Assinale V (verdadeiro) ou F (falso):

Item 3 - !$ \int^4_{-2}\sqrt{1+\dfrac{x^2}{4}}dx=\int^2_{-1}\sqrt{1+x^2}dx !$

As vendas de ingressos para os jogos de um time de futebol dependem do número de vitórias do time por temporada e do preço dos ingressos. Em outras palavras, a função demanda pelos ingressos é dada por !$ q=N(20-p) !$, em que !$ p !$ é o preço dos ingressos, !$ q !$ é a quantidade de ingressos (em milhares) e !$ N !$ é a proporção de jogos ganhos. O time pode aumentar N se investir !$ C !$ reais (em milhares) na contratação de novos talentos. Neste caso, tem-se que !$ N=0,7-\dfrac{1}{C} !$. Assuma que o custo marginal de vender um ingresso seja zero.

É correto afirmar que:

Item 1 - O valor do investimento em jogadores, C, que maximiza os lucros é 5 (em milhares).

Em relação aos modelos de séries temporais, é correto afirmar:

Item 0 - No processo AR(1), !$ Z_t = \phi Z_{t-1}+a_t+\theta_0, |\phi| < 1 !$, e !$ a_t !$ é um ruído branco, a média de !$ Z_t !$ será !$ \dfrac{\theta_0}{1-\phi} !$.

Conclusion

Criticism of the structuralist theory of inflation of course did not spell the end of structuralism as a broad anti-market ideology, either in developed or developing countries. In developed countries the doctrine of market failure has come under increasingly critical scrutiny, broadly on the ground, as H.G. Johnson once put it, that ‘the possibility of market failure is not sufficient to prove the certainty of government success’. The price system, with all its acknowledged defects, may yet, on balance, be the lesser evil, compared with the operation in practice of bureaucratic planning and controls – controls which are often, as at least one contributor to the Latin American debate pointed out, a major source of the very rigidities which hamper the working of the price system.

The text leads to the following conclusions:

Item 0 - Criticism of the struturalist theory of inflation is baseless

Em relação à teoria da produção, analise a seguinte questão:

Item 0 - Seja a função de produção !$ f(x_1,x_2)=10\,min\{3x_1,2x_1+x_2\} !$, em que !$ x_1 !$ e !$ x_2 !$ são os insumos. Pode-se afirmar que, no ponto !$ (x_1,x_2)=(20,40) !$, a isoquanta tem uma quebra (vértice).

The Origins of Structuralism

H.W. Arndt. Modern Political Economy and Latin America. Eds. Jeffry Frieden,
Manuel Pastor Jr., and Michael Tomz. Westview Press, 2000: 5-9.

Introduction

In his recent book on economic development, I.M.D. Little distinguishes two broad categories of development economics. He calls them ‘neoclassical economics’ and ‘structuralism’.

“The structuralist sees the world as inflexible. Change is inhibited by obstacles, bottlenecks and constraints. People find it hard to move or adapt, and resources tend to be stuck. In economic terms, the supply of most things is inelastic. Such general inflexibility was thought to apply particularly to LDC’s.... Entrepreneurs were lacking; and communications were poor.... This alleged inflexibility was married to the evident fact that the production structure of developing countries was very different from that of developed countries. To achieve development, it had to be changed rapidly.... The structuralist view of the world provides a reason for distrusting the price mechanism and for trying to bring about change in other ways. If supplies and demands are very inelastic large price changes are needed to achieve small quantitative adjustments. Large price changes are disturbing, both directly and also because they result in changes in income distribution.... If the losers are powerful, they may... be able to resist the change through organized industrial or political action... Structuralism primarily seeks to provide a reason for managing change by administrative action.”

The purpose of this article is to explore further the origins of structuralism, both in the broader sense and the more specific context of Latin American structuralist theories of inflation, and the links between them.

According to the Little quotation,

Item 4 - the primary objective of structuralism is to justify government intervention in the development process.

Sobre coeficiente de correlação, covariância e independência de variáveis aleatórias, é correto afirmar:

Item 0 - Seja!$ \rho(x,y) !$ o coeficiente de correlação entre as variáveis !$ x !$ e !$ y !$. Se !$ ab > 0 !$, então !$ \rho(ax,by)=\rho (x,y); !$; e se !$ \rho(ax,by)=-\rho(x,y) !$.