Valadier-like formulas for the supremum function II: The compactly indexed case

We generalize and improve the original characterization given by Valadier [20, Theorem 1] of the subdifferential of the pointwise supremum of convex functions, involving the subdifferentials of the data functions at nearby points. We remove the continuity assumption made in that work and obtain a general formula for such a subdifferential. In particular, when the supremum is continuous at some point of its domain, but not necessarily at the reference point, we get a simpler version which gives rise to Valadier formula. Our starting result is the characterization given in [10, Theorem 4], which uses the epsilon-subdiferential at the reference point.Comment: 23 page

Valadier-like formulas for the supremum function I

We generalize and improve the original characterization given by Valadier [18, Theorem 1] of the subdifferential of the pointwise supremum of convex functions, involving the subdifferentials of the data functions at nearby points. We remove the continuity assumption made in that work and obtain a general formula for such a subdiferential. In particular, when the supremum is continuous at some point of its domain, but not necessarily at the reference point, we get a simpler version which gives rise to the Valadier formula. Our starting result is the characterization given in [11, Theorem 4], which uses the epsilon-subdifferential at the reference point.Comment: 27 page

Acoustic displacement triangle based on the individual element test

A three node, displacement based, acoustic element is developed. In order to avoid spurious rotational modes, a higher order stiffness is introduced. The higher order stiffness is developed from an incompatible strain field which computes element volume changes under nodal rotational displacements fields. The higher order strain satisfies the IET requirements, non affecting convergence. The higher order stiffness is modulated, element by element, with a factor. Thus, the displacement based formulation is capable of placing the spurious rotational modes over the range of physical compressional modes that can be accurately captured by the mesh

International Transmission of Medium-Term Technology Cycles: Evidence from Spain as a Recipient Country

This paper documents stylized facts of international medium-term business cycles by exploring the pattern of comovement between a catching-up economy, Spain, and each of the obvious candidate countries to technological leadership of the 1950-2007 period, the U.S., France, Germany, Italy and the U.K. A remarkable feature of the international medium-term business cycle is the strong, positive lead displayed by the U.S. technology and terms of trade cycles over Spain's macroeconomic aggregates. The corresponding evidence when the counterpart to Spain is a large European economy is weaker, particularly in the case of Europe's medium-term technology cycles. Non-parametric tests results suggest that, over the medium-term cycle, a shift towards more economic integration may not necessarily be associated with increased international comovement.Medium-term business cycles; Stylized facts; International comovement; Technology diffusion.

THE COURNOT-BERTRAND PROFIT DIFFERENTIAL : A REVERSAL RESULT IN A DIFFERENTIATED DUOPOLY WITH WAGE BARGAINING

This paper compares Cournot and Bertrand equilibria in a downstream differentiated duopoly in which the input price (wage) paid by each downstream firm is the outcome of a strategic bargain with its upstream supplier (labour union). We show that the standard result that Cournot equilibrium profits exceed those under Bertrand competition - when the differentiated duopoly game is played in imperfect substitutes - is reversible. Whether equilibrium profits are higher under Cournot or Bertrand competition is shown to depend upon the nature of the upstream agents’ preferences, on the distribution of bargaining power over the input price and on the degree of product market differentiation. We find that the standard result holds unless unions are both powerful and place considerable weight on the wage argument in their utility function. One implication of this is that if the upstream agents are profit-maximising firms, then the standard result will obtain.differentiated duopoly ; wage bargaining ; Cournot ; Bertrand.

Extended linear-homothetic preferences and the Cournot-Bertrand profit differential

This paper introduces the ‘extended linear-homothetic’ preferences to model consumer choice. Specifically, we extend Datta and Dixon’s (2000) ‘standard linear-homothetic’ preferences by adding an additional term to the unit cost function. This term captures the relative importance of price interactions within sectors on the unit cost of utility. In an economy composed of a large number of sectors (K) with a sufficiently large number of firms (n) in each, the ‘extended linear-homothetic’ preferences yield (perceived) linear demands in own strategy and competitors’ strategies - where goods are characterized as substitutes. Thus, the linearity and homotheticity properties of the preferences open the possibility to develop a tractable model of oligopoly in general equilibrium. An additional novelty introduced by the ‘extended linear-homothetic’ preferences is the presence of a sectoral-specific price index in product demand. For n small, this implies that firms internalize the sectoral price effects of their individual pricing strategies. The latter, we argue, may provide us with a link between nonatomistic price and wage setters and the monetary authority

Macroeconomic Effects of Oligopolistic Competition with Wage Bargaining

Modelling oligopoly in general equilibrium is about understanding the aggregate effects of the strategic behavior that nonatomistic agents may exhibit in their markets. Real-world economies appear to be characterized by (monopoly) power-endowed agents behaving strategically - namely, firms and unions. By abstracting from this behavior, we risk missing some important features of the macroeconomy. We develop a general equilibrium model of unionized oligopoly aimed at addressing this point. We evaluate the macroeconomic effects of supply-side shocks under alternative product and labor market structures. In addition, the micro foundations of the model capture an alternative channel for the development of strategic interactions among firms, unions and the monetary authority. This channel creates a transmission mechanism for real effects of monetary policy-related shocks, which we investigate. Finally, in the light of the predictions of the model, we discuss macroecomic performance in Continental Europe over the 1990s

Services regulation, input prices and exports

Artículo de revistaThis article analyses the economic implications of a change in the regulatory framework designed to promote competition among firms, assessing the impact that barriers to competition in the services industry have on the cost of inputs and the exports of manufacturing firms in Spain. The estimates presented reveal that the reductions in barriers to competition over recent decades have had a significant impact on the real exports of manufacturing firms, especially larger ones, as a result of greater competition in the supply of their inputs. The results underline the fact that further improvements in the degree of competition may influence the competitiveness of the Spanish economy as a whol

The Cournot-Bertrand profit differential: a reversal result in a differentiated duopoly with wage bargaining

This paper compares Cournot and Bertrand equilibria in a downstream differentiated duopoly in which the input price (wage) paid by each downstream firm is the outcome of a strategic bargain with its upstream supplier (labour union). We show that the standard result that Cournot equilibrium profits exceed those under Bertrand competition - when the differentiated duopoly game is played in imperfect substitutes - is reversible. Whether equilibrium profits are higher under Cournot or Bertrand competition is shown to depend upon the nature of the upstream agents’ preferences, on the distribution of bargaining power over the input price and on the degree of product market differentiation. We find that the standard result holds unless unions are both powerful and place considerable weight on the wage argument in their utility function. One implication of this is that if the upstream agents are profit-maximising firms, then the standard result will obtain