Seja a função !$ f(x,y)=-x^3+y^3+x^2+y^2 !$. Esta função:

Item 0 - Apresenta um ponto de máximo em (2/3, -2/3).

Um indivíduo tem possibilidade de escolher entre 3 situações alternativas:

Situação (1): ganhar $7,5 milhões com probabilidade de 4/5 e $15 milhões com probabilidade de 1/5.
Situação (2): ganhar $10 milhões com probabilidade de 4/5 e $5 milhões com probabilidade de 1/5.
Situação (3): ganhar $9 milhões com 100% de certeza.

Diante disto:

Item 2 - Se para este indivíduo, a utilidade de ganhar uma soma x de dinheiro for dada por U(x) = 4x, então a situação (2) é melhor que a situação (1).

Indique se o item abaixo é certo ou errado, com base no texto a que se refere.

PART II

Cambridge versus Cambridge

In most universities today, economics is booming. To undergraduates and businesspersons it spells money-making; to graduate students it offers a lucrative slot in a bank or a confortable billet in a university; to governments it promises technical wheezes for balancing the books and boosting industries. The dismal science, it seems, can do no wrong.

Harvard and Cambridge are ideally placed to exploit this boom. They can both lay claim to some of the most illustrious names in the history of the subject. And they both boast well-connected alumni and high-powered students. But nobody inside the profession doubts that Harvard is having a far better boom than Cambridge. An Oxford professor admits that Harvard has probably the best economics department in the world. A Princeton professor ranks Cambridge along, say, Phennsylvania State University. cambridge graduates frequently go on to Harvard’s graduate school; the compliment is rarely returned. What is wrong with Cambridge?

The decline of its economics department dates from its defeat in one of the noisiest battles in post-war economics - the so-called Cambridge versus Cambridge controversy. In the early 1960s a group of Cambridge economists led by Joan Robinson mounted a furious assault on neoclassical orthodoxy. The Massashusetts Institute of Technology (MIT) took up the case for the defense (Harvard being a gentlemanly backwater).

At stake was nothing less than the soul of the subject. Robinson et al. argued that neoclassical economics was interested in the wrong thing (the optimal allocation of given resources) and based on a false assumption (that man is a rational “utility maximizer.”) In the Cambridge view, the hottest subjects were te accumulation of capital and the distribution of income. To add spice to the debate, the Cambridges disagreed about method and ideology. MIT preferred mathematics and markets; Cambridge favoured elegant prose and state intervention. To the likes of Robinson, the paddy fields of China were far preferable to the skyscrapers of Manhattan.

The world went the Massachusetts way. Neoclassical economics is now international orthodoxy; the Cambridge tradition is taken seriously only in East Anglia and the Italian provinces. Economics is an over more mathematical subject. And state planning is dead.

The Cambridge controbersy did more than marginalise the dominant faction in the Cambridgeshire fens. It also divided the faculty and politicised appointments. Some senior figures, like Frank Hahn and James Meade, did the unpatriotic thing and sided with the other Cambridge. The result was civil war. It was impossible to change the syllabus or appoint a lecturer without an ideological feud. The divided faculty made a number of light-weight appointments. It also lost a generation of stars. Just three of the dozen or so who fled - Amartya Sen, Christopher Bliss and Jim Mirrlees - would make the nucleus of a world-class department.

That was almost two decades ago. Why has Cambridge taken so long to repair the damage? Partly because the place is so enthralled by its glorious past. Naming a road ofter Sidgwick, a building after Marshall and a seminar room after Keynes is dangerously close to ancestor worship. But even more important than its over-developed sense of history is its underdeveloped appetite for competition. While Cambridge sank into faction fighting, Harvard challenged MIT for the position as the best department in the world. To understand their different fates, you need to examine their rival philosophies of academic life.

(The Economist, Dec. 1991 - Jan. 1992, p.43).

According to the text:

Item 2 - Two decades ago, Cambridge did not have the competitive edge to challenge the MIT.

Suponha uma economia caracterizada pelas seguintes relações:

C = 200 + 0,8Yd I = 300
T = 0,1Y M = 0,2Yd G = 240 X = 180
Em que:
Y = renda total; Yd = renda disponível após pagamento de impostos;
C = consumo, I = investimento, G = gasto do governo,
X = exportações, M = importações, T = imposto.

Indique se o item abaixo a respeito desta economia é certo ou errado:

Item 1 -

Suponha uma economia caracterizada pelas seguintes relações:

C = 200 + 0,8Yd I = 300
T = 0,1Y M = 0,2Yd G = 240 X = 180
Em que:
Y = renda total; Yd = renda disponível após pagamento de impostos;
C = consumo, I = investimento, G = gasto do governo,
X = exportações, M = importações, T = imposto.

Indique se o item abaixo a respeito desta economia é certo ou errado:

Item 4 - Um aumento das exportações de $92 levará a uma melhoria das contas do governo da ordem de $20.

Indique se o item abaixo é certo ou errado, com base no texto a que se refere.

PART II

Cambridge versus Cambridge

In most universities today, economics is booming. To undergraduates and businesspersons it spells money-making; to graduate students it offers a lucrative slot in a bank or a confortable billet in a university; to governments it promises technical wheezes for balancing the books and boosting industries. The dismal science, it seems, can do no wrong.

Harvard and Cambridge are ideally placed to exploit this boom. They can both lay claim to some of the most illustrious names in the history of the subject. And they both boast well-connected alumni and high-powered students. But nobody inside the profession doubts that Harvard is having a far better boom than Cambridge. An Oxford professor admits that Harvard has probably the best economics department in the world. A Princeton professor ranks Cambridge along, say, Phennsylvania State University. cambridge graduates frequently go on to Harvard’s graduate school; the compliment is rarely returned. What is wrong with Cambridge?

The decline of its economics department dates from its defeat in one of the noisiest battles in post-war economics - the so-called Cambridge versus Cambridge controversy. In the early 1960s a group of Cambridge economists led by Joan Robinson mounted a furious assault on neoclassical orthodoxy. The Massashusetts Institute of Technology (MIT) took up the case for the defense (Harvard being a gentlemanly backwater).

At stake was nothing less than the soul of the subject. Robinson et al. argued that neoclassical economics was interested in the wrong thing (the optimal allocation of given resources) and based on a false assumption (that man is a rational “utility maximizer.”) In the Cambridge view, the hottest subjects were te accumulation of capital and the distribution of income. To add spice to the debate, the Cambridges disagreed about method and ideology. MIT preferred mathematics and markets; Cambridge favoured elegant prose and state intervention. To the likes of Robinson, the paddy fields of China were far preferable to the skyscrapers of Manhattan.

The world went the Massachusetts way. Neoclassical economics is now international orthodoxy; the Cambridge tradition is taken seriously only in East Anglia and the Italian provinces. Economics is an over more mathematical subject. And state planning is dead.

The Cambridge controbersy did more than marginalise the dominant faction in the Cambridgeshire fens. It also divided the faculty and politicised appointments. Some senior figures, like Frank Hahn and James Meade, did the unpatriotic thing and sided with the other Cambridge. The result was civil war. It was impossible to change the syllabus or appoint a lecturer without an ideological feud. The divided faculty made a number of light-weight appointments. It also lost a generation of stars. Just three of the dozen or so who fled - Amartya Sen, Christopher Bliss and Jim Mirrlees - would make the nucleus of a world-class department.

That was almost two decades ago. Why has Cambridge taken so long to repair the damage? Partly because the place is so enthralled by its glorious past. Naming a road ofter Sidgwick, a building after Marshall and a seminar room after Keynes is dangerously close to ancestor worship. But even more important than its over-developed sense of history is its underdeveloped appetite for competition. While Cambridge sank into faction fighting, Harvard challenged MIT for the position as the best department in the world. To understand their different fates, you need to examine their rival philosophies of academic life.

(The Economist, Dec. 1991 - Jan. 1992, p.43).

According to the text:

Item 2 - The fact that Harvard undergraduates rarely seek Cambridge to pursue a graduate degee is used as an indication of the former’s superiority.

Seja X uma variável aleatória que representa o valor das vendas de um determinado produto em um mês. X é normalmente distribuída com média $500 e desvio padrão $50. Podemos afirmar que:

Item 3 - A distribuição normal é plenamente especificada pelo seu parâmetro média.

Com relação aos testes de hipóteses, podemos afirmar que:

Item 4 - Sejam duas amostras provenientes de duas populações normais independentes. Se as variâncias populacionais são iguais porém desconhecidas, a estatística a ser utilizada no teste de igualdade de médias é a “t” de Student com (n+m-2) graus de liberdade, onde n e m são os tamanhos das amostras e (n + m) < 30.

Considere 2 indivíduos para os quais as suas dotações e preferências por dois bens podem ser representadas por uma caixa de Edgeworth. Então:

Item 3 - O equilíbrio walrasiano depende das dotações de cada consumidor.

Um indivíduo tem possibilidade de escolher entre 3 situações alternativas:

Situação (1): ganhar $7,5 milhões com probabilidade de 4/5 e $15 milhões com probabilidade de 1/5.
Situação (2): ganhar $10 milhões com probabilidade de 4/5 e $5 milhões com probabilidade de 1/5.
Situação (3): ganhar $9 milhões com 100% de certeza.

Diante disto:

Item 3 - Se ele for indiferente às três situações ele tem posição neutra frente ao risco.

Em relação ao modelo de regressão múltipla !$ Y_i=\beta_0+\beta_1X_{1i}+\beta_2X_{2i}+ ...=\beta_kX_{ki}+e_1 !$, !$ i=1,2 !$

Pode-se afirmar que:

Item 3 - Os coeficientes !$ \beta_j !$, !$ j=0,1, ..., k !$ podem ser interpretados como as elasticidades entre os regressores !$ X_j !$ e a variável Y.