In chapter 2, we modeled growth in an economy by a growing population. We could also achieve a growing economy by having and endowment that increases over time. To see this, consider the following economy: Let the number of young people born in each period be constant atN. There is a constant stock of fiat money,M. Each young person born in periodtis endowed withytunits of the consumption good when young and nothing when old. The individual endowment grows over time so thaty_t=3 y_t-1. For simplicity, assume that in each periodt, individuals desire to hold real money balances equal to one-third of their endowment, so thatv_tm_t=y_t/3.

i.Write down equations that represent the constraints on first and second-period consumption for a typical individual. Combine these constraints into a lifetime budget constraint.Show your steps. (5 marks)

ii.Write down the condition that represents the clearing of the money market in an arbitrary periodt. (5 marks)

iii.Find the real rate of return of fiat money in a monetary equilibrium.Show all your steps and explain your answers to avoid grade penalty.(5 marks).