3 Individuals Work when Young and Old Consider the canonical Diamond OLG model with log10g utility, u(c1t.c2,g+1) = log(c1)t) +8 log(c;5t+1) wher E (0, 1) but now assume that individuals supply labour inelastically when young and old. Assume that the representative firm's production technology is given by Yt : Kthl_a. 1. Write down the individual's optimization problem and solve for the individual's savings function. 2. write down the representative firm's problem and find its first-order necessary conditions. 3. Define a competitive equilibrium. 4. Let kt 2: If? be the capital stock per worker in period t. Find an equation char acterizing the equilibrium transition function for the capital stock per worker. 5. Show that there is a unique steady state value of k'\" > 0