Modelling Environment Consider a representative household with discount factor 6 who maximizes the following utility function: 00 Cl\Q29. Derive the cash-inadvance constraint in real terms. Your expression should be written in terms of real money balances Tut1 = % [2 points]. Q30. Write down the Lagrangian for the household problem. Note that in addition to budget constraints (in real terms), you should also include cash-in- advance constraints. Use A; to denote the Lagrange multiplier associated with period t's budget constraint. Use qr; to denote the Lagrange multiplier associated with period t's cash-in-advance constraint. [3 points] Q31. Write down the rst order conditions. [5 points] Q32. Show that if the CIA constraint is not binding, the nominal interest rate has to be zero. Explain it intuitively. [4 points]