Intertemporal optimizing:

An agent is living in two different periods of time. She works in the first period and is retired in the second. The in income in period 1 is w1>0 and the income in period 2 is w2. The utility function is given by u=log(c1)+Blog(c2). Where c1 is consumption in the first periode and c2 is consumption in the second period.

a. How is B interpereted and what is a fair assumption?

The agent can lend and save to the interest rate i.

b. What is the consumers intertemporal budget condition?

c. Draw the budget condition.

d. What is the optimal savings for the consumer.

e. The goverment is considering to raise the w2 (retirerment payment). How does that affect the savings? Interpret?

f. The goverment is considering to tax the revenue of the private retirement savings (the nomially revenue). Calculate the savings as an expression exogene parameters and the tax on private savings.

g. Does the saving depend positive or negative og ?

I have solved a to d. And i have an idea for e. If the goverment raises w2, then the initiative to save falls. The more you can look forward to, the less you save? Is that a correct interpretation?

And then any help for f and g is highly apriciated?