Final Exam
Question 1 (40 points)
Consider the following neoclassical growth model. The equilibrium conditions of the model are given by
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· Log-linearize these four equations around the steady state. Note that “L” is a constant, not a variable.
Question 2 (40 points)
Consider a version of the model with the following preference. The model is identical to the baseline model discussed in the lecture, except that the household’s per period utility is given by
· Derive the private-sector equilibrium conditions of the model.
· Assuming that (i) the policy rate is determined by the standard Taylor rule, (ii) the inflation target is zero (that is, ), and (iii) , analytically compute the standard steady state of the model.
Question 3 (40 points)
A two-period model with a static PC with the ELB. There is a government spending shock financed by a consumption tax at time one:
with and . The payoff function for the central bank at each time is given by the standard quadratic objective function. That is,
for each t=1,2.
Assume that the policy rate is determined by the truncated Taylor rule:
Assume also that is sufficiently small so that . Solve the model analytically.
Now, assume that the government is optimizing under discretion.
· Formulate the optimization problem(s) of the central bank.
· Define the Markov-Perfect equilibrium.
Assume that the government is optimizing under commitment.
· Formulate the optimization problem of the central bank.
· Define the Ramsey equilibrium.
Question 4 (20 points)
Consider the following two-period loglinearized model with a static Phillips curve and with a time-one demand shock ( and ). The policy rule is given by a price-level targeting rule.
· Assuming that (i) and and (ii) the shock size is such that the policy rate is zero and positive at time one and two, respectively, solve the model analytically.
Question 5 (20 points)
Consider the following two-period loglinearized model with a static Phillips curve and with a time-one demand shock ( and ). The policy rule is given by a Reifschneider-Williams rule.
· Assuming that (i) and and (ii) the shock size is such that the policy rate is zero and positive at time one and two, respectively, solve the model analytically.
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