3. Worth 25 points. Consider a Korean investor who has I wons (the won is the Korean currency), and has decided to invest this won in Korea or Japan or both. Two things to note here. First, the "both" case involves investing a portion of the I wons in Korea and a portion of the won in Japan. Second, Korea is the "home" country. (a) Let wwon (0.1] be the fraction of the won that the investor invests in Korea. So, wwon = 0 means that the investor only invests in Korea, Wason = 1 means that the investor only invests in Japan, and won (0,1) means that the investor invests a portion of the I wons in Korea and a portion of the I wons in Japan. (b) The investor invests today and plans on "cashing out" next year. The one-year interest rate on the Korean investment is iwon and the one-year on the Japan investment is iy. Therefore, next year the investor gets Werond: (1 + ivon) + (1 wwon) 1. (1 Fwon/Y - Ewon/ + y + 100 -)] To be clear, if Wwon = 0 then the investor invested only in Japan, and if Wuron = 1 then the investor invested only in Korea. Indeed, with won 0 then the Ewon/ 2 expression above becomes [1+ (x +100 m) Evon/ the expression above reduces to I. (1+iwon) and if wwon = 1 then the earlier expression reduces to I. (1 + iwon). (c) Assume that the investor's instantaneous utility function is U = In (e) and that the investor's only source of income is the planned investment discussed above. Moreover, suppose that the investor can decide what Fwon/ is by "buying" a contract at the cost K.I. Fwon/4, where a > 0 is a parameter. It follows that the investor's budget constraint is c+k: 1. Fwon/* 0 is a parameter. It follows that the investor's budget constraint is c+k: 1. Fwon/*