a. At which rate is total utility increasing: a constant rate, a decreasing rate, or an increasing rate? How do you know?
b. "A rational consumer will purchase only 1 unit of the product represented by these data, since that amount maximizes marginal utility." Do you agree? Explain why or why not.
c. "It is possible that a rational consumer will not purchase any units of the product represented by these data." Do you agree? Explain.
Missing total utility data top -- bottom: 18; 33. Missing marginal utility data, top -- bottom: 7; 5; 1.
ANSWER:
(a) A decreasing rate; because marginal utility is declining.
(b) Disagree. The marginal utility of a unit beyond the first may be sufficiently great (relative to product price) to make it a worthwhile purchase. Consumers are interested in maximizing total utility, not marginal utility.
(c) Agree. This product's price could be so high relative to the first unit's marginal utility that the consumer would buy none of it.
21-4
Columns 1 through 4 of the accompanying table show the marginal utility, measured in utils, that Ricardo would get by purchasing various amounts of products A, B, C, and D. Column 5 shows the marginal utility Ricardo gets from saving. Assume that the prices of A, B, C, and D are $18, $6, $4, and $24, respectively, and that Ricardo has an income of $106.
a. What quantities of A, B, C, and D will Ricardo purchase in maximizing his utility?
b. How many dollars will Ricardo choose to save?
c. Check your answers by substituting them into the algebraic statement of the utility-maximizing rule.
ANSWER:
(a) 4 units of A; 3 units of B; 3 units of C, and 0 units of D.
(b) Save $4.
(c) 36/$18 = 12/$6 = 8/$4 = 2/$1. The marginal utility per dollar of the last unit of each product purchased is 2.
21-5
You are choosing between two goods, X and Y, and your marginal utility from each is as shown below. If your income is $9 and the prices of X and Y are $2 and $1, respectively, what quantities of each will you purchase to maximize utility? What total utility will you realize? Assume that, other things remaining unchanged, the price of X falls to $1. What quantities of X and Y will you now purchase? Using the two prices and quantities for X, derive a demand schedule (price-quantity-demanded table) for X.
ANSWER:
Buy 2 units of X and 5 units of Y. Marginal utility of last dollar spent will be equal at 4 (= 8/$2 for X and 4/$1 for Y) and the $9 income will be spent. Total utility = 48 (= 10 + 8 for X plus 8 + 7 + 6 + 5 + 4 for Y). When the price of X falls to $1, the quantity of X demanded increases from 2 to 4 (income effect). Total utility is now 58 (= 10 + 8 + 6 + 4 for X plus 8 + 7 + 6 + 5 + 4 for Y).
Demand schedule for X: P = $2; Q = 2. P = $1; Q = 4.
