Locally conformal symplectic nilmanifolds with no locally conformal K\"ahler metrics

We obtain an example of a compact locally conformal symplectic nilmanifold which admits no locally conformal K\"ahler metrics. This gives a new positive answer to a question raised by L. Ornea and M. Verbitsky.Comment: 7 pages, no figures. Comments are welcome

Coordinating short- and long-run public investment rules

Modelling the accumulation rule evolving public investment is an issue of utmost interest among economists and politicians. The present paper extends the Barro (1990) model of productive government expenditure by considering a time-adapted rule for the public investment/output ratio. The rule allows a particular target on the public investment ratio to be achievable in the long-run. Additionally, throughout the transition, the government may adjust its period-by-period public investment/output ratio in response to the current productivity of public capital relative to its long-run level. The degree of this response depends on a short-run policy instrument, which is decided by the fiscal authority simultaneously to the long-run target ratio. That way, the government problem could be interpreted as a coordination problem between short- and long-term policies. In comparison with a constant-ratio rule, and under alternative taxing scenarios, important welfare improvements are found when coordinating the short- and the long-run policy instruments in an optimal way.Public investment rule, policy coordination, transitional dynamics, Endogenous growth

The public investment rule in a simple endogenous endogenous growth model with public capital: active or pasive?

In dynamic settings with public capital, it is common to assume that the government claims a constant fraction of public investment to total output each period, which is clearly a restrictive assumption. The goal of the paper is twofold: first, to find out a more reasonable rule for public investment, consistent with US data, than the constant-ratio rule; second, to analyze the impact of that rule on welfare and judge the public investment downsizing process held in US since the end of the sixties. Calibrating for US, the model simulation captures the public investment downsizing process held during 1960-2001, as well as the post-1970 slowdown in private factors productivity. Downsizing would be optimal whenever the public capital elasticity is approximately smaller than 0.09, a lower level than the general consensus in the literature. Thus, it is more likely that our result be consistent to Aschauer (1989) and Munnell (1990), which put forth that policymakers would have reduced the stock of public capital below its optimum level along this time.Public investment rule, Policy coordination, Transitional dynamics, Endogenous growth, Public capital elasticity

Some linear Jacobi structures on vector bundles

We study Jacobi structures on the dual bundle $A^\ast$ to a vector bundle $A$ such that the Jacobi bracket of linear functions is again linear and the Jacobi bracket of a linear function and the constant function 1 is a basic function. We prove that a Lie algebroid structure on $A$ and a 1-cocycle $\phi \in \Gamma (A^\ast)$ induce a Jacobi structure on $A^\ast$ satisfying the above conditions. Moreover, we show that this correspondence is a bijection. Finally, we discuss some examples and applications.Comment: 6 pages, To appear in C. R. Acad. Sci. Paris, S\'erie