Borrowers and savers have utility function u (Cb, C)= log(C+Blog(C), u (CS. Ca)= log (C5)+Blog(C). with...

  

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Borrowers and savers have utility function u (Cb, C)= log(C+Blog(C), u (CS. Ca)= log (C5)+Blog(C). with 3b < Bs. The representative borrower is subject to the period-by-period budget constraints: CP= YP-qK+DP, C Y+q'K-(1 + r) Dp, where D1bis debt, Ytb is income in period t, 1 + r is the gross real interest rate, and K is a durable asset in fixed supply. The borrower is also subject to the following borrowing constraint: D1b s xq'K. (1) The representative saver is subject to the period-by-period budget constraints: C = Y$ + D, C=Y - (1 + r) D.. Explain the economic meaning of constraint (1). For each agent, derive the intertemporal budget constraint. Explain its meaning. For each agent, derive the Euler equation. Explain. Derive a representation of the equilibrium in terms of DB curve (demand of debt) and DS curve (supply of debt), in the space real interest rate-debt. Plot the DB-DS system, including the borrowing constraint. Comment on the difference between constrained and unconstrained equilibrium. (Hint: remember that, in equilibrium, DP = -D = D.) 5. Suppose the intersection between the DB and the DS above occurs on the decreas-ing part of the DB curve. Suppose now that savers become more patient, that is, as in- creases. Show the new equilibrium in the DB-DS diagram (consider all possible cases). Borrowers and savers have utility function u (Cb, C)= log(C+Blog(C), u (CS. Ca)= log (C5)+Blog(C). with 3b < Bs. The representative borrower is subject to the period-by-period budget constraints: CP= YP-qK+DP, C Y+q'K-(1 + r) Dp, where D1bis debt, Ytb is income in period t, 1 + r is the gross real interest rate, and K is a durable asset in fixed supply. The borrower is also subject to the following borrowing constraint: D1b s xq'K. (1) The representative saver is subject to the period-by-period budget constraints: C = Y$ + D, C=Y - (1 + r) D.. Explain the economic meaning of constraint (1). For each agent, derive the intertemporal budget constraint. Explain its meaning. For each agent, derive the Euler equation. Explain. Derive a representation of the equilibrium in terms of DB curve (demand of debt) and DS curve (supply of debt), in the space real interest rate-debt. Plot the DB-DS system, including the borrowing constraint. Comment on the difference between constrained and unconstrained equilibrium. (Hint: remember that, in equilibrium, DP = -D = D.) 5. Suppose the intersection between the DB and the DS above occurs on the decreas-ing part of the DB curve. Suppose now that savers become more patient, that is, as in- creases. Show the new equilibrium in the DB-DS diagram (consider all possible cases).

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Constraint 1 represents the borrowing constraint for the representative borrower It states that the amount of debt Dib that the borrower can have is limited by a fraction x of the value of the durable ... View the full answer