Unformatted text preview: PADP 6950 Fertig Fall 2011 UGA Homework 4 Solutions 1. Anna has an income of $2000 this year, and she expects an income of $1100 next year. She can borrow and lend money at an interest rate of 10%. Consumption goods cost $1 per unit this year and there is no inflation. a. What is the present value of Anna's endowment? NPV = 2000 + 1100/1.1 = $3000 b. On a graph show the combinations of consumption this year and consumption next year that she can afford. Label Anna's endowment with the letter E. Write down Anna's budget equation. What is the slope of Anna's budget line? (see graph below) C1 + C2/1.1 = 3000 C2/1.1 = 3000 C1 C2 = 3300 1.1 C1 slope = -1.1 c. Suppose that Anna's utility function is U=C1C2 where U=2,475,000. Plot the indifference curve and find the tangent point. How much will Anna consume in each period? Will she borrow or save in the first period? C2 = 2475000/C1 C1 500 1000 1500 2000 2500 3000 3500 4000 c2(budget) 2750 2200 1650 1100 550 0 -550 -1100 c2(utility) 4950.0 2475.0 1650.0 1237.5 990.0 825.0 707.1 618.8 3500 3000 2500 2000 1500 1000 500 0 0 500 1000 1500 2000 2500 3000 3500 She saves $500 in per. 1. d. If the interest rate went up to 20%, will she save or borrow? New budget line: C1 + C2/1.2 = 2000 + 1100/1.2 C2/1.2 = 2917 C1 C2 = 3500 1.2 C1 steeper slope than above She will still save. 2. John Pigskin has a utility function of the form U = c . John is beginning his senior year of college football. If he is not seriously injured, he will receive a $1,000,000 contract for playing professional football. If an injury ends his football career, he will receive a $10,000 contract as a refuse removal facilitator in his hometown. There is a 10% change that John will be injured badly enough to end his career. EU = 90%*u($1,000,000) + 10%*u($10,000) = .9*1000+.1*100 = 910 a. What is John's expected utility? b. If John pays $p for an insurance policy that would give him $1,000,000 if he suffered a career-ending injury while in college, then he would be sure to have an income of $1,000,000 p no matter what happened to him. Write an equation that can be solved to find the largest price that John would be willing to pay for such an insurance policy. Solve this equation for p. He would buy the insurance policy if it did not lower his expected utility. The most he would be willing to pay for the policy is such that his utility would be equal to his expected utility. U($1,000,000 p) = 910 Sqrt(1,000,000 p) = 910 1,000,000 p = 9102 p = 1,000,000 828,100 p = 171,900 ...
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