O custo X de produção de certo bem é uma variável aleatória com função densidade de probabilidade

!$ f(x)=\begin{cases} kx^2 & 1 \le x \le 4 \\ 0 & \text{caso contrário } \end{cases} !$

É correto afirmar que:

Item 4 - o custo é maior do que 3 com probabilidade 8/9.

Tendo em conta o modelo de crescimento de Solow, avalie o item:

Item 2 - Economias com maior propensão a poupar terão, ceteris paribus, uma taxa de crescimento de equilíbrio mais elevada do que economias com propensão a poupar menor.

Sobre a inserção internacional do Brasil na década de 1990 é correto dizer que:

Item 1 - a redução de barreiras comerciais pelo Brasil aumentou a elasticidade renda das importações e agravou a restrição externa ao crescimento, embora tenha contribuído para o aumento da produtividade da indústria brasileira;

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 relationship between rising interest rates and rising rates of resource degradation, the text leads to the conclusion that:

Item 3 - if r = 10 percent and n = 15 years, the sustainable path is chosen only if it produces 78 percent more than the exhaustive path;