1) A perpetuity is a bond that pays an amount per year forever. If a perpetuity
ID: 2507340 • Letter: 1
Question
1) A perpetuity is a bond that pays an amount per year forever. If a perpetuity pays $5 per year:
(a) what would the annual interest rate be if an investor paid a $50 perpetuity?
(b) what would be the annual interest rate if an investor paid $200? $600? Bonds are known as "fixed income" securities because the future payments that they will make to investors are fixed by the bond agreement in advance.
(c) Do the interest rates of bonds and other investments that offer fixed future payments vary positively or inversely with their current prices?
2) Tom's T-shirts is a price taker that has the following costs:
Output (t-shirts/hour)
Total cost ($/hour)
0
5
1
20
2
26
3
35
4
46
5
59
a. If t-shirts sell for $7.50 each, what is Tom's profit-maximizing output?
b. What is Tom's shutdown point?
c. Over what price range will Tom leave the t-shirt industry?
d. Over what price range will other firms with costs identical to Tom's enter the industry?
e. What is the price of a t-shirt in the long run?
3) The table below gives an individual's marginal utility schedule for good X and good Y. Suppose that X and Y are the only goods available, the price of X and the price of Y are $1 and the individual's income is $8 per time period and is all spent.
Indicate how this individual should spend his/her income in order to maximize total utility. Justify your answer.
What is the total amount of utility received by the individual when in equilibrium? Justify your answer.
State mathematically the equilibrium condition for this individual.
4) Carol quit her job at Microsoft where she earned $50,000 a year. She cashed in $50,000 in corporate bonds that earned 10% interest annually to buy a mini-bus. Carol has decided to buy the mini-bus and set up a commuter service between LA and San Francisco. There are 1000 people who will pay $400 a year each for the commuter service; $280 from each person goes for gas, maintenance, insurance, and depreciation. She estimates that her entrepreneurial skills would have typically yielded a normal profit of $5,000 in another business.
Output (t-shirts/hour)
Total cost ($/hour)
0
5
1
20
2
26
3
35
4
46
5
59
Explanation / Answer
1)
a)10%
b)2.5%
c) vary positively
2)
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