Considere um jogo simultâneo, G, representado em forma matricial, com dois jogadores. O jogo de compromisso derivado do jogo simultâneo consiste em permitir que um dos jogadores se mova antes, escolhendo sua estratégia pura, que é anunciada ao outro jogador. O segundo jogador pode, então, escolher alguma de suas ações como resposta à estratégia do primeiro jogador.

Pergunta-se:

Item 4 - Se a melhor resposta do segundo jogador à qualquer estratégia x do primeiro jogador sempre for única, o primeiro jogador sempre terá um ganho no Equilíbrio de Nash perfeito em subjogo no jogo de compromisso maior ou igual ao ganho que teria em qualquer um dos Equilíbrios de Nash no jogo original, G.

Sobre a Teoria do Consumidor, assinale Verdadeiro ou Falso na alternativa abaixo:

Item 2 - Um consumidor representativo de determinada comunidade com hábitos particulares tem preferências representadas por !$ U \, = \, U_t \, (x_t^*, \, y) !$ com !$ x^*_t \, = \, x_t \, - \, x_{t-1} !$. Para esse tipo de preferências, coeteris paribus, quanto mais consumo passado o indivíduo escolher do bem x, menor será o consumo atual escolhido.

Text 2

Excerpts from:

Small eruption in Iceland

A cloud of ash from an Icelandic volcano shut European airspace for several days. Our first article examines the science of volcanic emissions.

Our second looks at the past week's disruption of travel

Apr 22nd 2010 | From The Economist print edition

SOME natural disasters, like the Indian Ocean tsunami of 2004, strike out of the blue. Only with hindsight do they come to look like the sort of thing people should have been prepared for. Other events get dress rehearsals. The eruption of Eyjafjallajokull in the south of Iceland was one of these. In February 2008 officials from air-traffic-control services across Europe, as well as representatives of weather services and airlines, ran an exercise that simulated a strikingly similar eruption. The volcano they chose was not Eyjafjallajokull, but its neighbour, Katla; the weather conditions were not quite the same. But the procedures were.

(...)

If the exercise two years ago did not capture the range of problems that an Icelandic volcano might cause, it did show that the general situation was entirely foreseeable. A ridge of submerged mountains runs down the middle of the Atlantic Ocean; Iceland is the result of a “hotspot” in which material rises from deep within the Earth, pushing part of this ridge up into the air. Both hotspots and mid-ocean ridges are volcanic, so Iceland is doubly so. It boasts a fearsome array of volcanoes, 33 of which have erupted once or more since the end of the last ice age, around 12,000 years ago.

As these volcanoes go, Eyjafjallajokull is neither very big nor particularly prolific. It has erupted only three times since Iceland was settled in the ninth century. That is why the air-traffic exercise planners chose Katla, 25km (16 miles) away; it typically erupts every 30-80 years, and in a much more spectacular way. But a combination of circumstances meant that, though comparatively small, Eyjafjallajokull's current eruption punched above its weight in the ash-production league in its early days, emitting much more fine ash than is normal. Fine ash can travel farther than the heavier stuff, but still does a lot of harm to engines if encountered in significant quantities.

(...)

Katla is not the worst that Iceland can do. Its volcanoes do not have the explosive oomph of some eruptions in the “ring of fire” around the Pacific, such as those of Tambora and Krakatoa in the 19th century, let alone the prehistoric eruptions of Taupo, in New Zealand, and Toba, in Indonesia, which were large enough to have severe, if short-lived, effects on the global climate (...) But the eruption of Oraefajokull, in the south-east of the island, in 1362 is thought by some to have eclipsed that of Mount Vesuvius which destroyed Pompeii and Herculaneum in 79AD. It may have been the biggest bang in Europe since the eruption in the 17th century BC of Santorini, which devastated the Minoan civilisation on nearby Crete. Nor is explosive power the only measure of a volcano's spitefulness. The eruption of Laki, an Icelandic volcanic fissure, in 1783 sent poisonous gases across Europe.

Another concern is that Iceland's volcanoes, especially those under its central ice cap—which, other things being equal, will produce more explosive plumes if they break through—seem to show a cycle in activity, perhaps due to the hotspot that feeds them.

On this reading of the record, activity can be expected to increase for the next 40 years or so. The past few decades have been one of the quiet patches. It seems likely that the first 50 years of jet travel across the North Atlantic enjoyed particularly clear skies.

According to the text,one of the reasons Katla was chosen for a simulation of an eruption was because:

Item 3 - its eruptions are more discreet;

Text 2

Excerpts from:

Small eruption in Iceland

A cloud of ash from an Icelandic volcano shut European airspace for several days. Our first article examines the science of volcanic emissions.

Our second looks at the past week's disruption of travel

Apr 22nd 2010 | From The Economist print edition

SOME natural disasters, like the Indian Ocean tsunami of 2004, strike out of the blue. Only with hindsight do they come to look like the sort of thing people should have been prepared for. Other events get dress rehearsals. The eruption of Eyjafjallajokull in the south of Iceland was one of these. In February 2008 officials from air-traffic-control services across Europe, as well as representatives of weather services and airlines, ran an exercise that simulated a strikingly similar eruption. The volcano they chose was not Eyjafjallajokull, but its neighbour, Katla; the weather conditions were not quite the same. But the procedures were.

(...)

If the exercise two years ago did not capture the range of problems that an Icelandic volcano might cause, it did show that the general situation was entirely foreseeable. A ridge of submerged mountains runs down the middle of the Atlantic Ocean; Iceland is the result of a “hotspot” in which material rises from deep within the Earth, pushing part of this ridge up into the air. Both hotspots and mid-ocean ridges are volcanic, so Iceland is doubly so. It boasts a fearsome array of volcanoes, 33 of which have erupted once or more since the end of the last ice age, around 12,000 years ago.

As these volcanoes go, Eyjafjallajokull is neither very big nor particularly prolific. It has erupted only three times since Iceland was settled in the ninth century. That is why the air-traffic exercise planners chose Katla, 25km (16 miles) away; it typically erupts every 30-80 years, and in a much more spectacular way. But a combination of circumstances meant that, though comparatively small, Eyjafjallajokull's current eruption punched above its weight in the ash-production league in its early days, emitting much more fine ash than is normal. Fine ash can travel farther than the heavier stuff, but still does a lot of harm to engines if encountered in significant quantities.

(...)

Katla is not the worst that Iceland can do. Its volcanoes do not have the explosive oomph of some eruptions in the “ring of fire” around the Pacific, such as those of Tambora and Krakatoa in the 19th century, let alone the prehistoric eruptions of Taupo, in New Zealand, and Toba, in Indonesia, which were large enough to have severe, if short-lived, effects on the global climate (...) But the eruption of Oraefajokull, in the south-east of the island, in 1362 is thought by some to have eclipsed that of Mount Vesuvius which destroyed Pompeii and Herculaneum in 79AD. It may have been the biggest bang in Europe since the eruption in the 17th century BC of Santorini, which devastated the Minoan civilisation on nearby Crete. Nor is explosive power the only measure of a volcano's spitefulness. The eruption of Laki, an Icelandic volcanic fissure, in 1783 sent poisonous gases across Europe.

Another concern is that Iceland's volcanoes, especially those under its central ice cap—which, other things being equal, will produce more explosive plumes if they break through—seem to show a cycle in activity, perhaps due to the hotspot that feeds them.

On this reading of the record, activity can be expected to increase for the next 40 years or so. The past few decades have been one of the quiet patches. It seems likely that the first 50 years of jet travel across the North Atlantic enjoyed particularly clear skies.

The text remarks that Eyjaffallajokull:

Item 1 - has been constantly active;

Considere as retas !$ r_1 !$ e !$ r_2, !$ no plano, definidas por

!$ \begin {cases} a_1 \, \chi \, + \, b_1 \, y \, + \, c_1 \, = \, 0 \\ a_2 \, \chi \, + \, b_2 \, y \, + \, c_2 \, = \, 0 \end {cases} !$

em que !$ n_1 \, = \, (a_1, \, b_1) !$ e !$ (a_2, \, b_2) !$ são vetores não nulos ortogonais à !$ r_1 !$ e !$ r_2 !$, respectivamente. Denotamos por !$ d(P, \, r) !$ a distância de um ponto !$ P !$ à uma reta !$ r !$ do plano.

Julgue a alternativa:

Item 2 - Considere em !$ r_1 !$ os valores !$ c_1 \, = \, 0 !$ e !$ n_1 \, = \, (1, \, - 1). !$ Se pontos distintos !$ P \, = \, (3, y_1) !$ e !$ Q \, = \, (3, \, y_2) !$ são tais que !$ d(P, r_1) \, = \, d(Q, r_1) \, = \, \sqrt{2}, !$ então !$ y_1 \, + \, y_2 \, = \, 6. !$

Julgue a alternativa:

Item 3 - Seja !$ f: \, \mathbb{R} \, \rightarrow \, \mathbf{R} !$ dada por !$ f(\chi) \, = \,\mid 5 \, - \, \chi \mid \, + \, \mid \chi \, - \, 3 \mid. !$ A função !$ f !$ não é sobrejetiva e !$ f(\chi) \, \ge \, 2, !$ para todo !$ \chi \, \in \, \mathbf{R}. !$

Sobre o Programa de Ação Econômica do Governo Castello Branco (PAEG), é correto afirmar:

Item 1 - A eficácia do programa anti-inflacionário articulado pelas políticas fiscal, monetária e salarial foi parcialmente prejudicada pela “inflação corretiva” gerada pela introdução do sistema de minidesvalorizações cambiais em 1965.