Answer the following

7. (8 marks) Consider the standard OLG model with money. In each period t, N: young individuals are born, where N: : nNt_1 and n 2 1. There are No initial old. Individuals are endowed with y units of time when young and nothing when old. A production technology is available such that 1 unit of time can be used to produce 1 unit of the consumption good. Each individual values leisure when young and values consumption when old. Each generation has identical preferences 1:. (01. 2,t+1) = 01,: * c2,t+13 where c\" represents the amount of leisure that the young individual enjoys and c21+1 represents the amount of goods the old individual consumes. There exists one asset in the economy money. The money supply grows at a constant rate .3, where M: = 3M_1 and z > 1. The new money created is used to nance government purchases of g goods per young individual in every period. The initial old are endowed with Mo units of money. In the following, we focus on stationary allocations. (a) Find an individual's budget constraints when young and when old. Combine them to form the individual's lifetime budget constraint. (1 mark) (b) Solve for the optimal consumption allocation (CI, c3) chosen by the individual in a stationary monetary equilibrium. What is the labor supply f" chosen by the young? How do (cf, cg) depend on s? (2 marks) (0) Use the government budget constraint to solve for g\". (2 marks)