Question

Anna's consumption preferences are described by her life-time lity function lc1,c2)-2, where ct 1,2 denotes consumption in period t. She receives income in period i as yl = 4 and y2 =0 in period 2. The market rate of interest is 0%. a. Determine Anna's optimal intertemporal consumption plan. How much will she save? (2 point) How do her savings react to an increase in interest rates to 1%? (1 points) Is there a general lesson to be drawn from this example? Explain! (1 points) b. c.

No Graph included.

Answer 1

a) We know that Anna’s income is 4 in period 1 and 0 in period 2 and it is also given that the interest rate is 0%. This means that Anna will not get any interest on her savings in period 1.

Her utility function is given by u(c1,c2) = c1*c2

We can see that the utility will be maximum when she decides to consume equally in both the periods.

So, we can conclude that in period 1 , Anna will consume 2 and will save 2 for the next period.

b) Now , if the interest rate increases to 1%, then Anna will have an incentive to save more in period 1 , so that she can consume more in the second period, as she will get the interest on what she saves. So with an increase in interest rate to 1% , Anna will save more in period 1.

c) From this example, we can conclude a general lesson that as the interest rate increases, people will tend to save more. We can see that as the rate increases , a person will save more as he will fet the benefit of higher interest and will be able to consume more in future. So as interest rate increases , savings increases.