1.- Suppose that the consumer has a logarithmic utility function and a lifetime budget constraint where the government taxes a lump-sum taxt1 in the current period andt2 in the second period. Find the optimal consumption in the first and the second periods and compare it with your answer in previous question. Are the consumption levels different in both periods? Hint: the consumer solves the following maximization problem

maxc1,c2ln(c1)+ln(c2)

Subject to

c1+1+rc2=y1t1+1+ry2t2

The recommendation again is that you start by setting up the Lagrangian of this maximization problem and take FOCs to find the Euler equation. Then, use the lifetime budget constraint to leave the Euler equation only in terms of either C1 or C2 (whatever you find easier). This process will give the consumption level in say period 1, just in terms of the lifetime wealth, , and the interest rate. Finally, compute the consumption level in the other period, which will also be in terms of the lifetime wealth, , and the interest rate. For simplicity, just callmthe lifetime budget constraint, so thatm=y1t1+1+ry2t2

A)C1=1+m;C2=1+(1+r)m

B)C1=1+;C2=1+m

C)C1=1+(1+r)m;C2=1+(1+r)m

D)C1=1+(1+r)m;C2=1+(1+r)m

2.- Now, to see the Ricardian Equivalence in practice, let's give some specific values to the previous question and answer the following three questions. Suppose that =1 and =1/10

Use the information from the following table to find the optimal consumption in periods 1 and 2

Variable	Value
y1	100
y2	110
t1	10
t2	11

A) c1=90; c2=99

B) c1=90; c2=100

C) c1=90; c2=90

D) c1=100; c2=90

3.- Now assume that the government pretends to stimulate the economy by lowering taxes in period 1, so that now t1=5. If government spending has not changed, what would be the level of taxes in the second period to maintain a balanced government budget? Hint: Remember that the government's budget constrain is the following:

G1+1+rG2=T1+1+rT2

To simplify the analysis, you may assume that there is only one individual in the economy so that t=T. This is analogous to the general model where we supposed that there areN individuals in the economy, which implies thatNt=T

A) t2=16.5

B) t2=10

C) t2=13

D) t2=18.5

4.- Considering these changes from the government, find now the optimal consumption in periods 1 and 2.

A) c1=90 ; c2=99

B) c1=95 ; c2=100

C) c1=90 ; c2=115

D) c1=95 ; c2=99