Suppose you are given the utility function:

U=c+(c)/(1.10)

and the budget constraint:

c+(c)/(1+r)=y+(y)/(1+r)

where y = 5, y' = 10, and the interest rate r = 0.10.

a) What is the optimal value of current consumption c*?

b) What is the optimal value of future consumption, c'*?

Now suppose the consumer experiences a temporary rise in real income in period 1, so that y = 9.

c)What is the optimal value of current consumption c*?

d)What is the optimal value of future consumption, c'*?

Now suppose that y= 5 again, and there is only one consumer in the entire economy. If we add in government expenditures and taxation, the consumer's budget constraint is now:

c+(c)/(1+r)=y+(y)/(1+r)?(?)/(1+?)

If current and future government expenditure is: g = 1, g' = 3.3, and if current taxation t = 2:

e) What is the value of second period taxation, t'?

f) What is the optimal value of current consumption c*?

g) What is the optimal value of future consumption, c'*?

Suppose that current taxation decreases decrease from t = 2 to t =1.5.

h) What is now the value of second period taxation, t'?

i) What is the optimal value of current consumption c*?

j) What is the optimal value of future consumption, c'*?