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.

MFN status and the choice of tariff regime

The gradualist approach to trade liberalization views the uniform tariffs implied by MFN status as an important step on the path to free trade. We investigate whether a regime of uniform tariffs will be preferable to discriminatory tariffs when countries engage in non-cooperative interaction in multilateral trade. The analysis includes product differentiation and asymmetric costs. We show that with the cost asymmetry the countries will disagree on the choice of tariff regime. When the choice of import tariffs and export subsidies is made sequentially the uniform tariff regime may not be sustainable, because of an incentive to deviate to a discriminatory regime. Hence, an international body is needed to ensure compliance with tariff agreement

B\'ezier curves that are close to elastica

We study the problem of identifying those cubic B\'ezier curves that are close in the L2 norm to planar elastic curves. The problem arises in design situations where the manufacturing process produces elastic curves; these are difficult to work with in a digital environment. We seek a sub-class of special B\'ezier curves as a proxy. We identify an easily computable quantity, which we call the lambda-residual, that accurately predicts a small L2 distance. We then identify geometric criteria on the control polygon that guarantee that a B\'ezier curve has lambda-residual below 0.4, which effectively implies that the curve is within 1 percent of its arc-length to an elastic curve in the L2 norm. Finally we give two projection algorithms that take an input B\'ezier curve and adjust its length and shape, whilst keeping the end-points and end-tangent angles fixed, until it is close to an elastic curve.Comment: 13 pages, 15 figure

The Community Meat Ring

Fresh meat regularly and at reasonable prices” is what a rural community in Douglas county has adopted as its slogan. To have fresh meat whenever desired from farm butchered livestock is too often considered practically impossible on account of the rather limited amount of fresh meat that a family could use before the meat spoils. To get it regularly from a butcher shop involves added time aside from the fact that very high prices are charged. The salting, curing, smoking, and other methods of meat preservation are practiced to a certain extent by farmers throughout the country, but supplies of meat kept in this way generally become exhausted in late summer, and furthermore, meat so preserved cannot take the place of fresh meat. To remedy this meat problem, the rural community west of Armour, South Dakota, with the assistance of the Farm Bureau formed a “Community Meat Ring.” (See more in text.

Mathematical modelling of curtain coating

We present a simple mathematical model for the fluid flow in the curtain coating process, exploiting the small aspect ratio, and examine the model in the large-Reynolds-number limit of industrial interest. We show that the fluid is in free fall except for a region close to the substrate, but find that the model can not describe the turning of the curtain onto the substrate. We find that the inclusion of a viscous bending moment close to the substrate allows the curtain to “turn the corner”

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