Considere o seguinte problema de otimização condicionada:

!$ \begin{cases}Max_{x,y,z}&Q(x,y,z)=3xy+z^2\\s.a&x^2+y^2+z^2=81 \end{cases} !$

Julgue a afirmativa abaixo:

Item 0 - Quatro pontos diferentes satisfazem as condições de primeira ordem.

O crescimento expressivo da indústria brasileira, na segunda metade das década dos cinqüenta, deveu-se, em grande parte, à política desenvolvimentista então implementada — consubstanciada no Plano de Metas do Governo Kubitschek. Em relação a esse período, pode-se afirmar que:

Item 1 - a política cambial então implementada favoreceu a importação de bens de capital;

Indique se a proposição abaixo é falsas ou verdadeira:

Item 0 - A manutenção de um diferencial entre taxas de juros interna e externa muito superior à expectativa de desvalorização cambial tende a provocar uma fuga de capitais ou desvalorização imediata do câmbio.

A propósito da reforma monetária de Rui Barbosa (lei bancária de 17 de janeiro de 1890), é correto afirmar que:

Item 3 - essa reforma provocou uma imediata valorização do mil-réis, que perdurou por toda a década seguinte;

Seja X uma variável aleatória com função de densidade de probabilidade Uniforme no intervalo !$ [a,b] !$:

Item 3 - X tem distribuição unimodal.

Indique se a proposição abaixo é falsa ou verdadeira:

Item 2 - Uma elevação das reservas voluntárias e dos encaixes dos bancos comerciais, tudo o mais constante, reduz o multiplicador bancário.

Seja X₁,...,X_N uma amostra aleatória de uma população com média !$ \mu !$ e variância !$ \sigma^2 !$. Sejam W e Z estimadores de !$ \mu !$ dados por:

!$ W=\dfrac{\sum^N_{i=1}i\cdot X_1}{\sum^N_{i=1}};\,\,\,\,\, Z=\dfrac{\sum^N_{i=1}X_i}{N} !$

Pode-se afirmar que:

Item 2 - Z é consistente.

A função de densidade de probabilidade conjunta das variáveis aleatórias X e Y é dada por:

!$ f_{XY}(x,y)=\begin{cases}6x^2y,\,se\,0 < x < 1, 0 < y < 1 \\0, \,caso\,contrario \end{cases} !$

Pode-se afirmar que:

Item 2 - a função densidade de probabilidade condicional de X dado Y é !$ f_{X|Y}(x,y)=3x^2 !$.

Part II

Recruitment of Labour for the Mills in The Early Factory Masters - Transition of the Factory in the Midlands Textile Industry. By Stanley Chapman. Chapter 9 - pp 156-157.

One of the most difficult problems which entrepreneurs in the early cotton and worsted-spinning industry had to face was the recruitment and retention of a labour force. The problem was, in part, a consequence of the well-known reluctance of the working-classes to enter the factories, and certainly the domestic framework knitters and weavers of the region were not easily persuaded to exchange their freedom for factory discipline. The scarcity of labour was also a reflection of the general shortage in the manufacturing districts. The hosiery and lace industries were growing very rapidly, and their expansion coincided with that of the spinning industry. Wages appear to have been higher in hosiery and lace than for similar grades of workers (skilled, semi-skilled and unskilled) in the mills. In the rural areas, there was a steady drain of good workers to the towns and large manufacturing villages, where the best-paid work was to be found. The French war also aggravated the labour shortage after 1792 by drawing large numbers of men into the army.

It has already been noted that the wages paid in the spinning-mills were not sufficiently high to attract workers from regular employment in the towns. Farey points out that Derbyshire millworkers earned higher wages than farm labourers in the country and White records that, in Bakewell, 'wages were raised immediately' after Arkwright's mill began production there. Fitton and Wadsworth suggest that Arkwright and Strutt did not employ parish apprentices, and that their labour force was probably recruited in the villages within a four- or five-mile radius of the factories. This explanation is not very convincing since other evidence, overlooked by these two authors, shows that even juvenile and female labour had to be brought into Derbyshire from the main centres of the cotton industry at Manchester and Nottingham.

The author states that:

Item 2 - the French war aggravated the labour shortage after 1792.

Parte I.

Do the Poor Insure? A Synthesis of the Literature on Risk and Consumption in Developing Countries by Harold Alderman and Christina H. Paxson. In Economics in a Changing World Edited by Edmar L. Bacha

Income risk is a central feature of rural areas of developing countries. A major topic in development economics is how well households are able to mitigate the adverse effects of income risk. There are several sensible reasons why households will not be able to fully insure consumption against income fluctuations. The well-known problems of moral hazard, information asymmetries, and deficiencies in the ability to enforce contracts may result in incomplete or absent insurance markets. The dearth of formal insurance markets in developing countries is evidence that these problems are considerable. However, a large body of literature indicates that households in developing countries make use of a wide variety of mechanisms, often informal, to at least partially limit consumption risk. A key piece of information required to guide policy design is how, and how well, different households mitigate risk. This paper reviews various strategies for insuring consumption against income fluctuations, and examines evidence on how effectively these strategies work.

There is a wide range of possible strategies to mitigate risk. We offer two broad classifications for consideration:

Risk management. In the absence of perfect insurance markets, households may undertake actions to reduce the variability of income. Within agriculture this might include crop and field diversification. Households might also limit income risk by choosing a diverse portfolio of occupations, or through the strategic migration of family members. The optimal amount of diversification will depend on the household's preferences towards risk, its ability to smooth consumption against income fluctuations, and the costs of diversification in the form of reduced average incomes.

Risk coping. Risk-coping strategies can be classified as those that smooth consumption intertemporally, through saving behaviour, and those that smooth consumption across households, through risk-sharing. The primary distinction between these two is that intertemporal smooothing enables a household to spread the effects of income shocks on consumption forward through time. Risk-sharing, by contrast, spreads the effects of income shocks across households at any one point in time. A wide variety of mechanisms may be used for both intertemporal consumption smoothing and risk-sharing. Intertemporal smoothing may be accomplished through borrowing and lending in formal or informal markets, accumulating and selling assets, and storing goods for future consumption. Risk-sharing arrangements may be accomplished through formal institutions, such a insurance and futures markets, and forward contracts for harvests, and informal mechanisms, including state-contingent transfers and remittances between friends and neighbours. These are also a number of institutions that may offer 'disguised' insurance. For example, share tenancy, credit contracts with state-contingent repayments, and long-term labour contracts may each contain an insurance component, although none are explicitly insurance contracts.

The authors point to some strategies of risk coping, such as those that smooth consumption:

Item 2 - intertemporally.