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 y units of the consumption good and nothing when old. Suppose the en- dowment grows over time yay-1 for a > 1. For simplicity, assume that in each period t, people desire to hold real money balances equal to one-half of their endowment, so that vm, = 0.5- a) (5 points) Write down the budget constraints an agent born in period t faces when young and old. Combining these constraints, write the agent's lifetime budget constraint. b) (5 points) Write down the condition that represents the clearing of the money market in an arbitrary period t. Use this condition to find the real return of me fiat money in a monetary equilibrium, +1/1. c) (5 points) Derive the Quantity Theory of Money equation for this economy. Explain in words how it depends on the rate of endowment growth a. d) (5 points) Suppose a new technology arrives in which a increases. Explain in words the effect on an agent's optimal consumption path (2+1)