PLEASE ASNWER IF YOU UNDERSTAND AND CAN YOU ONLY ANS THE LAST 3 QUESTIONS THANKS!!

1. Consider the following money-in-utility model. The utility function is given by u(a, m+) = B* (In ct + y ln mi) = (1) t=0 and the budget constraint is given by: mt-1 + a + k + m+ +b= f(kt-1) + (1 - 1)kt-1+ 1+it (1+it-1)-1 1+ Tt + To (2) where & is real consumption, my real money balances, ky the capital stock, by real one- period bond, Tz real transfer from the government, Tt the inflation rate, it the nominal interest rate and t is a time index. There is no uncertainty in the model. The rate of depreciation is given by : such that It = kt - (1 - )kt-1 where It is investment. Assume that f(kt) = kom (i) Set up the optimization problem and derive the first order conditions. [10 marks) (ii) Find the Euler condition and interpret your answer. (5 marks] (iii) Find the Fisher relationship (the optimal condition relating money and the nominal interest rate) and interpret your answer. [5 marks] (iv) Find the steady-state levels of k, y and c. [5 marks] (v) Is money superneutral in this economy? Why or Why not? Please explain your answer carefully. [3 marks] (vi) Seignorage is the revenue that the government raises by printing money. Denote seignorage by s and assume that in steady-state, seignorage is given by s = am where steady-state values are represented with a bar. Using the Fisher relationship that you derived in (iii) (you should have obtained per it), express seignorage as a function of 7. [3 marks) mt 1+it 1. Consider the following money-in-utility model. The utility function is given by u(a, m+) = B* (In ct + y ln mi) = (1) t=0 and the budget constraint is given by: mt-1 + a + k + m+ +b= f(kt-1) + (1 - 1)kt-1+ 1+it (1+it-1)-1 1+ Tt + To (2) where & is real consumption, my real money balances, ky the capital stock, by real one- period bond, Tz real transfer from the government, Tt the inflation rate, it the nominal interest rate and t is a time index. There is no uncertainty in the model. The rate of depreciation is given by : such that It = kt - (1 - )kt-1 where It is investment. Assume that f(kt) = kom (i) Set up the optimization problem and derive the first order conditions. [10 marks) (ii) Find the Euler condition and interpret your answer. (5 marks] (iii) Find the Fisher relationship (the optimal condition relating money and the nominal interest rate) and interpret your answer. [5 marks] (iv) Find the steady-state levels of k, y and c. [5 marks] (v) Is money superneutral in this economy? Why or Why not? Please explain your answer carefully. [3 marks] (vi) Seignorage is the revenue that the government raises by printing money. Denote seignorage by s and assume that in steady-state, seignorage is given by s = am where steady-state values are represented with a bar. Using the Fisher relationship that you derived in (iii) (you should have obtained per it), express seignorage as a function of 7. [3 marks) mt 1+it