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.     

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).     

Increasing returns and the share economy

Under imperfect competition, profit maximization by firms results in the market price exceeding the marginal cost of production; Weitzman terms this “excess supply” Weitzman wishes to replicate in the cost function (in terms of labor) the properties of the revenue function (in terms of output), thus generating “excess demand” for labor. A revenue-sharing scheme will achieve this if and only if there are decreasing returns to scale. Hence increasing returns apparently play no role in Weitzman's analysis.     

Pricing inputs to induce efficient Make-or-Buy decisions

We investigate input pricing regimes that induce efficient Make-or-Buy decisions by entrants when there is constant returns in the production of the input(s) and simultaneous noncooperative price competition in downstream retail markets. Necessary and sufficient conditions for efficient Make-or-Buy decisions are derived. The necessary condition shows that input prices are relevant for Make-or-Buy decisions except under restrictive and often unverifiable assumptions on the demand structure, and that the least informationally-demanding way to ensure efficient Make-or-Buy decisions is to price inputs at marginal cost provided changes in the entrant’s cost have a “normal” effect on the entrant’s profit. The conditions also show that pricing the incumbent’s input at the entrant’s marginal cost always ensures efficient Make- or-Buy decisions. The extent to which input prices can depart from marginal cost while still inducing efficient Make-or-Buy decisions increases with the efficiency differential between the incumbent and entrant and with the demand displacement ratio.      

Technical and scale efficiencies of meat goat farms in the USA

This study determines i) scale and technical efficiencies, ii) marginal productive contributions for inputs and outputs and iii) efficiency drivers of meat goat farms in the USA. We estimate an input distance function (IDF) using a stochastic production frontier (SPF) technique. The average technical efficiency (TE) for the USA meat goat whole farm was 0.74. The operator education level, percentage of annual net farm income from the goat operation, regional differences and holding of an off farm job are the efficiency drivers of USA meat goat farms. We find increasing returns to scale (RTS) for USA meat goat farms. Our results suggest that USA meat goat farms can be scale efficient if their optimal size of operation is greater than approximately 64 goats or greater than 40 breeding does. Empirical Monte Carlo (MC) simulation techniques show the consistency of finite-sample properties for the input distance function.     

“Ideas” driven growth: the OECD evidence

This paper estimates the parameters of the ideas production function crucial to recent ideas-driven growth models. Using U. S. patents granted to residents in OECD countries to generate the stock of commercially used ideas, we provide evidence for two main findings. First, at the level of the production of ideas, we find evidence of increasing returns to scale in the stock of ideas and number of researchers, but marginal decreasing returns in each one of these factors. Second, we provide evidence of the association between ideas growth and economic growth for the OECD as a whole in the long run.JEL Classification: 031, 040The author would like to thank the helpful comments made by two anonymous referees, and by the editor, of the PEJ. The helpful discussions with Professor Mário Rui Silva are grateful acknowledged, too.     

An econometric analysis of skewed productivity outcomes

An econometric model is developed to help explain uncertain yields from processes that generate inherently skewed outcomes. The yield is modeled as the interaction of potential and effort functions, where potential represents maximum yield that would be observed if the effort was infinite. The potential function is determined by some endogenous factors, and the effort function is determined by an exogenous input and allows for increasing and decreasing marginal returns to effort. A non-linear model incorporating these features is theoretically derived and empirically tested using data on outcomes from sales-tax audits. The results document the superiority of this model in capturing the underlying relationships, and provide a better out-of-sample fit to the data compared to two OLS models. The proposed model can be applied in various business and non-business settings.     

Medical Expenditures and Health Status in Australia: A Story of Increasing or Decreasing Returns?

We use a three‐equation model to estimate a health production function for Australia using population data for 1996. Working at the level of the Statistical Local Area (n= 1335) we match (i) data on private practice medical services (derived from the Medicare scheme), (ii) mortality data derived from the de‐identified unit records produced by the Australian Bureau of Statistics (ABS), and (Hi) social and economic data from the Australian Census of Population and Housing (ABS 1997). We detect strong and statistically significant positive marginal effects of medical expenditure on health status as well as increasing returns. These findings are remarkably different from those of US health production studies, which have tended to lend support to the hypothesis of ‘flat‐of‐the‐curve (that is, zero marginal product) medicine’. Moreover, our conclusions are in stark contrast to those produced by Richardson and Peacock (2003, p. 6), who have argued that their econometric work indicates that ‘an increase in the [Australian] doctor supply is associated with increasing mortality’.     

Size and Foreign Ownership Effects on Productivity and Efficiency: An Analysis of Turkish Motor Vehicle and Parts Plants

The levels and interactions of foreign connections and size may be important determinants of plant productivity and efficiency, particularly in a developing country such as Turkey. We explore the productive contributions of foreign ownership (FDI), emphasizing its linkages with plant size and input composition, for plants in the Turkish motor vehicle and parts industry. We evaluate the implications of FDI for overall productivity, input-specific contributions, and returns to scale, using OLS, stochastic production frontier, and quantile (size-specific) regression estimates of a translog production function model. We find significantly higher productivity of plants with foreign ownership, driven by a higher marginal product of labor, particularly for smaller plants. This effect augments the productive contributions of technical progress, capital intensity, and increasing returns to scale. FDI is also associated with a greater productive contribution of imported capital investment.     

Can a larger market foster R&D under monopolistic competition with variable mark-ups?

We study monopolistic competition with symmetric directly additive preferences (generating variable mark-ups) and an endogenous technology choice. Each firm chooses an investment in R&D to decrease its marginal cost. We prove that the equilibrium R&D investment increases with market size (a larger population or trade) only if the price-elasticity of demand is an increasing function. Together with the output levels, such equilibrium investments may be socially excessive or insufficient, depending on whether the elasticity of the subutility is increasing or decreasing. The main implication is that opening up to free trade can foster R&D through variable mark-ups.     

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.     

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.     

Information Processing Hierarchies

This paper characterizes optimal stationary hierarchies based on an information processing model introduced by Radner. We show how the delay, size (number of processors), capacity (the size of each cohort processed), and throughput (frequency of cohort arrival) are related and determine a feasibility frontier in the space of these variables. The structure of efficient hierarchies implementing the points on the feasibility frontier is also specified. These structures are always nonregular; i.e., every agent has subordinates from several different levels. The nature of the long accepted maxim of decreasing returns to scale in management hierarchies is demonstrated. When the production function of the hierarchy is taken to be the number of information items it can process, we find that returns to size and delay are always decreasing in efficient hierarchies, but these variables are complementary in the design problem. Finally, we discuss how the underlying abilities of the processors affect the marginal returns to size and delay. Journal of Economic Literature Classification Numbers: L22, D83.     

Holdup and wage dispersion

This paper provides a search-theoretic model of the labor market, in which large firms hire workers sequentially and wages are bargained with full commitment. The firm's optimal vacancy-posting strategy trades off the fact that a larger size decreases marginal benefits from subsequent jobs, but avoids higher future recruiting costs attributable to the holdup effect. The holdup effect is dominant if the production function is not sufficiently concave, resulting in firm-size wage premium. The equilibrium features wage dispersion both within and between firms. When calibrated to the U.S. data, the extended model accounts for 67%–84% of the observed wage dispersion, among which 13%–27% is attributed to the holdup effect.     

RETURNS TO SCALE IN RETAIL TRADE*

This paper attempts to estimate genuine scale effects in retail trade from a cross section of retail stores in Israel. This is done by estimating a simple production function for several retail branches and employing the faithful old direct Cobb-Douglas structure with value added as output and labor and capital inputs. And indeed despite the well-known peculiarities of the retail industry, a cross section estimation produces “normal” production-function estimates with reasonable input elasticities. The estimates also identify marked increasing returns-to-scale parameters, higher in food and lower in branches less affected by consumer participation and geographical dispersion. These increasing returns may explain a good part of the increase in sales per unit of inputs observed in time series.     

Efficiency in an Economy with Fixed Costs

It is by now well known that in an economy with increasing returns, first-best efficiency may be impossible to attain through an equilibrium concept based on market prices, even if firms are regulated to follow marginal cost pricing. We examine the efficiency issue in a special but important class of economies in which the only source of nonconvexities is the presence of fixed costs. Even in this context, it is possible that none of the equilibria based on marginal cost pricing are efficient (unless additional, strong assumptions are made). We argue that available results on the existence of an efficient two-part tariff equilibrium rely on very strong assumptions, and we provide a positive result using a weak surplus condition. Our approach can also be used to establish the existence of an efficient marginal cost pricing equilibrium with endogenously chosen lump-sum taxes if the initial endowment is efficient in the economy without the production technology.     

Collective Risk Control and Group Security: The Unexpected Consequences of Differential Risk Aversion

We provide an analysis of odds‐improving self‐protection for when it yields collective benefits to groups, such as alliances of nations, for whom risks of loss are public bads and prevention of loss is a public good. Our analysis of common risk reduction shows how diminishing returns in risk improvement can be folded into income effects. These income effects then imply that whether protection is inferior or normal depends on the risk aversion characteristics of underlying utility functions, and on the interaction between these, the level of risk, and marginal effectiveness of risk abatement. We demonstrate how public good inferiority is highly likely when the good is “group risk reduction.” In fact, we discover a natural or endogenous limit on the size of a group and of the amount of risk controlling outlay it will provide under Nash behavior. We call this limit an “Inferior Goods Barrier” to voluntary risk reduction. For the paradigm case of declining risk aversion, increases in group size(wealth) will cause provision of more safety to change from a normal to an inferior good thereby creating such a barrier.     

Estimation of the value of the marginal product of emission in a country where emissions output is regulated — an empirical study

Emissions resulting from the production process can be characterized as use of the elimination and disposal services of the ecological system. Hence, they are use of natural resources and thus an input to production. The present paper discusses an approach to evaluate the returns of these kind of services as a production factor.First, four main types of industrial emission are chosen —SO ₂,CO ₂,NO _xandparticulate matter — and integrated in a Cobb-Douglas production function. With this approach, the production elasticities and the marginal product of these types of emission can be estimated.Based on these results and assuming that marginal product equals price, the demand curve for emission is estimated. With this demand curve the consequences of different kinds of environmental policy are considered. Under further assumptions of optimal behaviour it can be shown that the demand curve for emission is equal to the curve of marginal costs of avoidance (MCA). Thus, the estimates of the demand curves can be considered as estimates of the MCA-curves. Furthermore the price elasticities of these four types of emission are estimated with this approach. The method used in the paper is suggested for calibration of CGE models.     

Another Look at the Radner-Stiglitz Nonconcavity in the Value of Information

This paper revisits the well-known result of R. Radner and J. Stiglitz (1984, in “Bayesian Models of Economic Theory,” Elsevier, Amsterdam) which shows that, under certain conditions, the value of information exhibits increasing marginal returns over some range. Their result assumes that both the number of states and the number of signal realizations are finite, assumptions which preclude most analyses of optimal information acquisition. We provide sufficient conditions that yield this nonconcavity in the value of information in a general framework; the role that these conditions play is clarified and illustrated with several examples. We also discuss the robustness of the nonconcavity result, and the difficulties involved in getting the value of information to be globally concave. Journal of Economic Literature Classification Number: D83.     

A characterization of the normalized restricted profit function

A duality theorem between production functions and normalized restricted profit functions is derived under the assumptions of joint biconvexity and independence of the production possibilities sets. Biconvexity is a natural generalization of the concept of convexity to the case of overall increasing returns which maintains at the same time the conventional property of diminishing marginal rates of transformation (substitution) amongst certain subsets of commodities.Specializing to the twice differentiable, locally strongly convex case, certain identities linking the Hessians of the production function and the normalized restricted profit function are derived. Using these identities, Le Chatelier's principle is demonstrated.