3 Individuals Work when Young and Old Consider the canonical Diamond OLG model with log-log utility, "(621) = log() # log() where E (0, 1) but now assume that individuals supply labour inclastically when young and old. Assume that the representative firm's production technology is given by Y, = Kal|-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 k : K be the capital stock per worker in period . Find an equation char- actorizing the equilibrium transition function for the capital stock per worker. 5. Show that there is a unique steady state value of k. > 0