An investor has an initial endowment of $12000 ans is confronted with a prodcutive opportunity locus which is desccribed by the following equation: c1=300(12000-c0)^1/2 where c0 indicates consumption in $ at time=0 and c1 in $ at time=1. the interest rate is 50%. the investors utility fucntion for the period is: u(c0,c1)= (c0)(c1)

1) how much will the investor invest in production?

2) what is the time 0 net present value of the investment chosen by the investor?

3) what is the time 0 present value of his total consumption at times 0 and 1?

4) does the investor bowrrow or lend in the market and how much?

5) what is his optimal allocation of consumption for times 0 and 1?

6) illustrate all of the above with a single Fisherian diagram, not necessarily to scale.