Collusion and the elasticity of demand

The analysis of collusion in infinitely repeated Cournot oligopoly games has generally assumed that demand is linear, but this note uses constant-elasticity demand functions to investigate how the elasticity of demand affects the sustainability of collusion.cartel

State aid to investment and R&D

The prohibition of state aid to investment and R&D in an integrated market such as the European Community is analysed in a Cournot oligopoly model where firms undertake investment or R&D to reduce their costs. Both strategic and non-strategic investment and R&D are considered. Governments in the Member States give subsidies for investment and R&D, which are financed by distortionary taxation so the opportunity cost of government revenue exceeds unity. Prohibiting state aid to investment will always increase aggregate welfare. Prohibiting state aid to R&D will always increase aggregate welfare if spillovers from R&D are small. If spillovers from R&D are moderate then there exists a range of values for opportunity cost where governments give state aid and where the prohibition of state aid will increase aggregate welfare. Prohibiting state aid to R&D will reduce aggregate welfare if spillovers from R&D are large.State aid prohibition, Cournot oligopoly model, R&D spillovers, distortionary taxation, Collie, R&D, research and development

Export Taxes under Bertrand Duopoly

This article analyses export taxes in a Bertrand duopoly with product differentiation, where a home and a foreign firm both export to a third-country market. It is shown that the maximum-revenue export tax always exceeds the optimum-welfare export tax. In a Nash equilibrium in export taxes, the country with the low cost firm imposes the largest export tax. The results under Bertrand duopoly are compared with those under Cournot duopoly. It is shown that the absolute value of the export subsidy or tax under Cournot duopoly exceeds the export tax under Bertrand duopoly.

Product Differentiation and the Gains from Trade under Bertrand Duopoly

In the literature on the welfare effects of free trade under imperfect competition, one important case seems to have been overlooked and that is the Bertrand duopoly model with differentiated products. Although many authors have analysed the welfare effects of free trade under Cournot duopoly, and demonstrated the possibility of losses from trade, there has been no thorough analysis of the welfare effects of free trade under Bertrand duopoly. This paper presents a thorough analysis of the welfare effects of free trade under Bertrand duopoly with differentiated products, and it is shown that there are always gains from trade.gains from trade, Bertrand Oligopoly

Maximum-Revenue Tariffs versus Free Trade

Welfare with the maximum‐revenue tariff is compared to free‐trade welfare under Cournot duopoly with differentiated products; under Bertrand duopoly with differentiated products; and under perfect competition in the case of a large country able to affect its terms of trade. Under Cournot duopoly and Bertrand duopoly, assuming linear demands and constant marginal costs, welfare with the maximum‐revenue tariff is always higher than free‐trade welfare. Under perfect competition, assuming linear demand and supply, welfare with the maximum‐revenue tariff will be higher than free‐trade welfare if the country has sufficient market power

Taxation and the sustainability of collusion: ad valorem versus specific taxes

Assuming constant marginal cost, it is shown that a switch from specific to ad valorem taxation that results in the same collusive price has no effect on the critical discount factor required to sustain collusion. This result is shown to hold for Cournot oligopoly when collusion is sustained with Nash-reversion strategies or optimal-punishment strategies. In a Cournot duopoly model with linear demand and quadratic costs, it is shown that the critical discount factor is lower with an ad valorem tax than with a specific tax that results in the same collusive price. However, in contrast to Colombo and Labrecciosa (2013) it is shown that the revenue is always higher with an ad valorem tax than with a specific tax

Instantons, Fermions and Chern-Simons Terms

In five spacetime dimensions, instantons are finite energy, solitonic particles. We describe the dynamics of these objects in the presence of a Chern-Simons interaction. For U(N) instantons, we show that the 5d Chern-Simons term induces a corresponding Chern-Simons term in the ADHM quantum mechanics. For SU(N) instantons, we provide a description in terms of geodesic motion on the instanton moduli space, modified by the presence of a magnetic field. We show that this magnetic field is equal to the first Chern character of an index bundle. All of these results are derived by a simple method which follows the fate of zero modes as fermions are introduced, made heavy, and subsequently integrated out.Comment: 12 pages. v2: factor of 2 correcte

Pathophysiological correlations in maedi: a chronic lymphoid interstitial pneumonia of sheep

Maedi is a chronic lymphoid interstitial pneumonia (LIP) of sheep caused by the lentivirus, maedi-visna virus (MW). Following a long prepatent phase maedi progresses to clinical disease characterised by exercise intolerance and dyspnoea. Although maedi is well characterised at a pathological level, physiological studies of the disease have not been undertaken. As a consequence, the nature of the functional abnormality that underlies the clinical disease is unknown, whether there exists measurable functional deficit in the preclinical phase of the disease is unknown and the relationship between lung pathology and functional deficit is unknown. These questions are fundamental to understanding the way in which pathological events ultimately conspire to bring about organ dysfunction and clinical disease. Further, knowledge of the way in which pathology relates to measurable lung dysfunction offers a potential means of assessing the progress and prognosis of this disease. This thesis describes an investigation into the pathophysiological mechanisms responsible for inducing lung functional deficits in maedi.As a prelude to establishing the nature of the functional deficit in maedi, repeated measurements of static lung compliance (Cst), lung distensibility (K), effective alveolar volume (VA,eff) and transfer factor for carbon monoxide (TL,CO,'sb') were made in anaesthetized control sheep, seronegative for MW, over a period of 5 months. This study furnished regression equations and prediction intervals for lung function indices in normal sheep using bodyweight as the independent variable. By comparison with predicted normal values sheep naturally infected with MW had reduced lung volumes and gas diffusing capabilities and increased lung elastic recoil.A pathophysiological study was instigated to identify structural correlates of lung functional deficits. Preliminary investigation involved the quantitative morphometric characterisation of the normal sheep lung. Data from this study indicated that the ratio of fixed to physiological lung volume ranged from 0.49 to 0.59 and that this ratio was positively correlated with the time between euthanasia and inflation fixation of the lungs. Values for tissue volume fraction within the lung parenchyma (Fvt) ranged from 0.18 to 0.25 and values for alveolar surface density (Svt) ranged from 592 to 716 cm2/cm3. Pathophysiological correlations in MW-infected sheep indicated that lung volume and transfer factor measurements were more sensitive indices of pathology than measurements of Cst or K. Transfer factor was reduced even in sheep with minimal histopathology suggesting this index as a sensitive means of assessing this condition. The density of surface forces could not account for variation in K seen in vivo, however tissue factors such as the quantity and functional tone of contractile tissue in the parenchyma, airways or blood vessels may contribute. Given that parenchymal smooth muscle hyperplasia is a pathological feature of maedi, it was hypothesized that this tissue element is responsible for the observed reduction in K.In order to further investigate this relationship, the distribution and morphometric quantitation of a-smooth muscle actin (ASMA) in lung parenchyma from normal and MW-infected 4 sheep was determined and related to in vivo functional measurements. The volume density of ASMA (IVASMA1) was negatively correlated with K and Cst, however partial correlation coefficients indicated that IVASMA' and Fvt were strongly interdependent thus complicating interpretation of the link between Fv'ASMA' and K. In order to separate the influence of dynamic and passive tissue elements, histamine and clenbuterol were administered to normal and MWinfected sheep in an attempt to cause relaxation and contraction of parenchymal contractile tissue. The functional response of the cardiopulmonary system to intravenous infusion of these agents was measured and correlated with Fv'ASMA'. K and Cst were significantly increased following clenbuterol injection, however only the increase in K was correlated with the quantity of Fv'ASMA', and this correlation was negative. These results could be explained if the site of action of clenbuterol was not the contractile tissue at the level of the alveolar ducts, but rather that which surrounds conducting airways.The dose of histamine required to lower dynamic compliance to 65% of baseline values was negatively correlated with Fv'ASMA' and the attendant percentage change in K was positively correlated with Fv'ASMA'. These findings support the contention that parenchymal contractile tissue is of functional relevance and capable of regulating overall lung elastic properties.Maedi is a naturally occurring disease in sheep in which the aetiologic agent and target cell is known and in which the pathology is well characterised. As such it has potential as a model for LIP associated with human immunodeficiency virus infection in children and adults. The present study has both served to establish the functional characteristics of this disease and indicate structural correlates of observed functional deficits. Moreover, evidence is presented to suggest that the observed reduction in lung distensibility in maedi is a consequence of increased tissue forces associated with the parenchymal smooth muscle hyperplasia that is a feature of this disease