Optimal fiscal policy with robust control

This paper analyzes how consumer uncertainty affects optimal fiscal policy in the Lucas and Stokey (1983) framework. The consumers, lacking confidence in their knowledge of the stochastic environment, endogenously tilt their subjective probability model away from an approximating probability model. The government, though, is confident that the approximating probability model characterizes the stochastic environment. This confidence dichotomy reveals a range of possible objective functions for an altruistic government. I assume that the government maximizes the consumers' expected utility under the consumers' own subjective probability model. It is found that this government relies less heavily on labor taxes to absorb the fiscal shock than would be optimal if consumers were fully confident in their probability model. This policy helps mitigate the direct welfare cost associated with consumer uncertainty. I compare this policy to the one implemented by a government that maximizes the consumers' expected utility under the approximating probability model.     

Optimal pollution control with distributed delays

We present a model of optimal stock pollution control with general distributed delays in the stock accumulation dynamics. Using generic functional forms and a distribution structure covering a wide range of distributions, we solve analytically the complex dynamic system that arises from the introduction of these distributed delays. From a theoretical standpoint, our contribution extends the dynamic optimization literature that focused on single discrete delays and develops an original method to address control problems written as mixed type functional differential equations with general kernels. Our results show the qualitative impact of acknowledging these distributed delays on the optimal pollution paths dynamics. We study analytically the properties of the dynamics and we identify the conditions for the occurrence of limit cycles. This theoretical work contributes to the design of efficient environmental policies in the presence of complex delays.     

Stochastic optimal growth with bounded or unbounded utility and with bounded or unbounded shocks

This paper studies a one-sector stochastic optimal growth model with i.i.d. productivity shocks in which utility is allowed to be bounded or unbounded, the shocks are allowed to be bounded or unbounded, and the production function is not required to satisfy the Inada conditions at zero and infinity. Our main results are three-fold. First, we confirm the Euler equation as well as the existence of a continuous optimal policy function under a minimal set of assumptions. Second, we establish the existence of an invariant distribution under quite general assumptions. Third, we show that the density of optimal output converges to a unique invariant density independently of initial output under the assumption that the shock distribution has a density whose support is an interval, bounded or unbounded. In addition, we provide existence and stability results for general one-dimensional Markov processes.     

Existence of an equilibrium for infinite horizon economies with and without complete information

This work proves the existence of an equilibrium for an infinite horizon economy where trade takes place sequentially over time. There exist two types of agents: the first correctly anticipates all future contingent endogenous variables with complete information as in Radner [Radner, R. (1972). Existence of equilibrium of plans, prices and price expectations in a sequence of markets. Econometrica, 289–303] and the second has exogenous expectations about the future environment as in Grandmont [Grandmont, J. M. (1977). Temporary general equilibrium theory. Econometrica, 535–572] and information based on the current and past aggregate variables including those which are private knowledge. Agents with exogenous expectations may have inconsistent optimal plans but have predictive beliefs in the context of Blackwell and Dubbins [Blackwell, D., Dubins, L. (1962). Merging of opinions with increasing information. The Annals of Mathematical Statistics, 882–886] with probability transition rules based on all observed variables. We provide examples of this framework applied to models of differential information and environments exhibiting results of market selection and convergence of an equilibrium. The existence result can be used to conclude that, by adding the continuity assumption on the probability transition rules, we obtain the existence of an equilibrium for some models of differential information and incomplete markets.     

Optimal pest control in agriculture

Based on economic methodology we model an ecosystem with two species in predator–prey relationship: mice feed on grain and grain feeds on a resource. With optimizing behavior of individual organisms a short-run ecosystem equilibrium is defined and characterized that depends on the farmer's use of fertilizer and pesticide and on the mice population which, in turn, is affected by pesticides. In that way, a microfounded agricultural production function is derived. Linking a sequence of short-run ecosystem equilibria yields the growth function of the mice population which is thus derived rather than assumed. In each period the farmer harvests all grain in excess of some given amount of seed. If she maximizes her present-value profits, optimal farming is characterized by either using no pesticide or a moderate amount of pesticide or by applying a chattering control. Pest eradication is never optimal. On the other hand, if the farmer takes into account steady-state mice populations only, it may be optimal to eradicate mice or to use no or a moderate amount of pesticide depending on prices as well as on the shape of the grain production function which is determined by microparameters of grain reproduction.     

Optimal investment with taxes: an existence result

We study the deterministic control problem of maximizing utility from consumption of an agent who seeks to optimally allocate his wealth between consumption and investment in a financial asset subject to taxes on benefits with first-in–first-out priority rule on sales. Short sales are prohibited and consumption is restricted to be non-negative. Such a problem has been introduced in a previous paper by the same authors where the first-order conditions have been derived. In this paper, we establish an existence result for this non-classical optimal control problem.     

Optimal impulse control for cash management¶with quadratic holding-penalty costs

This paper studies optimal control for an infinite horizon cash management problem where the cash fund fluctuates as a Brownian motion. Holding-penalty costs are assumed to be a quadratic function of the cash level and there are fixed and proportional transaction costs. Using the “impulse technique”, we prove that optimal control exists and takes the form of a control band policy. Received: 4 January 2001 / Accepted: 5 June 2001     

Arbitrage and equilibrium in unbounded exchange economies with satiation

In his seminal paper on arbitrage and competitive equilibrium in unbounded exchange economies, Werner (1987) proved the existence of a competitive equilibrium, under a price no-arbitrage condition, without assuming either local or global nonsatiation. Werner’s existence result contrasts sharply with classical existence results for bounded exchange economies which require, at minimum, global nonsatiation at rational allocations. Why do unbounded exchange economies admit existence without local or global nonsatiation? This question is the focus of our paper. First, we show that in unbounded exchange economies, even if some agents’ preferences are satiated, the absence of arbitrage is sufficient for the existence of competitive equilibria, as long as each agent who is satiated has a nonempty set of useful net trades– that is, as long as agents’ preferences satisfy weak nonsatiation. Second, we provide a new approach to proving existence in unbounded exchange economies. The key step in our new approach is to transform the original economy to an economy satisfying global nonsatiation such that all equilibria of the transformed economy are equilibria of the original economy. What our approach makes clear is that it is precisely the condition of weak nonsatiation – a condition considerably weaker than local or global nonsatiation – that makes possible this transformation.     

Optimal and efficient repeated measurements designs for comparing test treatments with a control

Rearranging the sequence of test treatments and control treatment within each block of an A-optimal balanced treatment block design such that certain conditions are satisfied, the resulting design is an A-optimal repeated measurements designs when blocks are regarded as units or periods. The efficiencies of designs which are obtained from universally optimal repeated measurements designs with test treatments only by changing some treatment labels into control treatment are given.     

Optimal control of pricing strategy for diffusion model

This study presents a conceptual framework based on the new product diffusion and demand theory models. The proposed framework was creating a probability of demand function. Considering effectiveness of demand function transmitted by adopters, the optimal control policies of pricing are conducted according to the optimal control theorv.     

Manipulation of the Walrasian mechanism in production economies with unbounded short-selling

Hurwicz (1979) and Otani and Sicilian (1982, 1990) characterized the Nash equilibrium allocations of the Walrasian demand manipulation game in successively more general exchange environments. In this paper, I extend the analysis to production economies with short-selling. First, I generalize Hurwicz’s and Otani and Sicilian’s theorem that any allocation at which each agent’s consumption bundle lies above her true offer curve can be supported in Nash equilibrium. I then show that for finite economies of any size the set of such allocations is often topologically large.Received: 17 January 2003, Accepted: 4 April 2005, JEL Classification: D51, D82For comments on this and earlier versions of the paper, I wish to thank Rick Bond, Bhaskar Chakravorti, Tom Gresik, Costas Syropoulos and William Thomson. I would especially like to thank Mike Jerison for helping to overcome a difficulty with a previous version. Also, the comments of the anonymous referees are gratefully acknowledged.     

“拐点”即将来临——大整合时代的房地产企业发展之道

中国房地产会不会出现“泡沫”？这个目前地产市场最敏感的话题，在不久前举办的“房地产创新论坛”上再次成为论争的焦点。 “其兴也勃焉，其衰也忽焉”——管理学专家岳川博的“大胆假设“，来源于对美、日等国房地产数据的“小心求证”。然而在经济学家赵晓看来，所谓周期、规律，在中国“非典型性市场”中都可能水土不服——基于工业化、城市化等宏观层面的认识，房地产“泡沫”才刚刚开始。 此番唇枪舌剑，只是目前有关房地产“泡沫”问题争论的一个缩影。本刊对此暂不评论，个中三昧还可由读者自己品味。 本刊还将陆续刊发一系列地产市场相关热点话题的争论及评点。欢迎读者踊跃参评。     

The local stability of an open-loop Nash equilibrium in a finite horizon differential game

We propose a finite time differential game as a model for some economic processes and derive conditions for the Nash equilibrium solution to be locally asymptotically stable. We adopt the traditional ‘Cournot-reaction function’ notion of stability, which in our (continuous time) model becomes a function-to-function, or trajectory-to-trajectory, mapping. The conditions for stability seem to make economic sense. The equilibrium is less stable if the interaction terms in each period are large, if the game has a long duration, and if the discount rate is small.     

Optimal risk taking in an uneven tournament game with risk averse players

We analyze the optimal choice of risk in a two-stage tournament game between two players that have different concave utility functions. At the first stage, both players simultaneously choose risk. At the second stage, both observe overall risk and simultaneously decide on effort or investment. The results show that those two effects which mainly determine risk taking – an effort effect and a likelihood effect – are strictly interrelated. This finding sharply contrasts with existing results on risk taking in tournament games with symmetric equilibrium efforts where such linkage can never arise. Conditions are derived under which this linkage leads to a reversed likelihood effect so that the favorite (underdog) can increase his winning probability by increasing (decreasing) risk which is impossible in a completely symmetric setting.     

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.     

Wavelet decomposition of heterogeneous investment horizon

Building on the assumptions that investors are heterogeneous and that not all of them are fully rational, the market for trading any financial instrument can be separated into several segments, each associated with a different investment horizon. Thus, the expected return on an asset for each horizon maintains a different functional relationship with an expected market return. In other words, the trading of an asset by investors with heterogeneous investment horizons results in the coexistence of multiple security market lines. This proposed theory, which offers an alternative interpretation of investment behavior from that of the capital asset pricing model (CAPM) and the efficient markets hypothesis (EMH), is verified by using the newly introduced amalgamated discrete wavelet transform.     

The solution of the infinite horizon tracking problem for discrete time systems possessing an exogenous component

In this paper we derive an algorithm that yields, for a discrete-time system, a control minimizing a quadratic cost functional. The system considered is linear and possesses an exogenous component. The cost functional is a quadratic tracking equation over an infinite time horizon with positive semi-definite weighting matrices such that a weighted sum of these matrices is positive definite. The infinite planning horizon Minimum Variance cost criterion and the Linear Quadratic regulator are special cases. For stabilizable systems we give a characterization of the asymptotically admissible reference trajectories.