An investor with an initial wealth of 22,000 is planning investment and consumption for this
and the next period. The investment opportunity curve is:
C1 = 300⋅(22,000–C0)1/2,
where C0 is consumption in this period and C1 is consumption in the next period.
The risk-free return is 25%. The utility function of the investor is:
U(C0,C1) = 4⋅C0⋅C1
a) If the investor decides to invest 10,000 in this period, how much will she be able
to consume in the next period?
What is the average return and what is the marginal return on her investment?
b) Assuming that the investor wants to maximize utility, what will be the present value of the related consumption?
What will be the optimal consumption in the two periods?
How much will the investor lend or borrow in the capital market?
Show that the marginal return on the investor's investment equals the interest
rate of 25%.
c) Assuming an increase in productivity that changes the investment opportunity
curve to C1 = 350⋅(22,000–C0)1/2, what will be the optimal consumption in the two periods?
Compare your result with the answer you got under Question b) and explain why
the observed change in optimal consumption is reasonable.