Controlling Chaos Through Local Knowledge

We propose an duopoly game where quantity-setting firms have incomplete information about the demand function. In each time step, they solve a profit maximization problem assuming a linear local approximation of the demand function. In particular, we construct an example using the well known duopoly Puu's model with isoelastic demand function and constant marginal costs. An explicit form of the dynamical system that describes the time evolution of the duopoly game with boundedly rational players is given. The main result is the global stability of the system.Cournot duopoly, incomplete information, isoelastic demand function, time evolution, boundedly rational players.

New properties of the Cournot duopoly with isoelastic demand and constant unit costs.

The object of the work is to perform the global analysis of the Cournot duopoly model with isoelastic demand function and unit costs, presented in Puu (1991). The bifurcation of the unique Cournot fixed point is established, which is a resonant case of the Neimark-Shacker bifurcation. New properties associated with the introduction of horizontal branches are evidenced. These properties di¤er significantly when the constant value is zero or positive and small. The good behavior of the case with positive constant is proved, leading always to positive trajectories. Also when the Cournot fixed point is unstable, stable cycles of any period may exist.Cournot duopoly, isoelastic demand function, multistability, border-collision bifurcations.

Mathematical Properties of a Combined Cournot-Stackelberg model.

The object of this work is to perform the global analysis of a new duopoly model which couples the two points of view of Cournot and Stackelberg. The Cournot model is assumed with isoelastic demand function and unit costs. The coupling leads to discontinuous reaction functions, whose bifurcations, mainly border collision bifurcations, are investigates as well as the global structure of the basins of attraction. In particular, new properties are shown, associated with the introduction of horizontal branches, which di¤er significantly when the constant value is zero or positive and small. The good behavior of the model with positive constant is proved, leading to stable cycles of any period.Cournot-Stackelberg duopoly, Isoelastic demand function, Discontinuous reaction functions, Multistability, Border-collision bifurcations.

Isoelastic Agents and Wealth Updates in Machine Learning Markets

Recently, prediction markets have shown considerable promise for developing flexible mechanisms for machine learning. In this paper, agents with isoelastic utilities are considered. It is shown that the costs associated with homogeneous markets of agents with isoelastic utilities produce equilibrium prices corresponding to alpha-mixtures, with a particular form of mixing component relating to each agent's wealth. We also demonstrate that wealth accumulation for logarithmic and other isoelastic agents (through payoffs on prediction of training targets) can implement both Bayesian model updates and mixture weight updates by imposing different market payoff structures. An iterative algorithm is given for market equilibrium computation. We demonstrate that inhomogeneous markets of agents with isoelastic utilities outperform state of the art aggregate classifiers such as random forests, as well as single classifiers (neural networks, decision trees) on a number of machine learning benchmarks, and show that isoelastic combination methods are generally better than their logarithmic counterparts.Comment: Appears in Proceedings of the 29th International Conference on Machine Learning (ICML 2012

The Firm’s Perception of Demand Shocks and the Expected Profitability of Capital under Uncertainty

This paper revisits the results of the pioneering models of the firm under demand uncertainty and analyses the apparent disparity with respect to the signal of the investment-uncertainty relationship predicted by them. In the 1970’s-1980’s the modelling of demand uncertainty at the firm level taking into account the firm’s optimal choice of factor inputs constituted a cutting-edge research topic. But while setting the standards in the literature of the firm’s optimal behaviour under uncertainty, those models did not clarify the rationale behind the disparity of the results concerning the impact of increased uncertainty on the firm’s desired investment. In the context of an isoelastic stochastic demand function, where the shock variable may enter either linearly or non-linearly, we show it is the way the firm perceives the demand shocks that, by determining the shape of the profit function, establishes the signal of the investment-uncertainty relationship predicted by the model.Demand Uncertainty; Expected Profitability; Shock Perception; Jensen’s Inequality.

MODELLING THE EFFECTS OF EU SUGAR MARKET LIBERALIZATION ON AREA ALLOCATION, PRODUCTION AND TRADE

This paper presents a partial equilibrium simulation analysis of EU sugar market reforms with a version of the European Simulation Model (ESIM) addressing three issues: preferential EU imports are a function of the price differential between world market and EU price, EU supply functions are estimated based on FADN data, and the production of bioethanol in the EU and the rest of the world is taken into account as an important component in sugar beet and sugar cane demand. It is found that the current sugar market reform including the restructuring process until the end of 2007 is sufficient to allow the EU to comply with its WTO commitments only very narrowly. EU sugar supply is simulated to decrease from roughly 19 million tons in the base period to 15.5 million tons by 2015 and the EU price remains at a level of about 450 €/t and thus significantly above the reference price. In case of full liberalization production in the EU is projected to decrease to 7.5 million tonnes by 2015.Sugar, Common Agricultural Policy, Sugar Market Reform, Partial Equilibrium Modelling, Everything But Arms, Agricultural and Food Policy, Crop Production/Industries, International Relations/Trade,

On the Optimal Taxation of an Exhaustible Resource Under Monopolistic Extraction

In a simple model of resource depletion (isoelastic demand and constant unit extraction cost), we fully characterize the set of linear effiency-inducing tax/subsidy schemes. We show that this set is infinite and all the larger as the cost of extraction is low. Depending on the magnitude of the latter, we show that there may exist optimal linear strict taxes, thus allowing the regulator to induce efficiency without subsidizing the mine industry at any date. We illustrate and argue that the exhaustibility constraint the monopolist extractor faces can be exploited by the regulator to relax the standard trade-off between inducing efficiency and raising revenues from the monopoly.Exhaustible resources;Imperfect competition;Optimal taxation

The macroeconomics of subsistence points

This paper explores the macroeconomic consequences of preferences displaying a subsistence point. It departs from the existing related literature by assuming that subsistence points are specific to each variety of goods rather than to the composite consumption good. We show that this simple feature makes the price elasticity of demand for individual goods procyclical. As a result, markups behave countercyclically in equilibrium. This implication is in line with the available empirical evidence

Optimal taxation of a monopolistic extractor: are subsidies necessary?

In a standard partial equilibrium model of resource depletion, this paper charac- terizes and examines the solution to the optimal taxation problem when extraction is monopolistic. The main result is that the family of subgame perfect effciency- inducing tax/subsidy schemes may include some strict tax policies. This illustrates how the static trade-off between inducing effciency and raising tax revenues in the presence of market power is relaxed under exhaustibility.Exhaustible resources, Imperfect competition, Optimal taxation