we modeled growth in an economy by a growing population. We could also achieve a growing economy by having and endowment that increases overtime. To see this, consider the following economy: Let the number of young people born in each period be constant at N. There is a constant stock of fiat money, M. Each young person born in period t is endowed with gunits of the consumption good when young and nothing when old. The individual endowment grows over time so that It: 3 y\". For simplicity, assume that in each period 1', individuals desire to hold real money balances equal to one-third of their endowment, so that y; MFWB. 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. (5 marks} ii. Write down the condition that represents the clearing of the money market in an arbitrary period t. [5 marks) iii. Find the real rate of return of fiat money in a monetary equilibrium.|[5 marks)