Sejam !$ A= \begin{bmatrix} k & 0 & 0 \\ 0 & -1 & 1 \\ 1 & 1 & k \end{bmatrix} !$ e !$ B= \begin{bmatrix} k & 2 & 1 \\ 0 & -1 & 1 \\ 0 & 0 & k \end{bmatrix} !$. Julgue o item abaixo:

Item 1: Se k = 1 então 0 é autovalor de A.

Considere o jogo simultâneo na forma estratégica abaixo e julgue a afirmativa a seguir:

Jogador 2
Jogador 1		Estratégia A	Estratégia B
	Estratégia A	2 , 1	0 , 0
	Estratégia B	0 , 0	1 , 2

Item 1: Há apenas um equilíbrio de Nash, formado pelo par de estratégias (A,A).

Tall tales

(From The Economist print edition, May 24th 2008)

The rollercoaster, rags-to-riches story of a remarkable animation studio

PIXAR'S characters—whether the heroic toys of “Toy Story”, the father and son fish of “Finding Nemo”, the insects in “A Bug's Life” or the rat-chef of “Ratatouille”—are full of yearning; for a child to play with, a lost family member, or to become something that seems far out of reach. The small company that imagined them is just the same. Right from the beginning, Pixar, officially a computer-hardware business, secretly dreamed of a more creative life making feature films.

Ed Catmull's ambition at school had been to become an animator at Disney, but he gave up because he couldn't draw. Computer animation, he realised, having graduated in computer science and physics, could be a way to overcome this. So Mr Catmull brought together a small group of people to form a computer-graphics group, which later became Pixar. Their early attempts were uninspiring, however. Two years in the making, the 1977 film, “Tubby the Tuba”, looked bad and the story did not work. Mr Catmull and his colleagues quickly realised that fancy technology was not enough, and that story-telling was just as vital to computer animation as to the hand-drawn sort. Under John Lasseter, a young animator rejected by Disney, Pixar started to develop a new kind of cartoon, which eschewed fairy-tale plots and entertained adults as well as children.

Pixar soon drew the attention of George Lucas, director of the “Star Wars” films, and its future seemed assured. But all Mr Lucas really wanted was for the little company to make whizzy special effects for Lucasfilm's movies, not expensive computer-animated films of its own. At one point, in 1985, Pixar, losing money fast, was nearly sold to General Motors and Philips Electronics, which wanted its computer-graphics modelling tools to help design cars and transform medical scans into three-dimensional images. Even when Steve Jobs, a cofounder of Apple, came to the rescue, Pixar was still in danger. Its pretence to be a computer company was going badly: sales of the Pixar Image Computer were slow. The only significant way the company was earning money was by making cartoon advertisements to sell other companies' products.

But there was reason for hope. “Tin Toy”, a short animated film, won an Oscar in 1988, and that was enough to keep Pixar alive and, crucially, to attract the interest of Disney. Together, the two studios made “Toy Story”, which became a critical and financial success.

Several more hits followed, and Pixar astounded Hollywood with its consistency. The studio became widely revered for its creative culture and for its insistence on originality. There are few American companies with as saintly a reputation. In 2006 Disney bought Pixar for $7.4 billion, and promptly put Messrs Catmull and Lasseter in charge of Disney's own animation unit.

A number of interesting things about Disney emerge in this excellent, readable account of Pixar's early years. David Price claims, for instance, that Disney's chief executive, Michael Eisner, considered shutting down the company's animation unit after he took over as chief executive in 1984, an astonishing fact given the subsequent success of cartoon films such as “The Lion King”. Mr Price also makes clear just how much Pixar owes to Disney: it was the larger company's marketing for “Toy Story”, for instance, that gave Mr Jobs the confidence to launch an initial public offering of shares in Pixar in 2005.

Mr Price leaves Pixar and its animators in the arms of Mickey Mouse and friends, and assumes that all will be well. So far, the acquisition has undoubtedly benefited Disney. Creative types who left the animation giant in recent years are beginning to return, and morale is high at the company as Pixar prepares next month to launch its ninth feature film, “Wall-E”, about a robot in the year 2700. But will the company have the same energy in future, and what will happen when Mr Lasseter has his next “creative” spat with Disney? Pixar's life from here on, safely tucked away inside a powerful corporation, is likely to be less visible. But that does not mean it will be any less interesting.

According to the text, Pixar attracted Disney's interest due to:

Item 3: A “Crítica de Lucas” nos diz que, ao fazer previsões sobre os efeitos de uma mudança na política econômica, não se deve tomar como inalterado o comportamento dos agentes observado no passado.

Considere uma economia caracterizada pelo modelo IS-LM em economia aberta (Mundell-Fleming). O público mantém uma fração c de sua moeda na forma de moeda manual; os bancos mantêm uma fração r dos depósitos à vista na forma de reservas (o restante é emprestado). Há livre mobilidade de capitais. Julgue as seguintes afirmativas, supondo tudo o mais constante:

Item 1: Em um regime de câmbio fixo, um aumento no parâmetro r leva a uma redução do produto.