Download ECON 103: Homework Answers - Utility Maximization and Consumer Behavior and more Summaries Economics in PDF only on Docsity!
ECON 103, 2008-
ANSWERS TO HOME WORK ASSIGNMENTS
Due the Week of June 2
Chapter 5
WRITE [1] Complete the following table and answer the questions that follow:
Units consumed Total utility Marginal utility 0 0 -- 1 10 10 2 18 8 3 25 7 4 30 5 5 33 3 6 34 1 . a. At which rate is total utility increasing: a constant rate, a decreasing rate, or an increasing rate? How do you know? Ans: A decreasing rate; because marginal utility is declining.
b. “A rational consumer will purchase only one unit of the product represented by these data, since that amount maximizes marginal utility.” Do you agree? Explain why or why not. Ans: Disagree. The marginal utility of a unit beyond the first may be sufficiently great (relative to product price) to make it a worthwhile purchase.
c. “It is possible that a rational consumer will not purchase any units of the product represented by these data.” Do you agree? Explain why or why not. Ans: 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.
WRITE: [2] Mrs. Wilson buys loaves of bread and litres of milk each week at prices of $1 and $0.80, respectively. At present she is buying these two products in amounts such that the marginal utilities from the last units purchased of the two products are 80 and 70 utils, respectively. Is she buying the utility-maximizing combination of bread and milk? If not, how should she reallocate her expenditures between the two goods?
Ans. No she is not maximizing her utility because the utility maximizing rule does not hold. For bread the MU per 1¢ is 0.8 (i.e., 80utils/100¢) but for milk it is 0.875. She should buy less bread and more milk.
WRITE: [3] Columns 1 through 4 of the accompanying table show the marginal utility, measured in terms of utils, which 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 a money income of $106.
Column 1 Column 2 Column 3 Column 4 Column 5 Units of A MU
Units of B MU
Units of C MU
Units of D MU
No. of $ saved MU
a. What quantities of A, B, C, and D will Ricardo purchase in maximizing his satisfactions? 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.
Ans. (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.
The "trick" in getting this answer is to view a $ of savings as a product with a price of $1 per unit. So, for example, the first "unit" of savings costs $1 and generates utility of 5 utils (MU/$ =5). The second "unit" of savings costs $1 and generates 4 utils (MU/$ = 4).
WRITE [4]: 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.
Units of X MUx Units of Y MUy 1 10 1 8 2 8 2 7 3 6 3 6 4 4 4 5 5 3 5 4 6 2 6 3
_Ans: 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. Total utility is now 58 (= 10 + 8 + 6
- 4 for X plus 8 + 7 + 6 + 5 + 4 for Y)._
Demand schedule: Price Q demanded $1 4 $2 2
