Optimal lottery

This article proposes an equilibrium approach to lottery markets in which a firm designs an optimal lottery to rank-dependent expected utility (RDU) consumers. We show that a finite number of prizes cannot be optimal, unless implausible utility and probability weighting functions are assumed. We then investigate the conditions under which a probability density function can be optimal. With standard RDU preferences, this implies a discrete probability on the ticket price, and a continuous probability on prizes afterwards. Under some preferences consistent with experimental literature, the optimal lottery follows a power-law distribution, with a plausibly extremely high degree of prize skewness.     

Optimal consumption under uncertainty,liquidity constraints,and bounded rationality

I study how boundedly rational agents can learn a “good” solution to an infinite horizon optimal consumption problem under uncertainty and liquidity constraints. Using an empirically plausible theory of learning I propose a class of adaptive learning algorithms that agents might use to choose a consumption rule. I show that the algorithm always has a globally asymptotically stable consumption rule, which is optimal. Additionally, I present extensions of the model to finite horizon settings, where agents have finite lives and life-cycle income patterns. This provides a simple and parsimonious model of consumption for large agent based models.     

Co-state variables correctly value stocks at each instant A proof

We prove this often mentioned result by showing that the marginal rate of increase of the maximand of a control problem with respect to the level of stock at any instant in the interior of the horizon is the value of the associated costate variable at that instant. This implies as a corollary that the marginal gain to be made over the future is the same as could be made over past and future.     

Planning horizon results for the dynamic warehouse location problem

In the last decade, a number of models for the dynamic facility location problem have been proposed. The various models contain differing assumptions regarding the revenues and costs realized in the opening, operation, and closure of a facility as well as considering which of the facility sites are candidates for acquisition or disposal at the beginning of a time period. Since the problem becomes extremely large for practical applications, much of the research has been directed toward developing efficient solution techniques. Most of the models and solutions assume that the facilities will be disposed of at the end of the time horizon since distant future conditions usually can't be forecasted with any reasonable degree of accuracy. The problem with this approach is that the “optimal” solution is optimal for only one hypothesized post horizon facility configuration and may become nonoptimal under a different configuration. Post-optimality analysis is needed to assure management that the “optimal” decision to open or close a facility at a given point in time won't prove to be “nonoptimal” when the planning horizon is extended or when design parameters in subsequent time periods change. If management has some guarantee that the decision to open or close a facility in a given time period won't change, it can safely direct attention to the accuracy of the design parameters within that time period.This paper proposes a mixed integer linear programming model to determine which of a finite set of warehouse sites will be operating in each time period of a finite planning horizon. The model is general in the sense that it can reflect a number of acquisition alternatives—purchase, lease or rent. The principal assumptions of the model are: a) Warehouses are assumed to have infinite capacity in meeting customer demand, b) In each time period, any non-operating warehouse is a candidate for becoming operational, and likewise any operating warehouse is a candidate for disposal, c) During a given time period, the fixed costs of becoming operational at a site are greater than the disposal value at that site to reflect the nonrecoverable costs involved in operating a warehouse. These costs are separate from the acquisition and liquidation values of the site. d) During a time period the operation of a warehouse incurs overhead and maintenance costs as well as a depreciation in the disposal value.To solve the model, it is first simplified and a partial optimal solution is obtained by the iterative examination by both lower and upper bounds on the savings realized if a site is opened in a given time period. An attempt is made to fix each warehouse open or closed in each time period. The bounds are based on the delta and omega tests proposed by Efroymson and Ray (1966) and Khumawala (1972) with adjustment for changes in the value of the warehouse between the beginning and end of a time period. A complete optimal solution is obtained by solving the reduced model with Benders' decomposition procedure. The optimal solution is then tested to determine which time periods contain “tentative” decisions that may be affected by post horizon data by analyzing the relationship between the lower (or upper) bounds used in the model simplification time period. If the warehouse decisions made in a time period satisfy these relationships and are thus unaffected by data changes in subsequent time periods, then the decisions made in earlier time periods will also be unaffected by future changes.     

Dynamic competitive retail pricing behavior with uncertainty and learning

When competing retailers lack full information about rivals' decision processes, how will dynamic pricing behavior vary from patterns observed in more traditional static or full-information models? We investigate this question in a dynamic alternating-moves duopoly model. Retailers update (linear) conjectures about rivals' future prices in a Bayesian fashion. We show that as observed and expected prices converge, a pricing equilibrium is always achieved, whether or not the conjectured and actual values of the slope of the rival's best response function are consistent. Assuming specific parameter values, we compare equilibrium prices and associated profits in our Bayesian learning model with those obtained under the assumptions of static Nash behavior, collusive behavior and dynamically optimal behavior with full information. We apply the notions of strategic substitutability and strategic complementarity to the analysis and find that when products are strategic complements, conjectures of higher rival price responsiveness lead to higher steady-state prices and profits. The reverse is true for strategic substitutes. We also find that learning about a rival's behavior proceeds more quickly, the less intensely related in demand are products. We find, in general, that equilibrium pricing patterns and profits can vary considerably from those in full-information environments, but that even with grossly wrong beliefs about rival behavior, competing retailers are still attracted to an equilibrium. The analysis suggests not only the value of investigating lessthan-full information situations but also the potential incremental value of signalling greater or less aggressiveness than truly characterizes one's behavior as a strategic option.     

Seniority bias in a tournament

The paper presents a model where the probability of promotion tends to increase with seniority (overall labor market experience) without relying on the accumulation of general human capital. To this end, we consider the optimal design of a tournament (a relative compensation scheme) between two agents with different time horizon, the young and the old, in an overlapping generations framework. When the principal can only imperfectly monitor each agent’s effort level, the difference in time horizon leads to the ex post difference in the marginal value of effort between the two agents. In this case, the optimal tournament necessarily involves a bias towards the old agent. Within this framework, we also examine the relationship between: (1) the monitoring accuracy and the optimal bias; and (2) the value of outside options and the optimal bias.     

Real Options in an Asymmetric Duopoly: Who Benefits from Your Competitive Disadvantage?

This paper analyzes the impact of investment cost asymmetry on the optimal real option exercise strategies and the value of firms in duopoly. Both firms have an opportunity to invest in a project enhancing ( ceteris paribus ) the profit flow. We show that three types of equilibrium strategies exist. Furthermore, we express the critical levels of cost asymmetry delineating the equilibrium regions as functions of basic economic variables. The presence of strategic interactions among the firms leads to counterintuitive results. First, for a certain range of the asymmetry level, a marginal increase in the investment cost of the firm with the cost disadvantage can enhance this firm's own value. Moreover, such a cost increase can reduce the value of the competitor. Finally, we discuss the welfare implications of the optimal exercise strategies and show that the presence of identical firms can result in a socially less desirable outcome than if one of the competitors has a significant cost (dis)advantage.     

Feasibility and optimality of the initial capital stock in the Ramsey vintage capital model

Using a discrete-time version of the Ramsey Vintage Capital Model we provide a characterization of the set of initial capital stocks compatible with a predefined scrapping time, given the rate of technical progress and the level of capital productivity. Each profile of initial capital stock in that set generates a complete infinite horizon feasible capital path. From that characterization, we prove the existence of a minimum value for the scrapping time of the machines compatible with the rate of technological progress. Moreover, for each level of capital productivity, there exists an upper bound for the technological progress which allows the existence of feasible capital paths with full employment. Finally, we transform the infinite horizon dynamic programming problem into one of finite dimension. We use this to find the optimal lifetime for the machines as well as the optimal composition of the initial capital stocks. A numerical example shows that, in accordance with the infinite horizon approach to the problem, the increase in the rate of technological progress leads to a decrease in optimal scrapping time of capital goods.     

Cost sharing: efficiency and implementation

We study environments where a production process is jointly shared by a finite group of agents. The social decision involves the determination of input contribution and output distribution. We define a competitive solution when there is decreasing-returns-to-scale which leads to a Pareto optimal outcome. Since there is a finite number of agents, the competitive solution is prone to manipulation. We construct a mechanism for which the set of Nash equilibria coincides with the set of competitive solution outcomes. We define a marginal-cost-pricing equilibrium (MCPE) solution for environments with increasing returns to scale. These solutions are Pareto optimal under certain conditions. We construct another mechanism that realizes the MCPE.     

Properties of optimal forecasts under asymmetric loss and nonlinearity

Evaluation of forecast optimality in economics and finance has almost exclusively been conducted under the assumption of mean squared error loss. Under this loss function optimal forecasts should be unbiased and forecast errors serially uncorrelated at the single period horizon with increasing variance as the forecast horizon grows. Using analytical results we show that standard properties of optimal forecasts can be invalid under asymmetric loss and nonlinear data generating processes and thus may be very misleading as a benchmark for an optimal forecast. We establish instead that a suitable transformation of the forecast error—known as the generalized forecast error—possesses an equivalent set of properties. The paper also provides empirical examples to illustrate the significance in practice of asymmetric loss and nonlinearities and discusses the effect of parameter estimation error on optimal forecasts.     

Institutions and Foreign Subsidiary Growth in Transition Economies: The Role of Intangible Assets and Capabilities

Although transition economies experience significant institutional transformations that vary in their degree and pace, scholarly knowledge of what distinguishes more successful foreign subsidiaries from less successful ones in such environments is limited and inconsistent. We enhance the understanding of this subject by examining how variations in the institutional development of transition economies influence the usefulness of a subsidiary's intangible assets and capabilities and, in turn, their effectiveness in enhancing its growth. Prior research assumes that foreign subsidiaries that operate in any given environment are always better off when they possess strong intangible assets and capabilities. Our analysis of more than 33,000 observations in 14 transition economies challenges this view and enables us to explain why some subsidiaries grow more quickly in less‐developed institutional environments, whereas others more quickly in countries with institutions that are more developed. More specifically, we show that although a subsidiary's intangible assets enhance its growth in transition economies with stronger institutions, these effects are particularly weak or insignificant in transition countries with less developed institutional environments. Conversely, a completely different pattern emerges for subsidiary capabilities, with their marginal effects on subsidiary growth being significantly higher in countries that are institutionally less developed than in transition countries with more developed institutions.     

Dynamics in research joint ventures and R&D collaborations

We investigate the short- and long-term effects of different types of R&D collaborations on firms, consumers, and the industry. To that end, we consider a differentiated-product market in which firms compete à la Bertrand and invest in process innovation in order to lower the production cost over time. Investments are stochastic and there can be cartelization or competition strategies among firms at the moment of making the decision on the amount to invest in R&D. Our results show that in equilibrium, the long-run welfare is larger under a research joint venture than under other environments. Discounted present value profits increase with the level of the spillover but there are asymmetries that depend on the firms’ asymmetry on marginal costs.     

上升线性需求条件下变质性物品生产库存计划模型

研究了变质性物品生产库存系统在上升趋势线性需求条件下,在有限计划时间水平内,如何确定最优生产周期,各周期最优生产率,以及最优库存安排策略。     

Optimal agglomerations in dynamic economics

We study rational expectations equilibrium problems and social optimum problems in infinite horizon spatial economies in the context of a Ramsey type capital accumulation problem with geographical spillovers. We identify sufficient local and global conditions for the emergence (or not) of optimal agglomeration, using techniques from monotone operator theory and spectral theory in infinite dimensional Hilbert spaces. We show that agglomerations may emerge, with any type of returns to scale (increasing or decreasing) and with the marginal productivity of private capital increasing or decreasing with respect to the spatial externality. This is a fairly general result indicating the importance of the network structure of the spatial externality relative to the properties of the aggregate production function. Our analytical methods can be used to systematically study optimal potential agglomeration and clustering in dynamic economics.     

Optimal investment and reinsurance policies for an insurer with ambiguity aversion

In this paper, we study the optimal investment and reinsurance problem for an insurer based on the variance premium principle, in which three cases are considered. First, we assume that the financial market does not exist. The insurer only holds an insurance business, and the optimal reinsurance problem is studied. Subsequently, we assume that there exists a financial market with an accurately modeled risky asset. The optimal investment and reinsurance problem is investigated under these conditions. Finally, we consider the general case in which the insurer is concerned about the model ambiguity of both the insurance market and the financial market. In all three cases, the value function is set to maximize the expected utility of terminal wealth. By employing the dynamic programming principle, we derive the Hamilton–Jacobi–Bellman (HJB) equations, which are satisfied by the value functions and obtain closed-form solutions for optimal reinsurance and investment policies and the value functions in all three cases. Most interestingly, we elucidate how investment improves the insurer’s utility and find that the existence of ambiguity can significantly affect the optimal policies and value functions. We also compare the ambiguities in the two markets and find that ambiguity in the insurance market has much more significant impact on the value function than the ambiguity in the financial market. It implies that it is more valuable for insurer to precisely evaluate the insurance risk. We also provide some numerical examples and economic explanations to illustrate our results.     

Reputation, Honesty, and Efficiency with Insider Information: an Experiment

We conduct an experimental study of sales of insider information about an asset's future value, where the insiders cannot purchase the underlying asset. We examine whether such information is purchased, the quality of the information provided, and the subsequent accuracy of purchase decisions in the underlying asset market. Our design explores whether reputation, in a repeated game of finite (but uncertain) duration, is an effective constraint on deliberate strategic misinformation. The insiders have an immediate incentive to state that the asset value is high when its true value is low. We suggest an application to insider trading in financial information markets. With fixed matching, cooperative outcomes featuring truthful revelation are frequently achieved and sustained, even though this suggests subjects have sophisticated beliefs about the beliefs and behavior of others. As a comparison, we also conduct a control treatment with random rematching. Here, information purchase is less frequent, the rate of truthful revelation decreases, and efficiency is diminished. Our results suggest that most people anticipate that others realize the potential value of a good reputation.     

Dismissals and match-specific rents

Labor contracts that result in dismissals are quite common in the real world. The question that arises is why employers do not just offer reduced wages instead of asking workers with low realized productivity to leave. This paper argues that such behavior can be explained by workers' understandable unwillingness to agree to contracts that an employer will not have an incentive to honor in the future. Specifically, we construct a matching model in which the employer and the worker are both uncertain about the value the other places on the match. Because the worker's match-specific productivity is the employer's private information, a commitment to pay a wage equal to the worker's value of marginal product is not enforceable. In the absence of a wage guarantee, the employer will offer retained workers wages below their value of marginal product, which causes quits to be inefficiently high. The employer can reduce quits by contractually promising a guaranteed wage to retained workers. Although this will lead to some involuntary dismissals, the loss from dismissals will be less than the gain from lower quits if the wage guarantee is not too high.     

Goodness-of-fit tests for long memory moving average marginal density

This paper addresses the problem of fitting a known density to the marginal error density of a stationary long memory moving average process when its mean is known and unknown. In the case of unknown mean, when mean is estimated by the sample mean, the first order difference between the residual empirical and null distribution functions is known to be asymptotically degenerate at zero, and hence can not be used to fit a distribution up to an unknown mean. In this paper we show that by using a suitable class of estimators of the mean, this first order degeneracy does not occur. We also investigate the large sample behavior of tests based on an integrated square difference between kernel type error density estimators and the expected value of the error density estimator based on errors. The asymptotic null distributions of suitably standardized test statistics are shown to be chi-square with one degree of freedom in both cases of the known and unknown mean. In addition, we discuss the consistency and asymptotic power against local alternatives of the density estimator based test in the case of known mean. A finite sample simulation study of the test based on residual empirical process is also included.     

Investment and pricing strategies of competing firms: A computational approach

We analyze the classical investment and pricing problem of a dominant firm faced with competition from substitute industries or marginal firms in the same field. The firm owns a finite level of a resource (e.g. the stock of an exhaustible one), the consumption of which is to be divided optimally over a finite planning horizon. The competitors' measures affect the demand for the resource towards the dominating firm. Rising crude oil prices and investments in forms of alternative energy are representative examples of the strategic questions which involve competitive and contradictory interests among firms within an industry. The investment and pricing problem can be solved analytically only with strong, simplifying assumptions. To make the analysis simpler and to relax these restrictions, we combine a series of numerical tools, computerize them, and build up a user-oriented, computerized decision aid, which we call a ‘computerized approach’. We solve the problem under different sets of theoretical assumptions. This chosen incremental theory building allows us to study the theoretical sensitivity of the original problem.     

On revenue recycling and the welfare effects of second-best congestion pricing in a monocentric city

This paper examines congestion taxes in a monocentric city with pre-existing labor taxation. When road toll revenue is used to finance labor tax cuts, 35% of the optimal road tax in our numerical model does not reflect marginal external congestion costs, but rather functions as a Ramsey–Mirrlees tax, i.e. an efficiency enhancing mechanism allowing for an indirect spatial differentiation of the labor tax. This adds a quite different motivation to road pricing, since welfare gains can be produced even in absence of congestion. We find that the optimal road tax is non-monotonic across space, reflecting the different impacts of labor supply elasticity and marginal utility of income, which both vary over space. The relative efficiencies of some archetype second-best pricing schemes (cordon toll, flat kilometer tax) are high (84% and 70% respectively). When road toll revenue is recycled lump-sum, the optimal toll lies below its Pigouvian level. Extensions in a bimodal framework show that the optimality of using road toll revenue to subsidize public transport depends on the initial inefficiency in public transport pricing.