Optimal Minimum Wage Policy in Competitive Labor Markets

This paper provides a theoretical analysis of optimal minimum wage policy in a perfectly competitive labor market. We show that a binding minimum wage while leading to unemployment is nevertheless desirable if the government values redistribution toward low wage workers and if unemployment induced by the minimum wage hits the lowest surplus workers first. This result remains true in the presence of optimal nonlinear taxes and transfers. In that context, a minimum wage effectively rations the low skilled labor that is subsidized by the optimal tax/transfer system, and improves upon the second-best tax/transfer optimum. When labor supply responses are along the extensive margin, a minimum wage and low skill work subsidies are complementary policies; therefore, the co-existence of a minimum wage with a positive tax rate for low skill work is always (second-best) Pareto inefficient. We derive formulas for the optimal minimum wage (with and without optimal taxes) as a function of labor supply and demand elasticities and the redistributive tastes of the government. We also present some illustrative numerical simulations.minimum wages, tax policy, labor supply, demand elasticity

Is exponential gravity a viable description for the whole cosmological history?

Here we analysed a particular type of $F(R)$ gravity, the so-called exponential gravity which includes an exponential function of the Ricci scalar in the action. Such term represents a correction to the usual Hilbert-Einstein action. By using Supernovae Ia, Barionic Acoustic Oscillations, Cosmic Microwave Background and $H(z)$ data, the free parameters of the model are well constrained. The results show that such corrections to General Relativity become important at cosmological scales and at late-times, providing an alternative to the dark energy problem. In addition, the fits do not determine any significant difference statistically with respect to the $\Lambda$CDM model. Finally, such model is extended to include the inflationary epoch in the same gravitational Lagrangian. As shown in the paper, the additional terms can reproduce the inflationary epoch and satisfy the constraints from Planck data.Comment: 20 pages, 6 figures, analysis extended, version published in EPJ

A paradox in bosonic energy computations via semidefinite programming relaxations

We show that the recent hierarchy of semidefinite programming relaxations based on non-commutative polynomial optimization and reduced density matrix variational methods exhibits an interesting paradox when applied to the bosonic case: even though it can be rigorously proven that the hierarchy collapses after the first step, numerical implementations of higher order steps generate a sequence of improving lower bounds that converges to the optimal solution. We analyze this effect and compare it with similar behavior observed in implementations of semidefinite programming relaxations for commutative polynomial minimization. We conclude that the method converges due to the rounding errors occurring during the execution of the numerical program, and show that convergence is lost as soon as computer precision is incremented. We support this conclusion by proving that for any element p of a Weyl algebra which is non-negative in the Schrodinger representation there exists another element p' arbitrarily close to p that admits a sum of squares decomposition.Comment: 22 pages, 4 figure

Generalized f(R,ϕ,X)f(R,\phi,X) gravity and the late-time cosmic acceleration

High-precision observational data have confirmed with startling evidence that the Universe is currently undergoing a phase of accelerated expansion. This phase, one of the most important and challenging current problems in cosmology, represents a new imbalance in the governing gravitational equations. Historically, physics has addressed such imbalances by either identifying sources that were previously unaccounted for, or by altering the gravitational theory. Several candidates, responsible for this expansion, have been proposed in the literature, in particular, dark energy models and modified gravity models, amongst others. Outstanding questions are related to the nature of this so-called "dark energy" that is driving this acceleration, and whether it is due to the vacuum energy or a dynamical field. On the other hand, the late-time cosmic acceleration may be due to modifications of General Relativity. In this work we explore a generalised modified gravity theory, namely $f(R,\phi,X)$ gravity, where $R$ is the Ricci scalar, $\phi$ is a scalar field, and $X$ is a kinetic term. This theory contains a wide range of dark energy and modified gravity models. We considered specific models and applications to the late-time cosmic acceleration.Comment: 13 pages, 1 figure; slightly revised version, displayed name corrected. arXiv admin note: text overlap with arXiv:1412.086

Blended Learning in University Education: Activities, Results and Quality

Non