Avalie o item que segue sobre a função consumo:

Item 3 - Segundo a teoria da renda permanente, se as famílias forem induzidas a esperar uma redução permanente de renda, haverá um aumento imediato da poupança.

Para mercados em concorrência perfeita, é certo o item:

Item 2 - Como a rivalidade entre firmas é intensa, cada uma deve levar em conta as quantidades produzidas pelos concorrentes ao definir seu próprio nível ótimo de produção.

Considere a expansão de Taylor para a função !$ y = f(x) !$ em torno do ponto !$ x = 0 !$. Assinale certo ou errado:

Item 4 - O termo de terceira ordem da aproximação da função !$ y=e^{2x} !$ é maior que o termo de segunda ordem, em valores absolutos.

Rising real rates of interest, transmitted to LDCs and to their DRAs, are likely to cause rising rates of resource degradation, via private incentives and public capacities.

Suppose a farmer is choosing between a “sustainable” way to manage land, which generates a net return of y1 each year forever, and “exhaustive” way, which generates a higher return, y2 each year for n years, after which the land has been destroyed and yields nothing. It can easily be shown that the “sustainable” path yields a higher present value if, and only if

(y2/y1) < 1 – 1/ (1 – r)ⁿ⁺¹

Where r is the real interest rate for a n-year loan. For example, if r = 10 percent and n = 15 years, the sustainable path is chosen only if it produces at least 78 percent as much, forever, as the exhaustive path produces for 15 years before destroying the land. If r = 5 percent, the sustainable path needs to produce less, namely, 54 percent of “exhaustive” net returns, to be preferred. Clearly, the rise in real long-term rates of interest, if transmitted to DRAs, must have had enormous incentive effects on resource management, shifting it away from sustainability.

If risk is allowed for, the interest rate incentive to deplete is probably sharpened. Higher interest rates reduce the present-value burden of long-term-future downside risks, relative to that of near-term risks (and costs). The land use patterns are therefore shifted toward activities with long-term risks, such as possible long-term resource degradation.

In the analysis of the effects of risk on resource depletion, the text allows one to conclude that:

Item 0 - the presence of risk dampens the higher interest rate incentive to deplete;

Unfortunately, there has been little attempt to design the generation, selection, or availability of techniques supplied by international agricultural research in ways that increase the likelihood of resource-preserving outcomes as rural populations grow. This is partly because the problem of technology generation in agriculture remains exogenous to most of the developing countries and is not driven significantly by their resource-saving, or other, requirements.

On a global scale, agricultural research responds not to the needs of workers or small-holders experiencing rapid growth of person-land ratios (and degrading food growing resources), but to those of large farmers seeking to save labor and of research scientists seeking intellectual satisfaction and security by catering to the better-endowed and better-understood problems, environments, and crops of such farmers.

When focussing on the available set of technological options to farmers in developing countries, the text

Item 3 - criticizes scientists for not catering to the needs of small farmers;

Assinale certo ou errado:

Item 4 - Se !$ f''(x)>0 !$, para todo !$ x ∈ [a,b] !$, então !$ f(x)< f'(b)(x-b)+f(b) !$, para !$ x ∈ [a,b) !$.