1. Consider a Ramsey economy that is on its balanced growth path. The level of government
spending is G. Suppose that at time 0, the government goes into war and hence increases its
spending. Assume that this is an unanticipated shock. In response to this people anticipate
that the rate of population growth will be lower in the future.
(a) How does these affect the c˙ = 0 and ˙k = 0 (20%)
(b) What are dynamics after time 0? (20%)
(c) How do the values of c and k on the new balanced growth path compare to their values on
the old balanced growth path? (10%)
2. Consider a variation of the OLG model in which people may die at the end of the first period.
At the beginning of the second period of their lives, people die with probability (1 − p) and
live with probability p. They do not know during the first period of their lives whether they
will die or not. There is no time discounting. Their expected utility (which they maximize) is
E(U) = ln(c1) + p × ln(c2), where c2 is what they will consume in period 2, if they live that
long. The production function is y = k
, and there is no population growth.
Assume that when people die their wealth is distributed among the remaining members of
their generation. Assume that there are a sufficiently large number of people in each generation
so that there is no uncertainty about the size of bequests that survivors will receive. Also assume
that interest is earned by the capital belonging to the deceased before this capital is divided
up among the survivors.
(a) Write down the single period and lifetime budget constraints of an individual. Call the
amount that she receives as a bequest b. (10%)
(b) Solve for the individual’s optimal saving in period 1 as a function of b, r, and w. (10%)
(c) Solve for b as a function of the amount of capital in the second period. (10%)
(d) Put everything together into a difference equation for k. (10%)
(e) How does a decrease in p (that is, an increase in the probability of premature death) affect
the steady-state capital stock? (10%)
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