Questions And Problems

1. Walking down an unfamiliar street one day, you come across an old-fashioned candy store. They have red hots five for one penny, and rock candy—one small piece for transaction costs, or alternative tax treatment of income from different securities, can explain the existence of some differential rates but nothing like the variety and magnitude of differentials found in the marketplace.

Consumption in period 1

Figure 1.4 Investor's opportunity set with several alternatives.

one penny. You decide to purchase some for yourself and your friends, but you find that you only have $1.00 in your pocket. Construct your opportunity set both geometrically and algebraically. Draw in your indifference map (set of indifference curves). Explain why you have drawn your indifference curves as you have drawn them.

2. Let us solve a two-period consumption investment decision similar to the one presented in the text. Assume that you have income equal to $20 in each of two periods. Furthermore, you have the ability to both lend and borrow money at a 10% rate. Draw the opportunity set and your indifference map. Show the optimum amount of consumption in each period.

3. Assume you can lend and borrow at 10% and have $5,000 in income in each of two periods. What is your opportunity set?

4. Assume you can lend and borrow at 5% and have $20,000 in income in each of two periods. Further assume you have current wealth of $50,000. What is your opportunity set?

5. An individual has two employment opportunities involving the same work conditions, but different incomes. Job 1 yields Yl = 50, Y2 = 30. Job 2 yields Yl = 40, Y2 = 40. Given that markets are perfect and bonds yield 5%, which should be selected?

6. Assume you have income of $5,000 in each of two periods and can lend at 10% but pay 20% on borrowing. What is your opportunity set?

7. Assume your preference function P is P = Cl + C2 + CjC2. Plot the location of all points with P = 50, P = 100.

8. In Problem 3 what is the preferred choice if the preference function discussed in

Problem 7 holds?

9. Suppose you have $10.00 to spend on dinner. There are two possibilities: pizza at $2.00 a slice or hamburgers at $2.50 apiece. Construct an opportunity set algebraically and graphically. Add indifference curves according to your own individual taste.

10. Using the two-period consumption model, solve the following problem. Assume you can lend and borrow at 5% and your income is $50 in each period. Derive the opportunity set and add your indifference curves.

11. Assume you earn $10,000 in periods 1 and 2. Also you inherit $10,000 in period 2. If the borrowing/lending rate is 20%, what is the opportunity set? What is the maximum that can be consumed in the first period? In the second period?

12. Assume the borrowing rate is 10% and the lending rate is 5%. Also assume your income is $100 in each period. What is the maximum you can consume in each period? What is the opportunity set?

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