Lorenz integrable system moves \`a la Poinsot

A transformation is derived which takes Lorenz integrable system into the well-known Euler equations of a free-torque rigid body with a fixed point, i.e. the famous motion \`a la Poinsot. The proof is based on Lie group analysis applied to two third order ordinary differential equations admitting the same two-dimensional Lie symmetry algebra. Lie's classification of two-dimensional symmetry algebra in the plane is used. If the same transformation is applied to Lorenz system with any value of parameters, then one obtains Euler equations of a rigid body with a fixed point subjected to a torsion depending on time and angular velocity. The numerical solution of this system yields a three-dimensional picture which looks like a "tornado" whose cross-section has a butterfly-shape. Thus, Lorenz's {\em butterfly} has been transformed into a {\em tornado}.Comment: 14 pages, 6 figure

IVF, same-sex couples and the value of biological ties

Ought parents, in general, to value being biologically tied to their children? Is it important, in particular, that both parents be biologically tied to their children? I will address these fundamental questions by looking at a fairly new practice within IVF treatments, so-called IVF-with-ROPA ( Reception of Oocytes from Partner ), which allows lesbian couples to „share motherhood‟ with one partner providing the eggs while the other becomes pregnant. I believe that IVF-with-ROPA is, just like other IVF treatments, morally permissible; but here I argue that the increased biological ties which IVF-with-ROPA allows for do not have any particular value beside the satisfaction of a legitimate wish, because there is no intrinsic value in a biological tie between parents and children; further, I argue that equality within parental projects cannot be achieved by redistributing biological ties

I love my children: am I racist? On the wish to be biologically related to one’s children

Is the wish to be biologically related to your children legitimate? Here, I respond to an argument in support of a negative answer to this question according to which a preference towards having children one is biologically related to is analogous to a preference towards associating with members of one’s own race. I reject this analogy, mainly on the grounds that only the latter constitutes discrimination; still, I conclude that indeed a preference towards children one is biologically related to is morally illegitimate because, in the context of parental love, biological considerations are normatively irrelevant

Performance pay and shifts in macroeconomic correlations

A coincidence in time between the volatility break associated with the "Great Moderation" and large changes in the pattern of conditional and unconditional correlations between output, hours and labor productivity was detected by Galí and Gambetti (2009). We provide a novel explanation for these findings, based on the major changes that occurred in the U.S. design of labor compensation around the mid-1980s. These include a substantial increase in the incidence of performance pay coupled with a higher responsiveness of real wages to the business cycle. We capture this shift in the structure of labor compensation in a Dynamic New Keynesian (DNK) model and show that, by itself, it generates the disappearance of the procyclical response of labor productivity to non-technology shocks and a reduction of the contractionary effects of technology shocks on hours worked. Moreover, it accounts for a large share of the observed drop in output volatility after 1984 and for most of the observed changes in unconditional correlations.procyclical productivity, wage rigidities, performance pay.

Labor effort over the business cycle

Unobservable labor utilization is recognized as a crucial feature of economic fluctuations. Yet very little is known on the behavior of work effort over the business cycle. By using firm-level panel data drawn from two high-quality sources, we obtain a microeconomic estimate of variable labor effort from a dynamic cost minimization set-up. We argue that, contrary to common assumptions, the relationship between effort and hours is not monotonic. During a recovery, if a critical level of hours per capita is reached (say, because of labor market rigidities), every additional hour is worked with decreasing effort, due to physical fatigue. We provide supporting evidence by estimating the structural parameters of a Taylor approximation of the effort function. Corroborating evidence has been obtained by estimating the elasticity of effort with respect to hours at different business cycle conditions.labor effort, factor hoarding, business cycles

Lagrangians Galore

Searching for a Lagrangian may seem either a trivial endeavour or an impossible task. In this paper we show that the Jacobi last multiplier associated with the Lie symmetries admitted by simple models of classical mechanics produces (too?) many Lagrangians in a simple way. We exemplify the method by such a classic as the simple harmonic oscillator, the harmonic oscillator in disguise [H Goldstein, {\it Classical Mechanics}, 2nd edition (Addison-Wesley, Reading, 1980)] and the damped harmonic oscillator. This is the first paper in a series dedicated to this subject.Comment: 16 page

Unobserved Factor Utilization, Technology Shocks and Business Cycles

We derive a measure of technological change using firm-level panel data and controlling for imperfect competition, increasing returns and unobserved factor utilization. We show that the latter variable accounts for a relevant portion of the cyclicality of the Solow residual. Our key finding is that technological shocks result in a contraction of inputs on impact. Whilst this result is hard to reconcile with the transmission mechanism of real business cycle models, it is consistent with simple sticky-price models. Using survey information on the frequency and size of price revisions, we show that the evidence on the contractionary effects of technology shocks is indeed much stronger for firms with stickier prices.factor hoarding, technology shocks, business cycles

Pricing behavior and the comovement of productivity and labor: evidence from firm-level data

Recent contributions have suggested that technology shocks have a negative short-run effect on labor input, contrary to the predictions of standard flexible-price models of the business cycle. Some authors have interpreted this finding as evidence in favor of stickyprice models, while others have either augmented flexible-price models in a number of ways or disputed the empirical finding itself. In this paper we estimate a number of alternative measures of TFP growth for a representative sample of Italian manufacturing firms and find a negative impact of productivity shocks on labor input. Furthermore, by relying on the firmlevel reported frequency of price reviews, we find that the contractionary effect is strong for firms with stickier prices, but it is weaker or not significant for firms with more flexible prices, consistently with the prediction of sticky-price models.Productivity shocks, Labor input, price stickiness

Exchange Rate, Employment and Hours: What Firm-Level Data Say

Using a representative panel of manufacturing firms, we estimate the response of job and hours worked to currency swings, showing that it depends primarily on the firm's exposure to foreign sales and its reliance on imported inputs. Further, we show that, for given international orientation, the response to exchange rate fluctuations is magnified when firms exhibit a lower monopoly power and when they face foreign pressure in the domestic market through import penetration. The degree of substitutability between imported and other inputs and the distribution of workers by type introduce additional degrees of specificity in the employment sensitivity to exchange rate swings. Further, wage adjustments are also shown to provide a channel through which firms react to currency shocks. Finally, gross job flows within the firm are found to depend on exchange rate fluctuations, although the effect on job creation is predominant.Employment, Exchange Rate, Firm's Foreign Exposure

Gauge Variant Symmetries for the Schr\"odinger Equation

The last multiplier of Jacobi provides a route for the determination of families of Lagrangians for a given system. We show that the members of a family are equivalent in that they differ by a total time derivative. We derive the Schr\"odinger equation for a one-degree-of-freedom system with a constant multiplier. In the sequel we consider the particular example of the simple harmonic oscillator. In the case of the general equation for the simple harmonic oscillator which contains an arbitrary function we show that all Schr\"odinger equations possess the same number of Lie point symmetries with the same algebra. From the symmetries we construct the solutions of the Schr\"odinger equation and find that they differ only by a phase determined by the gauge.Comment: 12 page