The spatial structure of production with a Leontief technology

The structure of the optimal spatial pattern of production is studied when there are interdependencies among production units which can be described by a Leontief technology, and when there is a single marketplace of final demand, the CBD. Transportation cost is proportional to distance. It is shown that the various goods are produced in rings which can be ranked by distance from the CBD independently of the levels of final demand. Furthermore shipment of goods for meeting intermediate and final demand can only be in the direction of the CBD and no shipment of goods towards the periphery can occur. A finite algorithm is given for the construction of the optimal pattern and for determining a system of f.o.b. prices and land rents which sustain it as a competitive equilibrium.     

Age-specific dynamic labor demand and human capital investment

To study the optimal age-specific labor demand and human capital investment at the firm level we extend the standard dynamic labor demand model by introducing ‘age’ as a second dynamic variable and distinguish between two types of workers: ‘low skilled’ and ‘high skilled’. Applying an age-structured optimal control model we derive qualitative features of the optimal age-specific hiring and training effort. For the case of a linear revenue and production function we prove that firms do not anticipate changes in adjustment costs in their optimal decisions. This result no longer holds if a nonlinear revenue or production function is considered.     

A Hotelling model with a ceiling on the stock of pollution

Environmental agreements such as the Kyoto Protocol aim to stabilize the amount of carbon in the atmosphere, which is mainly caused by the burning of nonrenewable resources such as coal. We characterize the solution to the textbook Hotelling model when there is a ceiling on the stock of emissions. We consider both increasing and decreasing demand for energy. We show that when the ceiling is binding, both the low-cost nonrenewable resource and the high-cost renewable resource may be used jointly. A key implication is that if energy demand were to decline in the long run, we may supplement energy supply through ‘clean’ renewables to meet the environmental standard, but then revert back to using only ‘dirty’ fossil fuels in the future when the ceiling has become non-binding. That is, the much heralded societal ‘transition’ to clean energy resources may be short-lived.     

Two planar facility location problems with high-speed corridors and continuous demand

The planar minisam (‘median’) and minimax (‘center’) facility location problems are examined under the assumptions that: demand is continuously and uniformly distributed: the L₁ (right-angle) metric is in use; and the planar region is traversed by a high-speed corridor (highway) running parallel to one of the directions of travel. For the minisum problem in a rectangular region, it is shown that, for any combination of problem parameters, there are only two candidate points in the region for the optimum location of the facility. This is also shown to be true for any convex and symmetric planar region. For the minimax problem in a rectangular region, there are only three candidate points for the optimal location. Some extensions and conjectures for the minisum problem involving more than one highway are also discussed.     

On the convergence of Bayesian posterior processes in linear economic models Counting equations and unknowns

I propose a technique, counting ‘equations’ and ‘unknowns’, for determining when the posterior distributions of the parameters of a linear regression process converge to their true values. This is applied to examples and to the infinite-horizon optimal control of this linear regression process with learning, and in particular to the problem of a monopolist seeking to maximize profits with unknown demand curve. Such a monopolist has a tradeoff between choosing an action to maximize the current-period reward and to maximize the information value of that action. I use the above technique to determine the monopolist's limiting behavior and to determine whether in the limit it learns the true parameter values of the demand curve.     

Dynamic programming for non-additive stochastic objectives

We derive the existence of an optimum and the techniques of dynamic programming for non-additive stochastic objectives. Our key assumption for non-negative objectives is that asymptotic impatience exceeds asymptotic ‘mean’ growth, where ‘mean’ growth is derived not only from intertemporal inelasticity and the random return on investment but also from the curvature of the non-additive stochastic aggregator (i.e. the ‘certainty equivalent’). We provide broad families of new, interesting, and tractable examples. They illustrate that ‘mean’ growth can exist even when the distribution of returns has unbounded support, that power discounting often implies infinite asymptotic impatience, and that non-positive objectives are easily handled with few restrictions on growth.     

Self-organized criticality in evolutionary systems with local interaction

This paper studies a stylized model of local interaction where agents choose from an ever increasing set of vertically ranked actions, e.g. technologies. The driving forces of the model are infrequent upward shifts (‘updates’), followed by a rapid process of local imitation (‘diffusion’). Our main focus is on the regularities displayed by the long-run distribution of diffusion waves and their implication on the performance of the system. By integrating analytical techniques and numerical simulations, we come to the following two main conclusions. (1) If non-coordination costs are sufficiently high, the system behaves critically, in the sense customarily used in physics. (2) The performance of the system is optimal at the frontier of the critical region. Heuristically, this may be interpreted as an indication that (performance-sensitive) evolutionary forces induce the system to be placed ‘at the edge of order and chaos’.     

Thy neighbor’s jobs: geography and labor market dynamics

This paper develops three explanations for the extent of correlation between neighboring geographic areas’ economic outcomes. Export-oriented firms in neighboring counties might independently produce similar goods, or might be linked directly through the production of intermediate inputs. In either case, counties are exposed to similar demand shocks. Finally, regions share markets for goods and services that are both produced and consumed locally. Empirical results suggest that much of the ‘risk’ associated with economic decline in neighboring regions can be attributed to industrial similarity rather than direct dependence of jobs in one area on jobs in another.     

Social dumping and relocation: is there a case for imposing a social clause?

Public opinion in Europe seems worried about the relocation of production plants toward low wage countries often accused of practicing ‘social dumping’. To reduce the incentives for relocation trade unions proposed the adoption of ‘social clauses’ protecting domestic markets from commodities produced in countries where minimal labor condition are not met. We analyze the effects of the adoption of a social clause in a vertically differentiated Bertrand duopoly. We assess how such a policy affects firms’ relocation decisions in order to be able to assess its welfare implications. We also characterize the optimal social clause policy, both under domestic welfare maximization, and from an efficiency point of view. While we show that a social clause policy cannot be dismissed on domestic (or world) welfare grounds, its case is weaker the higher is the domestic wage and the lower is the foreign wage.     

Approximation of convex preferences

It is shown geometrically that a monotone concave preference order can be approximated by orders representable by a concave utility function. This is applied to proving that preferences with ‘desirable’ properties (such as inducing smooth excess demand functions, analyticity, strict convexity) are dense.     

Accessibility of optima in pure exchange economies

Assuming differentiable monotonicity and differentiable convexity of utility functions, we show that if y and z are allocations of a pure exchange economy with z optimal and preferred to y by every agent, then there is a trade curve of finite length from y to z. We make no assumption on utility functions designed to ‘keep away from the boundary’. The conclusion need not hold if z is not optimal, unless a special boundary condition is assumed and (l, m) ≠ (2, 2).     

On games without side payments arising from a general class of markets

The class of games without side payments obtainable from finite trader markets having possibly infinite dimensional commodity spaces, individual compact, convex consumption and production sets, and concave upper-semicontinuous utility functions is considered. It is shown that these market games are precisely the totally balanced games. In fact, each totally balanced game is shown to have both a finite commodity representation and an infinite commodity ‘simple’ representation.     

When does coordination pay?

In a continuous-time model of two symmetric open economies, with a floating exchange rate, we find that the pay-off to macroeconomic policy coordination depends systematically on how heterogeneous is their inflation experience. While monetary policy coordination improves welfare in handling a common rate of underlying inflation, it exacerbates the ‘time consistency’ problem arising when there are differences (as is illustrated diagrammatically). Since the principle of ‘certainty equivalence’ applies to time-consistent policy in linear quadratic models, we are also able to give a stochastic interpretation of the deterministic results.     

Stability and efficiency from a Neo-Keynesian viewpoint

This paper raises once more the Keynesian challenge of the classical doctrine that an unguided market economy has a natural tendency towards optimal employment of resources. By means of a simple macromodel, we show that if quantity expectations are incorporated into the Walrasian model, then it is no longer generally true that the ‘invisible hand’ leads the economy to Walrasian equilibrium. Instead, it may lead the economy to a kind of Keynesian equilibrium in which the firms' sales expectations constitute a binding constraint on production. Moreover, while Pareto optimum is unstable and hence unattainable in our model, a ‘second-best’ optimum among stable equilibria exists and requires a public sector. Accordingly, a trade-off between efficiency and other policy aims occurs only at tax rates above the positive tax rate in optimum     

Developing a typology of organisational forms of cooperative purchasing

This paper develops a typology for purchasing groups. In the typology, five main forms of cooperative purchasing are distinguished based on seven main dimensions. The forms are positioned in a matrix according to two distinguishing dimensions. These two dimensions are the ‘influence by all members on the group activities’ and the ‘number of different group activities’. Underlying the two-dimensional matrix, there are five other dimensions that do not distinguish all forms from each other, but further detail the forms of cooperative purchasing. The typology can serve as a guideline for purchasing groups when a suitable organisational form needs to be chosen. In a suitable form, the dimensions of a group fit together. For all groups, it is recommended to find this best fit. This is something in which the typology may help. The paper concludes by emphasising the importance of clearly defining and positioning studied forms, because different forms imply different research models and have different advantages, disadvantages, and critical success factors.     

The proportion of blocking coalitions in atomless economies

In this paper we investigate the number of coalitions that block a given non-competitive allocation. In an atomless economy with a finite number of types we identify coalition with its profile. Considering profiles π that represent coalitions with the same proportions of types as in the whole society, we prove that there is a ball B_π with π as its center so that ‘almost half’ of the profiles in B_π are blocking. This result is an analogous result to that of Mas-Colell (1978) who dealt with large finite markets.     

Economic dynamics of reservoir sedimentation management: Optimal control with singularly perturbed equations of motion

We analyze the economic dynamics of reservoir sedimentation management using the hydrosuction-dredging sediment-removal system. System dynamics depend on two interdependent hydraulic processes evolving at different rates. The accumulation of water impounded in the reservoir evolves on a ‘fast’ time scale, while the loss of water storage capacity to trapped sediments evolves on a ‘slow’ time scale. We formulate a multidimensional optimal control problem with singularly perturbed equations of motion to accommodate the disparate time scales. We apply singular perturbation methods to approximate (via polynomial series expansion) a ‘slow’ manifold reducing multi-dimensional solution space to the single-dimensional subspace confining long-term dynamics.     

Locally stable price mechanisms

This paper develops necessary conditions for a price adjustment mechanism to achieve local stability at regular competitive equilibria. Two principal questions are: how closely must a locally stable mechanism be tailored to particular excess demand functions, and can any such mechanism be interpreted as a market adjustment process. In response to the first question, a variant of the (local) Newton method, termed the ‘orthogonal Newton method’ is shown to require, in a dimensional sense, the minimal information about excess demand functions. The second question is answered in the negative by proving the non-existence of any locally stable mechanism with the property that the price of any given commodity is not changed when its own market is in equilibrium. These and other results are obtained by using convergent price paths to generate a homotopy between the adjustment dictated by the mechanism and the actual direction of the equilibrium.     

The Delphi technique as a forecasting tool: issues and analysis

This paper systematically reviews empirical studies looking at the effectiveness of the Delphi technique, and provides a critique of this research. Findings suggest that Delphi groups outperform statistical groups (by 12 studies to two with two ‘ties’) and standard interacting groups (by five studies to one with two ‘ties’), although there is no consistent evidence that the technique outperforms other structured group procedures. However, important differences exist between the typical laboratory version of the technique and the original concept of Delphi, which make generalisations about ‘Delphi’ per se difficult. These differences derive from a lack of control of important group, task, and technique characteristics (such as the relative level of panellist expertise and the nature of feedback used). Indeed, there are theoretical and empirical reasons to believe that a Delphi conducted according to ‘ideal’ specifications might perform better than the standard laboratory interpretations. It is concluded that a different focus of research is required to answer questions on Delphi effectiveness, focusing on an analysis of the process of judgment change within nominal groups.     

Aggregate stock market behavior and investors’ low risk aversion

This paper studies whether investors’ high risk aversion can be avoided in a representative-agent model that is able to explain aggregate stock market behavior in the US financial market. We present a consumption-based asset pricing model with a representative agent who has a ‘catching up with the Joneses’ preference to show that high risk aversion can be avoided in a representative-agent model that can help explain many of the empirically observed properties of the aggregate stock market return, including the equity premium and risk-free rate puzzles, the predictability of long-horizon stock returns, and the ‘leverage effect’ in return volatility.