ESEIG - MAT - Livros, partes de livro ou capítulos de livro
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- Avaliar?... Como?Publication . Soares, Filomena Baptista; Nunes, Maria Paula
- Cálculo diferencial e integral: exercíciosPublication . Machado, J. A. Tenreiro; Galhano, Alexandra; Ferreira, Flávio; Ferreira, Fernanda A.
- Fine structures of hyperbolic diffeomorphismsPublication . Pinto, Alberto A.; Rand, David A.; Ferreira, Flávio
- Flexibility in Stackelberg leadershipPublication . Ferreira, Fernanda A.; Ferreira, Flávio; Pinto, Alberto A.We consider a Stackelberg model with demand uncertainty, only for the first mover. We study the advantages of leadership and flexibility with the variation of the demand uncertainty. Liu proved for demand uncertainty parameter greater than three that the follower firm can have an advantage with respect to the leading firm for some realizations of the demand intercept. Here, we prove that for demand uncertainty parameter less than three the leading firm is always in advantage.
- Hausdorff dimension versus smoothnessPublication . Ferreira, Flávio; Pinto, Alberto A.; Rand, David A.There is a one-to-one correspondence between C1+H Cantor exchange systems that are C1+H fixed points of renormalization and C1+H diffeomorphisms f on surfaces with a codimension 1 hyperbolic attractor Λ that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Λ. However, there is no such C1+α Cantor exchange system with bounded geometry that is a C1+α fixed point of renormalization with regularity α greater than the Hausdorff dimension of its invariant Cantor set. The proof of the last result uses that the stable holonomies of a codimension 1 hyperbolic attractor Λ are not C1+θ for θ greater than the Hausdorff dimension of the stable leaves of f intersected with Λ.
- Investing to survive in a duopoly modelPublication . Pinto, Alberto A.; Oliveira, Bruno M. P. M.; Ferreira, Fernanda A.; Ferreira, MiguelWe present deterministic dynamics on the production costs of Cournot competitions, based on perfect Nash equilibria of nonlinear R&D investment strategies to reduce the production costs of the firms at every period of the game. We analyse the effects that the R&D investment strategies can have in the profits of the firms along the time. We show that small changes in the initial production costs or small changes in the parameters that determine the efficiency of the R&D programs or of the firms can produce strong economic effects in the long run of the profits of the firms.
- MOOC no Instituto Politécnico do Porto: um novo formato de ensino a distânciaPublication . Soares, Filomena Baptista; Lopes, Ana Paula
- Price-setting dynamical duopoly with incomplete informationPublication . Ferreira, Fernanda A.; Ferreira, Flávio; Pinto, Alberto A.We consider a price competition in a duopoly with substitutable goods, linear and symmetric demand. There is a firm (F 1) that chooses first the price p 1 of its good; the other firm (F 2) observes p 1 and then chooses the price p 2 of its good. The conclusions of this price-setting dynamical duopoly are substantially altered by the presence of either differentiated goods or asymmetric information about rival’s production costs. In this paper, we consider asymmetric information about rival’s production costs. We do ex-ante and ex-post analyses of firms’ profits and market prices. We compare the ex-ante firms’ expected profits with the ex-post firms’ profits.
- Privatization and government preferences in a mixed duopoly: Stackelberg versus CournotPublication . Ferreira, Fernanda A.; Ferreira, FlávioWe analyse the relationship between the privatization of a public firm and government preferences for tax revenue, by considering a (sequential) Stackelberg duopoly with the public firm as the leader. We assume that the government payoff is given by a weighted sum of tax revenue and the sum of consumer and producer surplus. We get that if the government puts a sufficiently larger weight on tax revenue than on the sum of both surpluses, it will not privatize the public firm. In contrast, if the government puts a moderately larger weight on tax revenue than on the sum of both surpluses, it will privatize the public firm. Furthermore, we compare our results with the ones previously published by an other author obtained in a (simultaneous) Cournot duopoly.
- Quantity competition in a differentiated duopolyPublication . Ferreira, Fernanda A.; Ferreira, Flávio; Ferreira, Miguel; Pinto, Alberto A.In this paper, we consider a Stackelberg duopoly competition with differentiated goods, linear and symmetric demand and with unknown costs. In our model, the two firms play a non-cooperative game with two stages: in a first stage, firm F 1 chooses the quantity, q 1, that is going to produce; in the second stage, firm F 2 observes the quantity q 1 produced by firm F 1 and chooses its own quantity q 2. Firms choose their output levels in order to maximise their profits. We suppose that each firm has two different technologies, and uses one of them following a certain probability distribution. The use of either one or the other technology affects the unitary production cost. We show that there is exactly one perfect Bayesian equilibrium for this game. We analyse the variations of the expected profits with the parameters of the model, namely with the parameters of the probability distributions, and with the parameters of the demand and differentiation.