I need help with exercise

Consider a perfectforesight small open economy populated by a large number of identical households with preferences described by the utility function - t glad/3 0:} where C, denotes consumption in period t, and ,8 E (O, 1) is a parameter. Households have access to the international nancial market, where they can borrow or lend at the constant interest rate 1'. Assume that (1+r):1+\"f where 7 > O is a parameter. Households are endowed with a constant amount of consumption goods denoted 3; each period and start period 0 with a level of debt equal to (L1 > 0. Finally, households are subject to a noPonzigame constraint of the form limt_,OO(1 +T)_tdt S 0, where dt denotes oneperiod debt acquired in period t and maturing at t + 1. (a) Formulate the household?s maximization problem. (b) Write down the complete set of optimality conditions. (0) Characterize the equilibrium paths of consumption and debt in this economy. In particular, express the equilibrium levels of at and (it, for t 2 0, in terms of the structural parameters (possibly B, 'r, 'y, and y) and the initial condition d_1