Suppose as in the Diamond model, that L, two-period-lived individuals are born in period t and that L, = (1+n) L-1. For simplicity, let utility be logarithmic with no discounting: u (c1, c2t+1) In C + In C2t+1-1 The production side of the economy is simpler than in the lecture. Each individual born at time t is endowed with A units of the economy's single good. The good can be either consumed or stored. Each unit stored yield R> 0 units of the good in the following period. Finally, assume that in the initial period, period 1, in addition to the L young individuals, there are Lo = L/(1+n) individuals who are alive only in period 1 (the initial old). Each of these "initial old" individuals is endowed with nothing; their utility is simply their consumption in the initial period, C2.1. 1. Suppose there is a social planner who wants to maximize agents' lifetime utility in steady state. Derive the planner allocation. 2. Derive the decentralized equilibrium of this economy. Is the decentralized equilibrium Pareto efficient?