Annahas an income of $1500 this year, andshe expectsan income of $2500 next year. She can borrow and lend money at an interest rate of8%. Consumption goods cost $1 per unit thisyear and there is no inflation.

a.What is thenetpresent value ofAnna's endowment?

b.On a graph show the combinations of consumption this year and consumption next year thatshe can afford. Label Anna's endowment with the letter E. Write downAnna's budget equation. What is the slope ofAnna's budget line?

c.Suppose thatAnna's utility function is U=C0C1wherethe marginal rate of substitution is1/0.Sketchthe indifference curve and find the tangent point. How much willAnnaconsume in eachperiod? Willshe borrow or save in the first period?

d.If the interest rate went downto5%, wouldshe save or borrow? How does the amountcompare to your answer in part c?

2. John Pigskin has autility function of the form=. John is beginning his senior year of college football. If he is not seriously injured, he will receive a $1,500,000 contract for playing professional football. If any injury ends his football career, he will take a job as a refuse removal facilitator in his hometown that pays $50,000. There is a15% chance that John will be injured badly enough to end his career.

a.What is John's expected utility?

b.How much would John be willing to pay to remove the financial risk he faces? That is, what $p would he payfor a $1,500,000 insurance policy so that he would have $1,500,000-$peven if he had a serious injury? Assumehe wouldn't work for $50,000 if he had the insurance and he was injured.Hint: You should set his utility with certainty (U($1,500,000-$p)) equal to his expectedutility with risk (found in part a) and solve for p.