The spatial structure of production with a leontief technology – II: Substitute techniques

The structure of the optimal spatial pattern of production is studied when there are dependencies among production units which can be described by a Leontief technology with substitute techniques, and when there is a single marketplace of final demand, the CBD. Transportation cost is proportional to distance. The various goods are produced in rings. There are a finite number of patterns in which these rings are arranged, and they can be obtained by a finite algorithm. The particular pattern depends on the final demand. Hence there is no ‘non- substitution’ theorem. ‘Reswitching’ of techniques can occur, that is, in an optimal pattern a technique may be operated at large and small distances from the CBD, but not at intermediate distances; this contradicts prevailing beliefs about optimal capital/land profiles.     

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.     

Linear-quadratic approximation, external habit and targeting rules

We examine the linear-quadratic approximation of nonlinear dynamic stochastic optimization problems. A discrete-time version of Magill [1977a. A local analysis of N-sector capital accumulation under uncertainty. Journal of Economic Theory 15(2), 211–219] is generalized to models with forward-looking variables paying special attention to second-order conditions. This is the ‘large distortions’ case in the literature. We apply the approach to monetary policy in a DSGE model with external habit in consumption. We then develop a condition for ‘target-implementability’, a concept related to ‘targeting rules’. Finally, we extend the approach to a comparison between cooperative and non-cooperative equilibria in a two-country model and show that the ‘small distortions’ approximation is inappropriate for this exercise.     

Existence of competitive equilibrium under financial constraints and increasing returns

This paper studies a ‘factor cost in advance’ model with increasing returns in production. In the model both partial equilibrium and general equilibrium may exist since working capital of firms limit their input demand. We provide a sufficient condition for the existence of partial equilibrium of a firm operating on a non-convex choice set. Furthermore we establish the existence and uniqueness of competitive equilibrium in the special case of logarithmic utility.     

Inside the queue:: hypercongestion and road pricing in a continuous time–continuous place model of traffic congestion

This paper develops a continuous-time–continuous-place dynamic economic model of traffic congestion, based on car-following theory. The model integrates two archetype congestion technologies used in the economics literature: ‘static flow congestion’ and ‘dynamic bottleneck congestion.’ With endogenous departure times and a bottleneck along the route, ‘hypercongestion’ arises as a dynamic equilibrium phenomenon on the upstream road segment. Congestion tolls based on an intuitive dynamic and space-varying generalization of the standard Pigouvian tax rule can hardly be improved upon. A naïve application of a toll schedule based on Vickrey's bottleneck model performs much worse and reduces welfare in the numerical model.     

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.     

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     

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.     

The latin model of welfare: Do ‘insertion contracts’ reduce long-term dependence?

This paper aims to present an assessment of the welfare policies implemented in most South European countries. Welfare programs in these countries try to combine a basic level of economic protection and measures favoring life and labor skills (‘insertion benefits’) of low-income households. We focus on a specific program set up with the twofold strategy of cash and ‘insertion benefits’ (Madrid's IMI) and, more precisely, on the so-called ‘insertion projects’, consisting in a gradual mix of job search assistance, training and subsidized jobs. We evaluate the effects of these ‘insertion projects’ on welfare recidivism and the duration of off-welfare spells using propensity score-matching methods. Our results suggest that propensity score estimators appear to reduce selectivity due to non-random participation. Both recidivism rates as well as the duration of off-welfare spells suggest potentially successful interventions.     

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’.     

Export restraints in a model of trade with capital accumulation

This paper examines the impact of voluntary export restraints (VERs) in an international duopoly modeled as a differential game. With a Ramsey capital accumulation dynamics, the game admits multiple steady states, and a VER cannot be ‘voluntarily’ employed by the foreign firm in case of Cournot behavior in demand substitutes. Hence, the dynamic framework confirms the results of the VERs literature with static interaction in output levels. In the case of price behavior, the adoption of an export restraint may increase the profits of both firms if products are substitutes and the steady state is ‘market-driven’. However, contrary to the acquired wisdom based upon the static approach, the dynamic analysis also admits an equilibrium outcome, identified by the Ramsey golden rule, where the incentive to adopt a VER is ruled out, irrespective of whether firms are quantity- or price-setters.     

Productivity, employment and labor demand in Polish industry in the 1980s: Some preliminary results from enterprise-level data

The paper uses annual data from a panel of 334 Polish industrial enterprises over the period 1983–1988 to test empirically a simple neoclassical approach to the socialist labor market. First, an enterprise production function is estimated. The paper finds that for most enterprises, the resulting estimated marginal product of labor exceeds the wage paid by the enterprise by a considerable margin, suggesting general excess demand for labor. The paper then looks at how the difference between the MPL and the wage is related to the rate of change of employment, and finds that firms where the MPL is higher than the wage — firms which in a neoclassical model would have a large excess demand for labor — do not shed labor any more slowly than other firms.     

Control of economic systems under the process of data improvement

The paper deals with optimal control of the systems with a certain part of economic parameters not defined completely, namely, in terms of an interval of uncertainty b ± δ. The important idea of our approach is that optimal control should take into account data improvement. The approach implies the process of introducing new data which make cost estimates more precise. The process is described as a random and exogenous one and by its nature may be named a process with ‘independent decrements’ (of entropy). The stationary model of a dynamic system is developed; the system has the interval of uncertainty as its phase point.     

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.     

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.     

The optimal consumption function in a Brownian model of accumulation Part A: The consumption function as solution of a boundary value problem

We consider a neo-classical model of optimal economic growth with c.r.r.a. utility in which the traditional deterministic trends representing population growth, technological progress, depreciation and impatience are replaced by Brownian motions with drift. When transformed to ‘intensive’ units, this is equivalent to a stochastic model of optimal saving with diminishing returns to capital. For the intensive model, we give sufficient conditions for optimality of a consumption plan (open-loop control) comprising a finite welfare condition, a martingale condition for shadow prices and a transversality condition as t→∞. We then replace these by conditions for optimality of a plan generated by a consumption function (closed-loop control), i.e. a function expressing log-consumption as a time-invariant, deterministic function of log-capital . Making use of the exponential martingale formula we replace the martingale condition by a non-linear, non-autonomous second-order o.d.e. which an optimal consumption function must satisfy; this has the form , where . Economic considerations suggest certain limiting values which and should satisfy as , thus defining a two-point boundary value problem (b.v.p.) — or rather, a family of problems, depending on the values of parameters. We prove two theorems showing that a consumption function which solves the appropriate b.v.p. generates an optimal plan. Proofs that a unique solution of each b.v.p. exists are given in a separate paper (Part B).     

基于订单生产的供应链价格与承诺交货时间决策和协调

针对订单生产需求受价格和承诺交货时间影响以及延期现象,建立由生产商和销售商组成的供应链价格与承诺交货时间决策模型。研究表明:最优承诺交货时间绑定在服务水平上,提高服务水平可以降低双重边际化效应;相对于集中决策,分散决策采用较高的价格和较短的承诺交货时间,其最优利润和最优需求较少;此外,采用收益分享方式构建了供应链协调模型,得出销售商收益分享比例处于某一范围内才能实现供应链的协调。     

On the asymptotic behavior of stochastic economic processes : Two examples from intertemporal allocation under uncertainty

Some of the recently developed models to deal with economic problems involving uncertainty are based on simplifying assumptions on the nature of the stochastic law of the environment influencing economic decisions. Relying on the theory of martingales, we derive some general results on the asymptotic behavior of two dynamic processes that are of interest in the theory of intertemporal resource allocation. The first example is related to the ‘turnpike’ theory of optimal allocation. The second is addressed to the question of allocation of a scarce resource by using prices when the supply of the resource is random.     

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.     

Production planning and inventories optimization: A backward approach in the convex storage cost case

We study the deterministic optimization problem of a profit-maximizing firm which plans its sales/production schedule. The firm controls both its production and sales rates and knows the revenue associated to a given level of sales, as well as its production and storage costs. The revenue and the production cost are assumed to be respectively concave and convex. In Chazal et al. [Chazal, M., Jouini, E., Tahraoui, R., 2003. Production planning and inventories optimization with a general storage cost function. Nonlinear Analysis 54, 1365–1395], we provide an existence result and derive some necessary conditions of optimality. Here, we further assume that the storage cost is convex. This allows us to relate the optimal planning problem to the study of a backward integro-differential equation, from which we obtain an explicit construction of the optimal plan.