the reverse flexible accelerator

We show that the flexible accelerator principle characterizes optimal investment behavior only when the firm's technology exhibits decreasing returns to scale throughout. When there are increasing returns we show that there is a range in which investment increases as the capital stock increases towards its long-run equilibrium level.     

Indeterminacy and cycles in two-sector discrete-time model

Summary. We consider a discrete-time two-sector Cobb-Douglas economy with positive sector specific external effects. We show that indeterminacy of steady states and cycles can easily arise with constant or decreasing social returns to scale, and very small market imperfections. This is in sharp contrast with most of the contributions in the literature in which increasing social returns are required to generate indeterminacy. Received: July 31, 2000; revised version: June 5, 2001     

On inferior inputs and marginal returns

An input is inferior if and only if an increase in its price raises all marginal productivities. A sufficient condition for input inferiority under quasi-concavity of the production function is then that there are increasing marginal returns with respect to the other input and a non-positive marginal productivity cross derivative. Thus, contrary to widespread opinion, input “competitiveness” is not needed. We discuss these facts and illustrate them by introducing a class of simple production function functional forms. Our results suggest that the existence of inferior inputs is naturally associated with increasing returns, and possibly strengthen the case for inferiority considerably.     

Increasing returns,entrepreneurship and imperfect competition

We study a simple bilateral oligopoly model in which individual agents, who are initially endowed with capital, decide sequentially (1) whether they want to act as producers (entrepreneurs) or as capital lenders (rentiers) and, then (2) which quantity of capital they would like to borrow or lend, though exchange of capital units against units of the produced good. Production takes place under increasing returns to scale. We show the existence of “natural equilibria”, at which wealthier capital owners become entrepreneurs while the remaining ones decide to be rentiers. We also study the efficiency of equilibria which is shown to increase by replication of the economy, but sometimes to decrease as a consequence of wealth redistribution.We thank an anonymous referee for his insightful comments     

Aumann-Shapley prices as a scarf social equilibrium

Considered are economies with a single output (a single consumption good) which is produced from l inputs by means of an increasing returns to scale production function f. We show that for quasi-concave and homogeneous functions f of degree r ? 1, the Aumann-Shapley prices constitute a simple Scarf Social Equilibrium. Put differently, Shapley value of the associated atomless game is in the core of that game. Such is not the situation, however, in the more general case when f exhibits increasing returns to scale (but in homogeneous).     

基于分工和报酬递增的经济增长理论演进

文章对分工、报酬递增和经济增长相关理论的演进进行了梳理和总结.古典经济增长理论奠定了思想基础.其中,斯密理论是通过拓展新的分工实现内生和自我持续增长理论的基础;马克思关于分工形式的划分推进了对于报酬递增机制的认识;杨格开创了分工、报酬递增和经济增长的动态分析思路.内生增长理论以技术进步、知识资本和人力资本积累促进经济增长为核心,将分工和技术进步、知识积累紧密联系起来,以分工为重要分析框架论证报酬递增和长期经济增长的实现,吸收和发展了分工理论.内生增长理论和相关模型分别依循由古典经济学开创的两种分工观进行分析,对分工、报酬递增和经济 增长的相关理论和模型进行了重要扩展和充实.