Chapter 7 - Utility Maximization
Suppose that Omar's marginal utility for cups of coffee is constant at 1.5 utils per cup no matter how many cups he drinks. In contrast, his marginal utility per doughnut is 11 for the first doughnut he eats, 10 for the second, 9 for the third, and so on (that is, declining by 1 util per additional doughnut). In addition, suppose that coffee costs $1 per cup, doughnuts $1 each, and Omar has a budget that he can spend on only doughnuts, coffee, or both. How big would that budget have to be before he will spend a dollar a first cup of coffee?
$11
Substitution Effect
(1) A change in the quantity in the quantity demanded of a consumer goods that results from a change in its relative expensiveness caused by a change in the good's own price. (2) The reduction in the quantity demanded of the second of a pair of substitute resources that occurs when the price of the first resource falls and causes firms that employ both resources to switch to using more of the first resource (whose price has fallen) and less of the second resource (whose price has remained the same).
3 Characteristics of Utility
- "Utility" and "usefulness" are not synonymous. - Utility is subjective. - Utility is difficult to quantify.
Income Effect
A change in the quantity demanded of a product that results from the change in real income (purchasing power) caused by a change in the product's price.
Indifference Curve
A curve showing the different combiantions of two products that yield the same satisfaction of utility to a consumer.
Demand curves slope downward because, other things equal?
A decrease in a product's price raises MU per dollar and makes consumers wish to purchase more units.
Budget Line
A line that shows the different combinations of two products a consumer can purchase with a specific money income, given the products' prices.
Indifference Map
A set of indifference curves, each representing a different level of utility, that togther show the preferences of a consumer.
Complete the following table and answer the questions below: a. At which rate is total utility increasing: a constant rate, decreasing rate, or an increasing rate? How do you know? b. T/F: "A rational consumer will purchase 1 unit of the product represented by these data, because that amount maximizes marginal utility." c. T/F: "It is possible that a rational consumer will not purchase any units of the product represented by these data."
Graph: 18, 33, 7, 5, 1 a. A decreasing rate, because marginal utility is declining. b. False, because rational consumers maximize total utility. c. True, because this product's price could be high relative to the first unit's marginal utility.
Rational Behavior
Human behavior based on comparison of marginal costs and marginal benefits; behavior desgined to maximize total utility. Reference *Rational*
Consumer Equilibrium
In marginal utility theroy, the combination of gooods purchased that maximizes total utility by applying the utility-maximizing rule.
Equilibrium Position
Indifference curve model, the combination of two goods at which a consumer maximizes his or her utility (reaches the highest attainable indifference curve), given a limited amount to spend (a budget contraint).
Frank spends $75 on 10 magazines and 25 newspapers. The magazines cost $5 each and the newspaper cost $2.50 each. Suppose that his MU from the final magazine is 10 utils while from the final newspaper is also 10 utils. According to the utility-maximizing rule, Frank should?
Reallocate spending from magazines to newspapers.
Marginal Utility
The extra utility a consumer obtains from the consumption of 1 additional unit of a good or serice; equal to the change in total utility divided by the change in the quantity consumed.
Budget Constraint
The limit that the size of a consumer's income (and the prices that must be paid for goods and services) imposes on the ability of that consumer to obtain goods and services.
Law of Diminishing Marginal Utility
The principle that as a consumer increases the consumption of a good or service, the marginal utility obtained from each additional unit of the good or service decreases.
Utility-Maximizing Rule
The principle that to obtain the greatest total utility, a consumer should allocate money income so that the last dollar spent on each good or service yields the same marginal utility (MU). For two goods X and Y, with prices Px and Py total utility will be maximized by purchasing the amounts of X and Y such that MUxIPx = MUyIPy for the last dollar spent on each good.
Marginal Rate of Substitution (MRS)
The rate at which a consumer is willing to substitute one good for another (from a given combination of goods) and remain equally satisfied ( have the same total utility); equal to the slope of a consumer's indifference curve at each point on the curve.
MUa/Pa = za = 10-1x MUb/Pb = zb = 21-2x Where z is marginal utility per dollar measured in utils, x is the amount spent on product A, and y is the amount spent on product B. Assume that the consumer has $10 to spend on A and B - this is, x+y=10. a. How is the $10 best allocated between A and B? b. How much utility will the marginal dollar yield?
a. $3 on A and $7 on B b. 7 utils
You are choosing between two goods. X and Y, and your marginal utility from each is shown in the following table. a. 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? b. What total utility will you realize? c. Assume that, other things remaining unchanged, the price of X falls to $1. What quantities of X and Y will you now purchase? d. Using the two prices and quantities for X, complete the table to derive the derived demand schedule (a table showing prices and quantities demanded) for X.
a. 2 units of X and 5 units of Y b. 106 utils c. 4 units of X and 5 units of Y d. Price of x: $2, $1 and quantity demanded of x: 2, 4
Suppose that with a budget of $140, Fatima spends $84 on sushi and $56 on bagels when sushi costs $2 per piece and bagels cost $2 per bagel. Then, after the price of bagels falls to $1 per bagel. a. How many pieces of sushi and how many bagels did Fatima consume before the price change? b. At the new prices, how much money would it have cost Fatima to buy those quantities (that is, the quantities that she consumed before the price change)? c. Given that it used to take Fatima's entire $140 to buy those quantities, how big is the income effect caused by the lower price of bagels?
a. 42 pieces of sushi and 28 bagels b. $112 c. $28
Columns 1 through 4 in the following table show the amrginal 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 get from saving. Assume that the prices of A, B, C, and D are, respectively, $18, $6, $4, and $24 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.
a. A - 4 units B - 3 units C - 3 units D - 0 units b. $4 c. (18*4)+(6*3)+(4*3)+(24*0)+4 = 106
Consider the following comment: "Want to make millions of dollars? Invent a product that saves Americans lots of time." This statement recognizes that?
time can be used to earn money
In the last decade or so, there has been a dramatic expansion of small retail convenience stores (such as 7-Eleven, Kwik Trip, and Circle K), although their prices are generally much higher than prices in large supermarkets. The success of these convenience stores can be partially explained by?
The time consumers save when purchasing good there.
Total Utility
The total amount of satisfaction derived from the consumption of a single product or a combination of products.
Utility
The want-satisfying power of a good or service; the satisfaction or pleasure a consumer obtains from the consumptions of a goood or service (or from the consumption of a collection of goods and serices).
Many apartment-complex owners are installing water meters for each apartment and billing the occupants according to the amount of water they use. This system with the former procedure of having a central meter for the entire complex and dividing up the collective water expense as part of the rent. Where individual meters have been installed, water usage has declined 10 to 40 percent. This decline is water usage?
Would be expected since people now have to pay according to the amount of water they use.
John likes Coca-Cola. After consuming one Coke, John has a total utility of 10 utils. After two Cokes, he has a total utility of 25 utils. After three Cokes, he has a total utility of 50 utils. a. Complete the table below to show John's marginal utility for each Coke. b. Does John show diminishing marginal utility for Coke, or does he show increasing marginal utility for Coke? c. Suppose that John has $6 in his pocket. If Coke costs $2 each and John is willing to spend one of his dollars on purchasing a first can of Coke, would he spend his second dollar on a Coke, too? d. What about the third Dollar? e. If John's marginal utility for Coke keeps on increasing no matter how many Cokes he drinks, would it be fair to say that he is addicted to Coke?
a. MU: 10, 15, 25 b. Increasing marginal utility c. Yes d. Yes e. Yes
Mylie's total utility from singing the same song over and over is 70 utils after one repetition, 110 utils after two repetitions, 90 utils after three repetitions, 40 utils after four repetitions, -30 utils after five repetitions, and -180 utils after six repetitions, as shown in the table below. a. Write down her marginal utility for each repetition. b. Once Mylie's total utility begins to decrease, does each additional singing of the song hurt more than the previous song or less than the previous song?
a. MU: 70, 40, -20, -50, -70, -150 b. More than the previous song
Mrs Simpson buys loaves of bread and quarts of milk each week at prices of $2 and 1.60 cents, respectively. At present she is buying these products in amounts such that the marginal utilities from the last units purchased of the two products are 160 and 140 utils, respectively. a. Is she buying the utility-maximizing combination of bread and milk? b. If not, how should she allocate her expenditures between the two goods?
a. No, the marginal utility per cent on bread is 0.80 and the marginal utility per cent spent on milk is 0.875. b. She should buy more milk and less bread.
The theory of consumer behavior accounts for time:
because time can be used to earn money
