Week 8 Problem Set

Question 1:

Strategic debt accumulation when there is initial debt [Romer 13.7]

Consider the Tabellini-Alesina (1990) model of strategic debt accumulation we studied in the lecture. Suppose that there is some initial level of debt, D_0. How, if at all, does D_0 affect the deficit in period 1?

Question 2:

Comparative statics in the model of delayed stabilization [Romer 13.11]

Consider the Alesina-Drazen (1991) model of delayed stabilization we studied in the lecture. Describe how, if at all, each of the following developments affects workers’ proposal and the probability of reform:

a) A fall in T.

b) A rise in B.

c) An equal rise in A and B.

Question 3:

Crises and reforms [Romer 13.12]

Consider the Alesina-Drazen (1991) model of delayed stabilization we studied in the lecture. Suppose, however, that if there is no reform, workers and capitalists both receive payoffs of -C rather than 0, where C \geq 0. In other words, a failure to agree leads to a deeper crisis.

a) Find expressions analogous to (17) and (18) in the lecture slides for workers’ proposal and the probability of reform.

b) Define social welfare as the sum of the expected payoffs of workers and capitalists. Show that an increase in C can raise this measure of social welfare.

Question 4:

A model of sovereign debt crises [Romer 13.16]

Consider the model of sovereign debt crises we studied in the lecture. Suppose T is distributed uniformly on some interval [\mu - X,\mu + X], where X > 0 and \mu - X \geq 0. Describe how, if at all, each of the following developments affects the debt demand and default probability curves in the (R, \pi) space, as well as determination of R and \pi in equilibrium:

a) A rise in \mu.

b) A fall in X.