Optimal law enforcement under asymmetric information

In this paper, we focus on the problem created by asymmetric informationabout the enforcer's (agent's) costs associated to enforcement expenditure. This adverse selection problem affects optimal law enforcement because a low cost enforcer may conceal its information by imitating a high cost enforcer, and must then be given a compensation to be induced to reveal its true costs. The government faces a trade-off between minimizing the enforcer's compensation and maximizing the net surplus of harmful acts. As a consequence, the probability of apprehension and punishment is usually reduced leading to more offenses being committed. We show that asymmetry of information does not affect law enforcement as long as raising public funds is costless. The consideration of costly raising of public funds permits to establish the positive correlation between asymmetry of information between government and enforcers andthe crime rate.

Transportation choices and the value of statistical life

This paper exploits an unusual transportation setting to estimate the value of a statistical life(VSL). We estimate the trade-offs individuals are willing to make between mortality risk andcost as they travel to and from the international airport in Sierra Leone (which is separated fromthe capital Freetown by a body of water). Travelers choose from among multiple transportoptions ? namely, ferry, helicopter, hovercraft, and water taxi. The setting and original datasetallow us to address some typical omitted variable concerns in order to generate some of the firstrevealed preference VSL estimates from Africa. The data also allows us to compare VSLestimates for travelers from 56 countries, including 20 African and 36 non-African countries, allfacing the same choice situation. The average VSL estimate for African travelers in the sample isUS$577,000 compared to US$924,000 for non-Africans. Individual characteristics, particularlyjob earnings, can largely account for the difference between Africans and non-Africans; Africansin the sample typically earn somewhat less. There is little evidence that individual VSL estimatesare driven by a lack of information, predicted life expectancy, or cultural norms around risktakingor fatalism. The data implies an income elasticity of the VSL of 1.77. These revealedpreference VSL estimates from a developing country fill an important gap in the existingliterature, and can be used for a variety of public policy purposes, including in current debateswithin Sierra Leone regarding the desirability of constructing new transportation infrastructure.

Optimal management of microgrids

Desenvolupament dels models matemàtics necessaris per a controlar de forma òptima la microxarxa existent als laboratoris del Institut de Recerca en Energia de Catalunya. Els algoritmes s'implementaran per tal de simular el comportament i posteriorment es programaran directament sobre els elements de la microxarxa per verificar el seu correcte funcionament.. Desenvolupament dels models matemàtics necessaris per a controlar de forma òptima la microxarxa existent als laboratoris del Institut de Recerca en Energia de Catalunya. Els algoritmes s'implementaran per tal de simular el comportament i posteriorment es programaran directament sobre els elements de la microxarxa per verificar el seu correcte funcionament.

Optimal fiscal policy in overlapping generations models

[eng] This paper provides, from a theoretical and quantitative point of view, an explanation of why taxes on capital returns are high (around 35%) by analyzing the optimal fiscal policy in an economy with intergenerational redistribution. For this purpose, the government is modeled explicitly and can choose (and commit to) an optimal tax policy in order to maximize society's welfare. In an infinitely lived economy with heterogeneous agents, the long run optimal capital tax is zero. If heterogeneity is due to the existence of overlapping generations, this result in general is no longer true. I provide sufficient conditions for zero capital and labor taxes, and show that a general class of preferences, commonly used on the macro and public finance literature, violate these conditions. For a version of the model, calibrated to the US economy, the main results are: first, if the government is restricted to a set of instruments, the observed fiscal policy cannot be disregarded as sub optimal and capital taxes are positive and quantitatively relevant. Second, if the government can use age specific taxes for each generation, then the age profile capital tax pattern implies subsidizing asset returns of the younger generations and taxing at higher rates the asset returns of the older ones.

Interiority of the optimal population growth rate with endogenous fertility

This paper analyzes the issue of the interiority of the optimal population growth rate in a two-period overlapping generations model with endogenous fertility. Using Cobb-Douglas utility and production functions, we show that the introduction of a cost of raising children allows for the possibility of the existence of an interior global maximum in the planner¿s problem, contrary to the exogenous fertility case

Optimal generalized quantum measurements for arbitrary spin systems

Positive-operator-valued measurements on a finite number of N identically prepared systems of arbitrary spin J are discussed. Pure states are characterized in terms of Bloch-like vectors restricted by a SU(2J+1) covariant constraint. This representation allows for a simple description of the equations to be fulfilled by optimal measurements. We explicitly find the minimal positive-operator-valued measurement for the N=2 case, a rigorous bound for N=3, and set up the analysis for arbitrary N.

Universality of optimal measurements

We present optimal and minimal measurements on identical copies of an unknown state of a quantum bit when the quality of measuring strategies is quantified with the gain of information (Kullback-or mutual information-of probability distributions). We also show that the maximal gain of information occurs, among isotropic priors, when the state is known to be pure. Universality of optimal measurements follows from our results: using the fidelity or the gain of information, two different figures of merits, leads to exactly the same conclusions for isotropic distributions. We finally investigate the optimal capacity of N copies of an unknown state as a quantum channel of information.

Optimal estimation of two-qubit pure-state entanglement

We present optimal measuring strategies for an estimation of the entanglement of unknown two-qubit pure states and of the degree of mixing of unknown single-qubit mixed states, of which N identical copies are available. The most general measuring strategies are considered in both situations, to conclude in the first case that a local, although collective, measurement suffices to estimate entanglement, a nonlocal property, optimally.

Minimal optimal generalized quantum measurements

Optimal and finite positive operator valued measurements on a finite number N of identically prepared systems have recently been presented. With physical realization in mind, we propose here optimal and minimal generalized quantum measurements for two-level systems. We explicitly construct them up to N = 7 and verify that they are minimal up to N = 5.

Optimal strategies for sending information through a quantum channel

Quantum states can be used to encode the information contained in a direction, i.e., in a unit vector. We present the best encoding procedure when the quantum state is made up of N spins (qubits). We find that the quality of this optimal procedure, which we quantify in terms of the fidelity, depends solely on the dimension of the encoding space. We also investigate the use of spatial rotations on a quantum state, which provide a natural and less demanding encoding. In this case we prove that the fidelity is directly related to the largest zeros of the Legendre and Jacobi polynomials. We also discuss our results in terms of the information gain.

Optimal network topologies for local search with congestion

The problem of searchability in decentralized complex networks is of great importance in computer science, economy, and sociology. We present a formalism that is able to cope simultaneously with the problem of search and the congestion effects that arise when parallel searches are performed, and we obtain expressions for the average search cost both in the presence and the absence of congestion. This formalism is used to obtain optimal network structures for a system using a local search algorithm. It is found that only two classes of networks can be optimal: starlike configurations, when the number of parallel searches is small, and homogeneous-isotropic configurations, when it is large.

Optimal fiscal policy in overlapping generations models

[eng] This paper provides, from a theoretical and quantitative point of view, an explanation of why taxes on capital returns are high (around 35%) by analyzing the optimal fiscal policy in an economy with intergenerational redistribution. For this purpose, the government is modeled explicitly and can choose (and commit to) an optimal tax policy in order to maximize society's welfare. In an infinitely lived economy with heterogeneous agents, the long run optimal capital tax is zero. If heterogeneity is due to the existence of overlapping generations, this result in general is no longer true. I provide sufficient conditions for zero capital and labor taxes, and show that a general class of preferences, commonly used on the macro and public finance literature, violate these conditions. For a version of the model, calibrated to the US economy, the main results are: first, if the government is restricted to a set of instruments, the observed fiscal policy cannot be disregarded as sub optimal and capital taxes are positive and quantitatively relevant. Second, if the government can use age specific taxes for each generation, then the age profile capital tax pattern implies subsidizing asset returns of the younger generations and taxing at higher rates the asset returns of the older ones.

Interiority of the optimal population growth rate with endogenous fertility

This paper analyzes the issue of the interiority of the optimal population growth rate in a two-period overlapping generations model with endogenous fertility. Using Cobb-Douglas utility and production functions, we show that the introduction of a cost of raising children allows for the possibility of the existence of an interior global maximum in the planner¿s problem, contrary to the exogenous fertility case

Optimal stop-loss reinsurance: a dependence analysis

The stop-loss reinsurance is one of the most important reinsurance contracts in the insurance market. From the insurer point of view, it presents an interesting property: it is optimal if the criterion of minimizing the variance of the cost of the insurer is used. The aim of the paper is to contribute to the analysis of the stop-loss contract in one period from the point of view of the insurer and the reinsurer. Firstly, the influence of the parameters of the reinsurance contract on the correlation coefficient between the cost of the insurer and the cost of the reinsurer is studied. Secondly, the optimal stop-loss contract is obtained if the criterion used is the maximization of the joint survival probability of the insurer and the reinsurer in one period.

Optimal capital structure: a trade-off model and its empirical testing

In the present research we have set forth a new, simple, Trade-Off model that would allow us to calculate how much debt and, by default, how much equity a company should have, using easily available information and calculating the cost of debt dynamically on the basis of the effect that the capital structure of the company has on the risk of bankruptcy; in an attempt to answer this question. The proposed model has been applied to the companies that make up the Dow Jones Industrial Average (DJIA) in 2007. We have used consolidated financial data from 1996 to 2006, published by Bloomberg. We have used simplex optimization method to find the debt level that maximizes firm value. Then, we compare the estimated debt with real debt of companies using statistical nonparametric Mann-Whitney. The results indicate that 63% of companies do not show a statistically significant difference between the real and the estimated debt.