Chapter 4

1.Natalie is always willing to give up 10 ounces of licorice for 1 ounce of chocolate.

Mitchell, on the other hand, will always give up 10 ounces of chocolate for 1 ounce

of licorice. Based on this information, answer the following questions:

a. Do Natalie’s preferences exhibit a diminishing marginal rate of substitution between

chocolate and licorice? Why or why not?

b. Assuming that Natalie and Mitchell have the same amount of money to spend on

chocolate and licorice, who will purchase the most licorice? Why? Hint: Include a graph with your answer.

2. A stockholder named Sue must cast a vote for chair of the board. Sue prefers Mr. Lee

to Ms. Doe, Ms. Doe to Mr. James, and Mr. James to Mr. Lee.

a. Are Sue’s preferences consistent with our assumptions about consumer behavior?

Explain.

b. If all stockholders had the same preferences as Sue, who would win the

appointment as chair of the board? Explain.

3. Over the past decade medical costs have increased more rapidly than other prices. In

order to illustrate how rising medical costs have affected consumer alternatives, let X

represent the quantity of medical services, and let Y represent the quantity of other

goods. Furthermore, let income (M) be measured in hundreds of dollars, the price of

medical services and other goods in terms of dollars per minute, with M = 100, P_x = 4,

P_y = 5.

a. Graph the budget line, and determine the market rate of substitution.

b. Illustrate the budget set.

c. Show in your graph what happens to the budget constraint if P_x increases to $10.

d. What is the meaning of the slope of the two budget constraints?

4. Draw the opportunity set of a consumer with an income of $200 who faces prices of

P_x = 5 and P_y = 10. What is the market rate of substitution between the two goods?

5. Ms. Caffeine enjoys coffee(Y) and tea (X) according to the function U (X, Y) = 3Y+ 4X.

1. What is her MRS of coffee for tea? What do her indifference curves look like?
2. If coffee and tea cost $3 each and Ms. Caffeine has $12 to spend on these products, how much coffee and tea should she buy to maximize her utility? As part of your answer, draw the graph of her indifference curve map and her budget constraint, and show that the utility-maximizing point occurs only on the X-axis where no coffee is bought.
3. How could her consumption change if the price of the coffee fell to $2?

6. Mr. A derives utility from martinis in proportion to the numbers he drinks, U (M) = M.

Mr. A is very particular about his martinis, however: He only enjoys them made in the exact proportion of two parts gin (X) to one part vermouth (Y).

1. Graph Mr. A’s indifference curve in terms of X and Y for various levels of martini consumption.
2. Extra Credit: Show that regardless of the prices of the two ingredients, Mr. A will never alter the way he mixes martinis. Graph this result.