PLEASE SOLVE 1 (B) ONLY

1. lE'.'.'.Insider the following small open economy model with production. At dates 1 end 2, the home country receives exogenous fixed endowments fl and y: respectively. The home country has access to the international capital market at a xed interest rate r' at which it can save or borrow. Let the net saving of the home countryr he s: and its consumption stream in two periods be given by cl and {:2 respectively. The home country solves the following maximilltion problem: ier Incl+|nr31 But. If." +.S'| =y] c2 =slfl +rt)+ PE 3] Derive the optimal consumption and current account functions for the home country and carefully interpret it in terms of a two-period Fisherian graph. {50 marks} b] Refer to [a] once again. Suppose the home country also has an access to an investment technology which means that if it invests x units at date 1. it produces 3,12 2 At\" units of output in the next period where A r: [i and [i