Economia V; Instructor: Marco Del Negro

Problem set 3

The setup of the problem is as follows:

• the economy has two periods, 1 and 2.
• there is only one agent in the economy, her income in periods 1 and 2 is equal to Y1=2, Y2=0, respectively.
• The agent can borrow from or lend to international financial markets at the world interest rate r^w, which is 0%.
• the utility function of the agent is logarithmic, that is:
  
  $$U(C1,C2)=\ln{C1}+\beta\ln{C2}$$
  
  
  with $\beta=\frac{1}{1+r^w}$.
• the government is spending G1=.5 in the first period, G2=.5 in the second period, and is taxing the individual in the first period only (T1) for an amount that satisfies the intertemporal budget constraint of the government.

a) Compute how much taxes T1 the government has to collect in the first period in order to satisfy its intertemporal budget constraint.
b) Write the intertemporal budget constraint of the agent.
c) Solve the agent's problem and find the optimal consumption in periods 1 and 2 (C1 and C2).
d) Find the Current Account Surplus (Deficit) in the first period.