Consider the standard OLG set up with two generations at every point in time.Old agents value the consumption of the current young generation, with a weight ho and so they consume part of their savings and distribute the rest as bequest for the current young generation. Young agents use labour income and the received bequest to consume and save. Assume further that there is no population growth, no capital depreciation and that labour is inelastically supplied by the young.

(a) Setup the households problem

(b) Find the household optimality conditions. How do the conditions compare to those of the planners problem seen in class?

Suppose at time t =0, all agents, regardless of whether or not they are born, can trade in a competitive market. That is, an auctioneer calls out a price sequence of consumption, {pt}\infty t=0. So generation t can buy/sell xt+1 of time t goods at price pt and sell/buy ptxt+1/pt+1 of time t +1 goods.

(d) Suppose that pt = pt+1ak is the price sequence announced for all t >0. Show that autarky is an equilibrium but argue it is not an unique equilibrium.