(6 marks) Consider the standard OLG model with money and growing population. Individuals are endowed withyunits of a perishable consumption good when young and nothing when old. Individuals want to consume both when young and when old. LetNt=nNt1andMt=zMt1for every periodt, whereNtare the number of people born in periodtandMtis the money stock in periodt. Consider the case in whichzandnare both greater than1. The money created each period is distributed as a lump-sum transfer to each old individual worthatunits of consumption goods. Each generation has identical preferences where

u(c1;t; c2;t+1) = ln(c1;t) + ln(c2;t+1);

wherec1;tis the amount of the good that is consumed in the rst period of life by an individual born in periodt, andc2;t+1is the amount the same individual consumes in the second period of life. is the discount factor and0< <1.

(a) Find an individuals budget constraints when young and when old. Combine them to form the individuals lifetime budget constraint. (2 marks)

(b) Solve for the optimal consumption allocation (c1;c2) chosen by the individual in a stationary monetary equilibrium. Note: express (c1; c2) as a function of exogenous parame- ters (z; y; ; n) in the model.atisnotan exogenous variable. (2 marks)

(c) Solve for the social planners golden-rule allocation. Under what condition(s) will the monetary equilibrium coincide with the golden-rule allocation? How would you interpret your results? (2 marks)