International Oligopoly and Asymmetric Labour Market Institutions

Asymmetries in labour relations can have important effects on imperfectively competitive rivalries between firms. Such asymmetries are particularly striking in cross-country comparisons and are therefore of greatest interest in international markets. Using a simple duopoly model, we focus on two asymmetries. First, one firm may face a noncooperative union and second, institutional factors may allow one firm to commit itself to particular labour input before its rival sets output, giving it a natural Stackelberg leadership role. We examine the trade policy incentives resulting from these labour asymmetries, focusing on profit shifting tariffs, quotas and subsidies.

Export Subsidies and International Market Share Rivalry

Countries often perceive themselves as being in competition with each other for profitable international markets. In such a world export subsidies can appear as attractive policy tools, from a national point of view, because they improve the relative position of a domestic firm in noncooperative rivalries with foreign firms, enabling it to expand its market share and earn greater profits. In effect, subsidies change the initial conditions of the game that firms play. The terms of trade move against the subsidizing country, but its welfare can increase because, under imperfect competition, price exceeds the marginal cost of exports. International noncooperative equilibriumis characterized by such subsidies on the part of exporting nations, even though they are jointly suboptimal.

Trade Warfare: Tariffs and Cartels

National governments have incentives to intervene in international markets, particularly in encouraging export cartels and in imposing tariffs on imports from imperfectly competitive foreign firms. Although the optimal response to foreign monopoly is usually a tariff, a specific subsidy will be optimal if demand is very convex, as with constant elasticity demand. If ad valorem tariffs or subsidies are considered, a subsidy is optimal if the elasticity of demand increases as consumption increases.The critical conditions in both ad valorern and specific cases hold generally for Cournot ologopoly. Noncooperative international policy equilibrium will be characterized by export cartels and rent-extracting tariffs.

Generalized DPW method and an application to isometric immersions of space forms

Let $G$ be a complex Lie group and $\Lambda G$ denote the group of maps from the unit circle ${\mathbb S}^1$ into $G$, of a suitable class. A differentiable map $F$ from a manifold $M$ into $\Lambda G$, is said to be of \emph{connection order $(_a^b)$} if the Fourier expansion in the loop parameter $\lambda$ of the ${\mathbb S}^1$-family of Maurer-Cartan forms for $F$, namely F_\lambda^{-1} \dd F_\lambda, is of the form $\sum_{i=a}^b \alpha_i \lambda^i$. Most integrable systems in geometry are associated to such a map. Roughly speaking, the DPW method used a Birkhoff type splitting to reduce a harmonic map into a symmetric space, which can be represented by a certain order $(_{-1}^1)$ map, into a pair of simpler maps of order $(_{-1}^{-1})$ and $(_1^1)$ respectively. Conversely, one could construct such a harmonic map from any pair of $(_{-1}^{-1})$ and $(_1^1)$ maps. This allowed a Weierstrass type description of harmonic maps into symmetric spaces. We extend this method to show that, for a large class of loop groups, a connection order $(_a^b)$ map, for $a<0<b$, splits uniquely into a pair of $(_a^{-1})$ and $(_1^b)$ maps. As an application, we show that constant non-zero curvature submanifolds with flat normal bundle of a sphere or hyperbolic space split into pairs of flat submanifolds, reducing the problem (at least locally) to the flat case. To extend the DPW method sufficiently to handle this problem requires a more general Iwasawa type splitting of the loop group, which we prove always holds at least locally.Comment: Some typographical correction

Bailouts in a common market: a strategic approach

Governments in the EU grant Rescue and Restructure Subsidies to bail out ailing firms. In an international asymmetric Cournot duopoly we study effects of such subsidies on market structure and welfare. We adopt a common market setting, where consumers from the two countries form one market. We show that the subsidy is positive also when it fails to prevent the exit. The reason is a strategic effect, which forces the more efficient firm to make additional cost-reducing effort. When the exit is prevented, allocative and productive efficiencies are lower and the only gaining player is the rescued firm

Mathematical Model of Easter Island Society Collapse

In this paper we consider a mathematical model for the evolution and collapse of the Easter Island society, starting from the fifth century until the last period of the society collapse (fifteen century). Based on historical reports, the available primary sources consisted almost exclusively on the trees. We describe the inhabitants and the resources as an isolated system and both considered as dynamic variables. A mathematical analysis about why the structure of the Easter Island community collapse is performed. In particular, we analyze the critical values of the fundamental parameters driving the interaction humans-environment and consequently leading to the collapse. The technological parameter, quantifying the exploitation of the resources, is calculated and applied to the case of other extinguished civilization (Cop\'an Maya) confirming, with a sufficiently precise estimation, the consistency of the adopted model.Comment: 9 pages, 1 figure, final version published on EuroPhysics Letter

Curved Flats, Pluriharmonic Maps and Constant Curvature Immersions into Pseudo-Riemannian Space Forms

We study two aspects of the loop group formulation for isometric immersions with flat normal bundle of space forms. The first aspect is to examine the loop group maps along different ranges of the loop parameter. This leads to various equivalences between global isometric immersion problems among different space forms and pseudo-Riemannian space forms. As a corollary, we obtain a non-immersibility theorem for spheres into certain pseudo-Riemannian spheres and hyperbolic spaces. The second aspect pursued is to clarify the relationship between the loop group formulation of isometric immersions of space forms and that of pluriharmonic maps into symmetric spaces. We show that the objects in the first class are, in the real analytic case, extended pluriharmonic maps into certain symmetric spaces which satisfy an extra reality condition along a totally real submanifold. We show how to construct such pluriharmonic maps for general symmetric spaces from curved flats, using a generalised DPW method.Comment: 21 Pages, reference adde

Supernova 1987A: Rotation and a Binary Companion

In this paper we provide a possible link between the structure of the bipolar nebula surrounding SN1987A and the properties of its progenitor star. A Wind Blwon Bubble (WBB) scenario is emplyed, in which a fast, tenuous wind from a Blue Supergiant expands into a slow, dense wind, expelled during an earlier Red Supergiant phase. The bipolar shapre develops due to a pole-to-equator density contrast in the slow wind (ie, the slow wind forms a slow torus). We use the Wind Compressed Disk (WCD) model of Bjorkman & Cassinelli (1992) to determine the shape of the slow torus. In the WCD scenario, the shape of the torus is determined by the rotation of the progenitor star. We then use a self-similar semi-analytical method for wind blown bubble evolution to determine the shape of the resulting bipolar nebula. We find that the union of the wind-compressed-disk and bipolar-wind-blown- bubble models allows us to recover the salient properties of SN1987A's circumstellar nebula. In particular, the size, speed and density of SN1987A's inner ring are easily reproduced in our calculations. An exploration of parameter space shows the the red supergiant progenitor must be been rotating at > 0.3 of its breakup speed. We conclude that the progenitor was most likely spun up by a merger with a binary companion. Using a simple model for the binary merger we find that the companion is likely to have had a mass > 0.5 M_sun.Comment: 30 pages, 4 figure