Consider the OLG model set up with two generations at every point in time. Old agents value the consumption of the current young generation, with a weight 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 standard OLG model