I am having trouble proving or answering the claim for section 3 below. How do you get the variables to meet?

Consider a small open economy that lives for two periods, only, (t and t + 1; for all purposes to some extent if it makes it easier you can think of this as t = 0 and t = 1) and is inhabited by a continuum of identical individuals grouped into an aggregate risk-sharing household. Each period aggregate output Y is produced via the function Yt = Z+L, where Z, is exogenous productivity and L, is labor. If output is not consumed or loaned out in any one period, then it spoils and cannot be carried over to the following period (this just means that the economy cannot save internally, it's only way to save would be to make international loans). This is a small open economy, so it can borrow and lend freely at the constant-across-periods international interest rate r. The household's instantaneous utility is given by Ct/L: and the household discounts the future at rate , where: B E (0, 1) is the household's (constant) subjective discount factor (i.e., 0