Multiple Choice
Janet consumes two commodities x and y. Her utility function is min{x + 2y, y + 2x}. She chooses to buy 10 units of good x and 20 units of good y. The price of good x is $1. Janet's income is
$20.
Elmer's utility function is U(x, y) = min{x, y2}. If the price of x is $10 and the price of y is $15 and if Elmer chooses to consume 4 units of y, what must his income be?
$220
Ads in a slick business magazine are read by 300 lawyers and 1,000 M.B.A.s. Ads in a consumer publication are read by 250 lawyers and 300 M.B.A.s. If Harry had $3,750 to spend on advertising, the price of ads in the business magazine were $500, and the price of ads in the consumer magazine were $250, then the combinations of M.B.A.s and lawyers whom he could reach with his advertising budget would be represented by the integer values along a line segment that runs between the two points
(3, 750, 4, 500) and (2, 250, 7, 500).
Mort's utility function is U(x1, x2) = x1x2. His income is $100. The price of good 2 is $10. Good 1 is priced as follows. The first 6 units cost $10 per unit and any additional units cost $5 per unit. What consumption bundle does Mort choose?
(5, 5)
Jean-Pierre has preferences represented by the utility function U(x, y) = min{ 2x + y, x + 6y}. If x is on the horizontal axis and y is on the vertical axis, what is the slope of his indifference curve at the point
-2
Charlie's utility function is U(A, B) = AB, where A and B are the numbers of apples and bananas, respectively, that he consumes. When Charlie is consuming 20 apples and 80 bananas, if we put apples on the horizontal axis and bananas on the vertical axis, the slope of his indifference curve at his current consumption is
-4
Charlie's utility function is U(A, B) = AB, where A and B are the numbers of apples and bananas, respectively, that he consumes. When Charlie is consuming 15 apples and 90 bananas, if we put apples on the horizontal axis and bananas on the vertical axis, the slope of his indifference curve at his current consumption is
-6
Toby Talkalot subscribes to a local phone service that charges a fixed fee of $10 per month and allows him to place as many local phone calls as he likes without further charge. Let good 1 be an aggregate of commodities other than local phone use and let good 2 be local phone use. (Measure good 1 on the horizontal axis and good 2 on the vertical axis.) On Monday, Toby didn't use the telephone at all. The slope m of his indifference curve at the consumption bundle he chose on Monday was
0
Ollie has a utility function U(x, y) = (x + 2)(y + 3). The price of x is $1 and the price of y is $1. When he maximizes his utility subject to his budget constraint, he consumes positive amounts of both goods. Ollie consumes
1 more unit of x than he consumes of y.
Clara spends her entire budget and consumes 5 units of x and 13 units of y. The price of x is twice the price of y. Her income doubles and the price of y doubles, but the price of x stays the same. If she continues to buy 13 units of y, what is the largest number of units of x that she can afford
10
Maria spends her entire budget and consumes 5 units of x and 6 units of y. The price of x is twice the price of y. Her income doubles and the price of y doubles, but the price of x stays the same. If she continues to buy 6 units of y, what is the largest number of units of x that she can afford?
10
Minnie Applesauce is shopping for a summer lake cottage. Minnie hates mosquito bites, but the cheapest lake cottages have the most mosquitos. The price of a lake cabin is related to b, the number of mosquito bites you can expect per hour, according to the formula p = $20,000 - 100b. Minnie's utility function is u = x - 5b2, where x is her expenditure on all goods other than her lake cabin. If Minnie makes her best choice of lake cabin, how many mosquito bites per hour will she get?
10
Our old friend, Edmund Stench, of Chapter 2 loves punk rock video tapes. He has no income and therefore has to accept garbage in his backyard in return for money. Each video tape cost $2 and each sack of garbage that he accepts brings him $1. His utility function is given by U(c, g) = min{ 2c, 20 - g}, where c is the number of video tapes and g is the number of sacks of garbage that he gets per month. Each month he will choose to accept
10 sacks of garbage.
Ambrose's utility function is U(x1, x2) = . If the price of nuts (good 1) is $1, the price of berries (good 2) is $5, and his income is $145, how many units of nuts will Ambrose choose?
100
Henri's utility function is min{x, 5y + 2z}. The price of x is $1, the price of y is $15, and the price of z is $7. Henri's income is $44. How many units of x does Henri demand?
11
If we graph Mary Granola's indifference curves with avocados on the horizontal axis and grapefruits on the vertical axis, then whenever she has more grapefruits than avocados, the slope of her indifference curve is 22. Whenever she has more avocados than grapefruits, the slope is . Mary would be indifferent between a bundle with 14 avocados and 20 grapefruits and another bundle that has 26 avocados and
11 Grapefruits
If she spends all of her income on uglifruits and breadfruits, Maria can just afford 11 uglifruits and 4 breadfruits per day. She could also use her entire budget to buy 3 uglifruits and 8 breadfruits per day. The price of uglifruits is 6 pesos each. How much is Maria's income per day?
114
Ambrose has the utility function . If Ambrose is initially consuming 25 units of nuts and 17 units of berries, then what is the largest number of berries that he would be willing to give up in return for an additional 39 units of nuts?
12
Angela has preferences represented by the utility function U(x, y) = 2x + 2y. She consumes 10 units of good x and 6 units of good y. If her consumption of good x is lowered to 4, how many units of y must she have in order to be exactly as well off as before?
12
Harmon's utility function is U(x1, x2) = x1x2. His income is $100. The price of good 2 is p2 = 4. Good 1 is priced as follows. The first 15 units cost $4 per unit and any additional units cost $2 per unit. What consumption bundle does Harmon choose?
12.5, 12.5)
Charlie has the utility function U(xA, xB) = xAxB. His indifference curve passing through 35 apples and 18 bananas will also pass through the point where he consumes 5 apples and
126 Bannanas
Ambrose's utility function is U(x1, x2) = . If the price of nuts (good 1) is $1, the price of berries (good 2) is $6, and his income is $264, how many units of nuts will Ambrose choose?
144
Wanda Littlemore's utility function is U(x, y) = x + 47y - 3y2. Her income is $107. If the price of x is $1 and the price of y is $23, how many units of good x will Wanda demand?
15
If you spent your entire income, you could afford either 6 units of x and 13 units of y or 13 units of x and 6 units of y. If you spent your entire income on x, how many units of x could you buy?
19
Leo's utility function is min{x, 3y + 2z}. The price of x is $1, the price of y is $9, and the price of z is $8. Leo's income is $8. How many units of x does Leo demand?
2
If we graph Mary Granola's indifference curves with avocados on the horizontal axis and grapefruits on the vertical axis, then whenever she has more grapefruits than avocados, the slope of her indifference curve is 22. Whenever she has more avocados than grapefruits, the slope is . Mary would be indifferent between a bundle with 22 avocados and 37 grapefruits and another bundle that has 37 avocados and
22 Grapefruits
Doreen has preferences represented by the utility function U(x, y) = 10x + 5y. She consumes 10 units of good x and 9 units of good y. If her consumption of good x is lowered to 1, how many units of y must she have in order to be exactly as well off as before?
27
This weekend, Martha has time to read 40 pages of economics and 30 pages of sociology. Alternatively, she could read 30 pages of economics and 50 pages of sociology. Which of these equations describes all combinations of pages of economics, E, and sociology, S, that she could read over the weekend?
2E + S = 110.
This weekend, Martha has time to read 40 pages of economics and 30 pages of sociology. Alternatively, she could read 10 pages of economics and 90 pages of sociology. Which of these equations describes all combinations of pages of economics, E, and sociology, S, that she could read over the weekend?
2E+S=110
Harold lives on Doritos and seafood salads. The price of Doritos is 1 dollar per bag and the price of seafood salads is 2 dollars each. Harold allows himself to spend no more than 11 dollars a day on food. He also restricts his consumption to 6,500 calories per day. There are 1,500 calories in a bag of Doritos and 500 calories in a seafood salad. If he spends his entire money budget each day and consumes no more calories than his calorie limit, he can consume up to
3 bags of Doritos per day but no more.
Charlie has a utility function U(xA, xB) = xAxB, the price of apples is $1, and the price of bananas is $2. If Charlie's income were $120, how many units of bananas would he consume if he chose the bundle that maximized his utility subject to his budget constraint?
30
Ambrose has the utility function . If Ambrose is initially consuming 64 units of nuts and 10 units of berries, then what is the largest number of berries that he would be willing to give up in return for an additional 17 units of nuts?
4
Quincy lives on pretzels and seafood salads. The price of pretzels is 1 dollar per bag and the price of seafood salads is 2 dollars each. Quincy allows himself to spend no more than 14 dollars a day on food. He also restricts his consumption to 3,400 calories per day. There are 600 calories in a bag of pretzels and 200 calories in a seafood salad. If he spends his entire money budget each day and consumes no more calories than his calorie limit, he can consume up to
4 Bags
If you could exactly afford either 4 units of x and 24 units of y, or 9 units of x and 4 units of y, then if you spent all of your income on y, how many units of y could you buy?
40
Clara's utility function is U(x, Y) = (x + 2)(Y + 1). If her marginal rate of substitution is -3 and she is consuming 12 units of good x, how many units of good Y must she be consuming?
41
Charlie's utility function is U(xA, xB) = xAxB. If Charlie's income is $40, the price of apples is $4, and the price of bananas is $2, how many apples are there in the best bundle that Charlie can afford?
5
Charlie has a utility function U(xA, xB) = xAxB, the price of apples is $1, and the price of bananas is $2. If Charlie's income were $200, how many units of bananas would he consume if he chose the bundle that maximized his utility subject to his budget constraint?
50
Your budget constraint for the two goods A and B is 8A + 4B = I, where I is your income. You are currently consuming more than 18 units of B. In order to get 3 more units of A, how many units of B would you have to give up?
6
Clara's utility function is U(x, y) = (x + 2)(y + 1). If her marginal rate of substitution is -4 and she is consuming 14 units of good x, how many units of good y must she be consuming?
63
Charlie has the utility function U(xA, xB) = xAxB. His indifference curve passing through 32 apples and 8 bananas will also pass through the point where he consumes 4 apples and
64 bananas
Josephine's utility function is U(x, y) = y + 5x.5. She has 1 unit of x and 2 units of y. If her consumption of x is reduced to zero, how much y must she have in order to be exactly as well off as before?
7 units
Wanda Littlemore's utility function is U(x, y) = x + 46y - 2y2. Her income is $135. If the price of x is $1 and the price of y is $18, how many units of good x will Wanda demand
9
Angela consumes goods x and y. Her indifference curves are described by the formula . Higher values of k(X=3)correspond to better indifference curves.
Angela prefers bundle (8, 9) to bundle (9, 8).
Charles's utility function is U(x, y) = xy. Anne's utility function is U(x, y) = 1,000xy. Diana's utility function is -xy. Elizabeth's utility function is . Fergie's utility function is xy - 10,000. Margaret's utility function is . Philip's utility function is x(y + 1). (The goods x and y are two very expensive goods. We leave you to speculate about what they are.) Which of these persons have the same preferences as Charles?
Anne, Fergie, and Elizabeth
Arthur's preferences are defined over two basic food groups, beer, x1, and ice cream, x2. His utility function is u(x1, x2) = x21 + x2. He has $100 to spend, and each of these goods costs $10 per quart.
Arthur will find that 10 quarts of beer and no ice cream is the best bundle.
Isabella thrives on two goods: lemons and tangerines. The cost of lemons is 40 guineas each and the cost of tangerines is 20 guineas each. If her income is 320 guineas, how many lemons can she buy if she spends all of her income on lemons?
B.8
Billy Bob wants to gain some weight so that he can play football. Billy consumes only milk shakes and spinach. Milk shakes cost him $1 each and spinach costs $2 per serving. A milk shake has 850 calories and a serving of spinach has 200 calories. Billy Bob never spends more than $20 a day on food and he always consumes at least 8,000 calories per day. Which of the following is necessarily true?
Billy Bob never consumes more than 6 servings of spinach a day.
Coke and Pepsi are perfect substitutes for Mr. Drinker and the slope of his indifference curves is - 1. One day he bought 2 cans of Coke and 20 cans of Pepsi. (The cans of both drinks are the same size.)
Coke and Pepsi cost the same.
Colette consumes goods x and y. Her indifference curves are described by the formula . Higher values of k/(x+7)correspond to better indifference curves.
Colette prefers bundle (12, 16) to bundle (16, 12).
Georgina thrives on two goods: pears and bananas. The cost of pears is 30 pesos each and the cost of bananas is 15 pesos each. If her income is 180 pesos, how many pears can she buy if she spends all of her income on pears?
D.6
Ernie's utility function is U(x, y) = 32xy. He has 10 units of good x and 8 units of good y. Waldo's utility function for the same two goods is U(x, y) = 3x + 5y. Waldo has 9 units of x and 13 units of y.
Ernie prefers Waldo's bundle to his own bundle, but Waldo prefers his own bundle to Ernie's.
Martha's utility function is U(x, y) = min{x + 2y, 2x + y}. George's utility function is U(x, y) = min{ 2x + 4y, 4x + 2y}. If George and Martha have the same income and face the same prices for the goods x and y,
George and Martha will both demand the same amount of y.
Jane's utility function is U(x, y) = x + 2y, where x is her consumption of good X and y is her consumption of good Y. Her income is $2. The price of Y is $2. The cost per unit of X depends on how many units she buys. The total cost of x units of X is the square root of x.
Given her budget, Jane would maximize her utility by spending all of her income on good X.
Peter consumes no commodities other than Miller Lite and Bud Light. His annual budget for these two commodities is described by the equation 5x + 30y = 300, where x is sixpacks of Miller Lite and y is cases of Bud Light. Peter considers 2 cases of Bud Light to be perfect substitutes for 6 sixpacks of Miller Lite
He will consume 60 sixpacks of Miller Lite per year.
Roger consumes no commodities other than Miller Lite and Bud Light. His annual budget for these two commodities is described by the equation 5x + 25y = 300, where x is sixpacks of Miller Lite and y is cases of Bud Light. Roger considers 2 cases of Bud Light to be perfect substitutes for 6 sixpacks of Miller Lite.
He will consume 60 sixpacks of Miller Lite per year.
Andrew's utility function is U(x1, x2) = 4x21 + x2. Andrew's income is $32, the price of good 1 is $16 per unit, and the price of good 2 is $1 per unit. What happens if Andrew's income increases to $80 and prices do not change? (Hint: Does he have convex preferences?)
He will reduce his consumption of good 2
Henry's utility function is x2 + 16xw + 64w2, where x is his consumption of x and w is his consumption of w.
Henry's indifference curves are straight lines.
Danny Featherweight is taking a tough course in law school. His professor agreed to give him a course grade of max{ 2x, 3y} where x and y are the number of answers he gets right on the first and second midterms, respectively. Danny needs a course grade of 150 to pass. He finds that for the first midterm, for every A minutes of study, he will get one more answer right. For the second midterm, for every B minutes that he studies, he will get one more answer right. If he doesn't study at all, Danny will get nothing right on either exam. All Danny cares about is passing. He doesn't want to waste any time getting a higher grade than he needs
If A/B < 2/3 , then Danny will not study for the second exam.
Mac's utility function is U(x, y) = max{ 2x - y, 2y - x}.
If Mac has more x than y, any increase in his consumption of y would lower his utility.
Badger Madison consumes only beer and sausages. His income is $100. Beer costs him $.50 per can and sausages cost $1 each. Where x is the number of cans of beer and y the number of sausages he consumes per week, Badger's utility function is U(x, y) = -[(x - 50)2 + (y - 40)2].
If his income increases, he won't change the commodity bundle that he buys.
Which of the following could possibly change a rational consumer's demand?
Increasing all prices and his income by $3
Jim's utility function is U(x, y) = xy. Jerry's utility function is U(x, y) = 1,000xy + 2,000. Tammy's utility function is U(x, y) = xy(1 - xy). Oral's utility function is - . Billy's utility function is . Pat's utility function is U(x, y) = -xy.
Jim, Jerry, and Pat all have the same indifference curves, but Jerry and Oral are the only ones with the same preferences as Jim
If she spends all of her income on breadfruits and melons, Natalie can just afford 9 breadfruits and 10 melons per day. She could also use her entire budget to buy 3 breadfruits and 12 melons per day. The price of breadfruits is 8 yen each. How much is Natalie's income per day?
None of the Above
In year 1, the price of good x was $3, the price of good y was $2, and income was $90. In year 2, the price of x was $9, the price of good y was $6, and income was $90. On a graph with x on the horizontal axis and y on the vertical, the new budget line is
None of the Above
Angela consumes only two goods, x and y. Her income doubles and the prices of the two goods remain unchanged. Assuming that she is a utility maximizer and likes both goods,
None of the above
I prefer 6 apples and 1 orange to 5 apples and 2 oranges. My preferences
None of the above.
If two goods are both desirable and preferences are convex, then
None of the above.
If two goods are perfect complements,
None of the above.
Waldo's utility function is U(x, y) = xy. Waldo consumes 5 units of x and 25 units of y.
None of the above.
Paul's utility function is min{x + 3y, 3x + y}. Simon's utility function is min{ 3x + 9y, 9x + 3y}. Paul and Simon have the same income and face the same prices.
Paul and Simon will demand the same amount of good x.
As you may know, Mungoites each have two left feet and one right foot. Their preferences for left and right shoes display perfect complementarity. Mungoites find shoes useful only in trios of two lefts and a right. The price of each type of shoe is $10 a shoe, and Mungoites consume nothing other than shoes. A Mungoite's Engel curve for right shoes has the equation
R=m/30
The prices of goods x and y are each $1. Jane has $20 to spend and is considering choosing 10 units of x and 10 units of y. Jane has nice convex preferences and more of each good is better for her. Where x is drawn on the horizontal axis and y is drawn on the vertical axis, the slope of her indifference curve at the bundle (10, 10) is -2.
She would be better off consuming more of good x and less of good y.
Steven's indifference curves are circles, all of which are centered at (15, 13). Of any two indifference circles, he would rather be on the inner one than the outer one.
Steven prefers (12, 10) to (22, 18).
The absolute value of Mar's MRS at his current consumption bundle is greater than 3. (That is, MU1/MU2 ). Mars has convex preferences and is currently consuming positive amounts of both goods.
Taking away some of good 1 and giving Mars 3 units of good 2 for each unit of good 1 taken away will necessarily make him worse off.
The relation "is preferred to" between commodity bundles is just one example of a binary relation. Another example is the relation "is a full brother of" defined over the set of all human beings. Let xRy mean person x is a full brother of person y.
The relation R is transitive but not complete or reflexive.
Ed and Al both consume only bread and cheese. Both of them always choose to have some bread and some cheese, and both have strictly convex preferences. However, Ed likes to have a great deal of bread with a little cheese, and Al likes lots of cheese with a little bread. Both face the same prices for both goods and have chosen bundles to maximize their utilities subject to their budgets.
Their marginal rates of substitution are the same.
Joe Bob's cousin Peter consumes goods 1 and 2. Peter thinks that 4 units of good 1 is always a perfect substitute for 2 units of good 2. Which of the following utility functions is the only one that would not represent Peter's preferences?
U(x1, x2) = min{ 2x1, 4x2}.
Joe Bob's cousin Leonard consumes goods 1 and 2. Leonard thinks that 2 units of good 1 is always a perfect substitute for 3 units of good 2. Which of the following utility functions is the only one that would not represent Leonard's preferences?
U(x1, x2) = min{ 3x1, 2x2}.
Janet consumes x1 and x2 together in fixed proportions. She always consumes 2 units of x1 for every unit x2. One utility function that describes her preferences is
U(x1, x2) = min{x1, 2x2}.
Mary Granola consumes apples and uglifruits. Mary's indifference curves are kinky. When she is consuming more apples than uglifruits, she is just willing to trade 3 apples for 1 uglifruit. When she is consuming more uglifruits than apples, she is just willing to trade 4 uglifruits for 1 apple. Let P1 be the price of uglifruits and P2 the price of apples. Mary maximizes her utility subject to her budget constraint. (Hint: Sketch one of her indifference curves.)
When P1 > 3P2, she must consume only apples.
Mary Granola consumes tomatoes and nectarines. Mary's indifference curves are kinky. When she is consuming more tomatoes than nectarines, she is just willing to trade 3 tomatoes for 1 nectarine. When she is consuming more nectarines than tomatoes, she is just willing to trade 4 nectarines for 1 tomato. Let P1 be the price of nectarines, and P2 the price of tomatoes. Mary maximizes her utility subject to her budget constraint. (Hint: Sketch one of her indifference curves.)
When P1 > 3P2, she must consume only tomatoes.
Joseph's utility function is given by UJ = xA + 2xB, where xA denotes his consumption of apples and xB his consumption of bananas. Clara's utility function is given by UC = 3xA + 2xB. Joseph and Clara shop at the same grocery store.
When we observe that Joseph leaves the store with some apples, then we can deduce that Clara also buys some apples.
Isobel consumes positive quantities of both jam and juice. The price of jam is 5 cents per unit and the price of juice is 10 cents per unit. Her marginal utility of jam is 10 and her marginal utility of juice is 5.
Without changing her total expenditures, she could increase her utility by consuming more jam and less juice.
Professor Stern's colleague, Dr. Schmertz, gives one midterm exam and a final exam. He weights the final twice as heavily as the midterm to determine the course grade. No grades can be dropped. If the midterm score is represented on the horizontal axis and the final score on the vertical axis, and if a student in Dr. Schmertz's class cares only about her course grade, her indifference curve is
a line with slope 20.5
Ads in a slick business magazine are read by 300 lawyers and 1,000 M.B.A.s. Ads in a consumer publication are read by 250 lawyers and 300 M.B.A.s. If Harry had $3,000 to spend on advertising, the price of ads in the business magazine were $500, and the price of ads in the consumer magazine were $250, then the combinations of M.B.A.s and lawyers whom he could reach with his advertising budget would be represented by the integer values along a line segment that runs between the two points
a. (3, 000, 3, 600) and (1, 800, 6, 000).
Ambrose has indifference curves with the equation x2 = constant - , where larger constants correspond to higher indifference curves. If good 1 is drawn on the horizontal axis and good 2 on the vertical axis, what is the slope of Ambrose's indifference curve when his consumption bundle is (9, 5)?
a. -0.67
Ike's utility function is U(x, y) = 25xy. He has 12 units of good x and 8 units of good y. Ben's utility function for the same two goods is U(x, y) = 4x + 4y. Ben has 9 units of x and 13 units of y.
a. Ike prefers Ben's bundle to his own bundle, but Ben prefers his own bundle to Ike's.
Young Alasdair loves lollipops and hates oatmeal. To induce him to eat enough oatmeal and to restrain him from eating too many lollipops, his mum pays him 10 pence for every quart of oatmeal that he eats. The only way that he can get lollipops is to buy them at the sweet shop, where lollipops cost 5 pence each. Besides what he earns from eating oatmeal, Alasdair gets an allowance of 10 pence per week. If Alasdair consumes only oatmeal and lollipops and if his consumption bundles are graphed with quarts of oatmeal on the horizontal axis and lollipops on the vertical axis, then Alasdair's budget line has a slope
a. of 2.
In year 1, the price of good x was $4, the price of good y was $1, and income was $70. In year 2, the price of x was $9, the price of good y was $2, and income was $70. On a graph with x on the horizontal axis and y on the vertical, the new budget line is.
a. steeper than the old one and lies below it.
Scholastica is taking a class from Professor Chaos. Professor Chaos gives two tests in this course and determines a student's grade as follows. He determines the smaller of the following two numbers: half of the score on the first test (which is a relatively easy test) and the total score on the second test. He gives each student a numerical score equal to the smaller number and then ranks the students. Scholastica would like to be ranked as high as possible in Professor Chaos's rankings. If we represent her score on the first exam on the horizontal axis and her score on the second exam on the vertical axis, then her indifference curves
are L-shaped with kinks where the exam 1 score is twice the exam 2 score.
In the economy of Mungo, discussed in your workbook, there is a third person called Ike. Ike has a red income of 94 rcus and a blue income of 25 bcus. (Recall that red prices are 2 rcus [red currency units] per unit of ambrosia and 6 rcus per unit of bubble gum. Blue prices are 1 bcu [blue currency unit] per unit of ambrosia and 1 bcu per unit of bubble gum. You have to pay twice for what you buy, once in red currency and once in blue currency.) If Ike spends all of his blue income but not all of his red income, then he consumes
at least 14 units of ambrosia.
In the economy of Mungo, discussed in your workbook, there is a third person called Ike. Ike has a red income of 92 rcus and a blue income of 20 bcus. (Recall that red prices are 2 rcus [red currency units] per unit of ambrosia and 6 rcus per unit of bubble gum. Blue prices are 1 bcu [blue currency unit] per unit of ambrosia and 1 bcu per unit of bubble gum. You have to pay twice for what you buy, once in red currency and once in blue currency.) If Ike spends all of his blue income but not all of his red income, then he consumes
at least 17 units of bubble gum.
Murphy used to consume 100 units of X and 50 units of Y when the price of X was $2 and the price of Y was $4. If the price of X rose to $4 and the price of Y rose to $9, how much would Murphy's income have to rise so that he could still afford his original bundle?
b. $450
Charlie has a utility function U(x, y) = (x + 3)(y + 4). The price of x is $1 and the price of y is $1. When he maximizes his utility subject to his budget constraint, he consumes positive amounts of both goods. Charlie consumes
b. 1 more unit of x than he consumes of y.
Eduardo spends his entire income on 9 sacks of acorns and 4 crates of butternuts. The price of acorns is 6 dollars per sack and his income is 90 dollars. He can just afford a commodity bundle with A sacks of acorns and B crates of butternuts that satisfies the budget equation.
b. 12A + 18B = 180.
Will spends his entire income on 8 sacks of acorns and 8 crates of butternuts. The price of acorns is 9 dollars per sack and his income is 88 dollars. He can just afford a commodity bundle with A sacks of acorns and B crates of butternuts that satisfies the budget equation
b. 18A + 4B = 176.
Tim consumes only apples and bananas. He prefers more apples to fewer, but he gets tired of bananas. If he consumes fewer than 29 bananas per week, he thinks that 1 banana is a perfect substitute for 1 apple. But you would have to pay him 1 apple for each banana beyond 29 that he consumes. The indifference curve that passes through the consumption bundle with 30 apples and 39 bananas also passes through the bundle with A apples and 21 bananas, where A equals
b. 28.
Hans has $27 which he decides to spend on x and y. Commodity x costs $16 per unit and commodity y costs $10 per unit. He has the utility function U(x, y) = 5x2 + 2y2 and he can purchase fractional units of x and y. Hans will choose
b. only y.
Recall that Tommy Twit's mother measures the departure of any bundle from her favorite bundle for Tommy by the sum of the absolute values of the differences. Her favorite bundle for Tommy is (2, 7), that is, 2 cookies and 7 glasses of milk. Tommy's mother's indifference curve that passes through the point (c, m) = (4, 5) also passes through
b. the points (2, 3), (6, 7), and (4, 9).
Thomas consumes coffee (C) and doughnuts (D). His budget line was described by the equation D = 20 - 2C. At a later time, his budget line could be described by the equation D = 10 - C. The change between the earlier budget line and the later could be explained by the fact that
b. the price of coffee increased and Thomas's income decreased.
Nancy Lerner is taking a course from Professor Goodheart who will count only her best midterm grade and from Professor Stern who will count only her worst midterm grade. In one of her classes, Nancy has scores of 20 on her first midterm and 70 on her second midterm. When the first midterm score is measured on the horizontal axis and her second midterm score on the vertical, her indifference curve has a slope of zero at the point (20, 70). Therefore this class could
be Professor Goodheart's but could not be Professor Stern's.
Nancy Lerner is taking a course from Professor Goodheart who will count only her best midterm grade and from Professor Stern who will count only her worst midterm grade. In one of her classes, Nancy has scores of 30 on her first midterm and 50 on her second midterm. When the first midterm score is measured on the horizontal axis and her second midterm score on the vertical, her indifference curve has a slope of zero at the point (30, 50). Therefore this class could
be Professor Goodheart's but could not be Professor Stern's.
If a consumer maximizes her preferences subject to her budget by choosing a consumption bundle where the ratio of her marginal utilities of shelter and food, , is greater than the ratio of the prices of shelter and food, , then she must
be consuming shelter but no food
Murphy used to consume 100 units of X and 50 units of Y when the price of X was $2 and the price of Y was $4. If the price of X rose to $3 and the price of Y rose to $8, how much would Murphy's income have to rise so that he could still afford his original bundle?
c. $300
Ambrose has indifference curves with the equation x2 = constant - , where larger constants correspond to higher indifference curves. If good 1 is drawn on the horizontal axis and good 2 on the vertical axis, what is the slope of Ambrose's indifference curve when his consumption bundle is (16, 17)?
c. -0.50
If you spent your entire income, you could afford either 3 units of x and 9 units of y or 9 units of x and 3 units of y. If you spent your entire income on x, how many units of x could you buy
c. 12
If she spends her entire budget, Heidi can afford 39 peaches and 12 pears. She can also just afford 24 peaches and 17 pears. The price of peaches is 9 cents. What is the price of pears in cents?
c. 27 cents
Molly's utility function is U(x, y) = y + 4x.5. She has 25 units of x and 12 units of y. If her consumption of x is reduced to 0, how many units of y would she need in order to be exactly as well off as before?
c. 32
Edmund must pay $6 each for punk rock video cassettes, V. If Edmund is paid $24 per sack for accepting garbage, G, and if his relatives send him an allowance of $48, then his budget line is described by the equation
c. 6V - 24G = 48.
While traveling abroad, Tammy spent all of the money in her purse to buy 5 plates of spaghetti and 6 oysters. Spaghetti costs 8 units of the local currency per plate and she had 82 units of currency in her purse. If s denotes the number of plates of spaghetti and o denotes the number of oysters purchased, the set of commodity bundles that she could just afford with the money in her purse is described by the equation.
c. 8s + 7o = 82.
Harry thrives on two goods, paperback novels and bananas. The cost of paperback novels is 4 dollars each and the cost of bananas is 3 dollars per bunch. If Harry spent all of his income on bananas, he could afford 12 bunches of bananas per week. How many paperback novels could he buy if he spent all of his income on paperback novels
c. 9
Bella's budget line for x and y depends on all of the following except
c. her preferences between x and y.
George has $49 which he decides to spend on x and y. Commodity x costs $5 per unit and commodity y costs $11 per unit. He has the utility function U(x, y) = 3x2 + 6y2 and he can purchase fractional units of x and y. George will choose
c. only x.
The Chuzzlewits have an income of $m per week. Let x be food and let y be all other goods. Let px be the price of c. food and py be the price of other goods. They can use food stamps to buy food at a price of px(1 - s) for up to x* units of food per week. If they buy more food than x*, they have to pay the full price px for additional units. Their weekly income is greater than px(1 - s)x*. The maximum amount of food that they can buy per week is
c.(m/px)+sx*
Tim has preferences represented by the utility function U(x, y) = min{ 6x + y, x + 2y}. If x is on the horizontal axis and y is on the vertical axis, what is the slope of his indifference curve at the point (8, 9)?
c.-1/2
Harry Mazzola has the utility function U(x1, x2) = min{x1 + 2x2, 2x1 + x2}. He has $40 to spend on corn chips and french fries. If the price of corn chips is $3 per unit and the price of french fries is $4, then Harry will
consume equal amounts of french fries and corn chips.
Elmer's utility function is U(x, y) = min{x, y2}. If the price of x is $25 and the price of y is $15 and if Elmer chooses to consume 7 units of y, what must his income be?
d. $1,330
Leo consumes only apples and bananas. He prefers more apples to fewer, but he gets tired of bananas. If he consumes fewer than 24 bananas per week, he thinks that 1 banana is a perfect substitute for 1 apple. But you would have to pay him 1 apple for each banana beyond 24 that he consumes. The indifference curve that passes through the consumption bundle with 31 apples and 36 bananas also passes through the bundle with A apples and 18 bananas, where A equals
d. 25.
If you could exactly afford either 5 units of x and 21 units of y, or 9 units of x and 5 units of y, then if you spent all of your income on y, how many units of y could you buy?
d. 41
Lars consumes only potatoes and herring. When the price of potatoes was 9 crowns per sack and the price of herring was 5 crowns per crock, he spent his entire income to buy 5 sacks of potatoes and 10 crocks of herring per month. Now the government subsidizes potatoes. Market prices haven't changed, but consumers get a subsidy of 5 crowns for every sack of potatoes consumed. To pay for this subsidy, the government introduced an income tax. Lars pays an income tax of 20 crowns per month. If s is the number of sacks of potatoes and c is the number of crocks of herring, what is Lars's new budget equation?
d. 4s + 5c = 75.
Edmund must pay $6 each for punk rock video cassettes, V. If Edmund is paid $24 per sack for accepting garbage, G, and if his relatives send him an allowance of $96, then his budget line is described by the equation
d. 6V - 24G = 96.
If she spends her entire budget, Betsy can afford 74 peaches and 9 pineapples. She can also just afford 14 peaches and 21 pineapples. The price of peaches is 17 cents. What is the price of pineapples in cents?
d. 85 cents
Your budget constraint for the two goods A and B is 12A + 4B = I, where I is your income. You are currently consuming more than 27 units of B. In order to get 3 more units of A, how many units of B would you have to give up?
d. 9
Nick's indifference curves are circles, all of which are centered at (12, 12). Of any two indifference circles, he would rather be on the inner one than the outer one.
d. Nick prefers (8, 8) to (17, 21).
Suppose that the price of good x triples and the price of good y doubles while income remains constant. On a graph where the budget line is drawn with x on the horizontal axis and y on the vertical axis, the new budget line
d. is steeper than the old one and lies below it.
Harry Mazzola has the utility function U(x1, x2) = min{x1 + 2x2, 2x1 + x2}. He has $40 to spend on corn chips and french fries. If the price of corn chips is $1 per unit and the price of french fries is $4, then Harry will
definitely spend all of his income on corn chips.
Ike's utility function is U(x, y) = xy. Ike consumes 2 units of x and 8 units of y.
e. None of the above.
Suppose that the prices of good x and good y both double and income triples. On a graph where the budget line is drawn with x on the horizontal axis and y on the vertical axis,
e. None of the above.
Raymond's preferences are represented by the utility function U(x, y) = if y > 0 and U(x, y) = 0 if y = 0.
e. Raymond has indifference curves that are upward-sloping straight lines if y > 0.
Charlie's indifference curves have the equation , where larger constants denote better indifference curves. Charlie strictly prefers the bundle (6, 16) to
e. none of these bundles.
Justin consumes goods x and y and has a utility function U(x, y) = x2 + y. The price per unit of x is px and the price per unit of y is py. He has enough money so that he can afford at least 1 unit of either good. When he chooses his best affordable bundle,
he must consume only y if exceeds his income.
Phil Rupp's sister Ethel has the utility function U(x, y) = min{ 4x + y, 5y}. Where x is measured on the horizontal axis and y on the vertical axis, her indifference curves consist of a
horizontal line segment and a negatively sloped line segment which meet in a kink along the line x = y.
Phil Rupp's sister Ethel has the utility function U(x, y) = min{ 5x + y, 6y}. Where x is measured on the horizontal axis and y on the vertical axis, her indifference curves consist of a
horizontal line segment and a negatively sloped line segment which meet in a kink along the line x = y.
If his wage rate increases, then a utility maximizing consumer will necessarily
increase (or leave constant) his labor supply if leisure is an inferior good but otherwise might reduce his labor supply.
Emily's utility function is U(x, y) = 3min{x, y} + y. If we draw her indifference curves with x on the horizontal axis and y on the vertical axis, these indifference curves are
made up of two line segments that meet where x = y. One of these line segments is horizontal and the other has slope -3.
Isabella's utility function is U(x, y) = 4min{x, y} + y. If we draw her indifference curves with x on the horizontal axis and y on the vertical axis, these indifference curves are
made up of two line segments that meet where x = y. One of these line segments is horizontal and the other has slope -4.
Oswald Odd consumes only goods 1 and 2. His utility function is U(x1, x2) = x1 + x2 + min{x1, x2}. Each of Oswald's indifference curves is
made up of two line segments with slopes -2 and - 1/2
Preferences are said to be monotonic if
more is always preferred to less.
Harold's utility function is U(x, y) = (x + 3)(y + 2). The price of x is $1. The price of y is $2. At all incomes for which Harold consumes positive amounts of both goods, he will consume
more than twice as many units of x as of y.
Lorenzo lives on x and y alone. His utility function is U(x, y) = min{ 3x + 4y, 7y}. The prices of both goods are positive. He will
never buy more x than y.
Charlie's indifference curves have the equation where larger constants denote better indifference curves. Charlie strictly prefers the bundle (10, 17) to
none of these bundles.
If there are only two goods, if more of good 1 is always preferred to less, and if less of good 2 is always preferred to more, then indifference curves
slope upward.
In Professor Meanscore's class, the first midterm exam and the second midterm exam are weighted equally toward the final grade. With the first midterm's score on the horizontal axis, and the second midterm's score on the vertical axis, indifference curves between the two exam scores are
straight lines with slope 21
Recall that Tommy Twit's mother measures the departure of any bundle from her favorite bundle for Tommy by the sum of the absolute values of the differences. Her favorite bundle for Tommy is (2, 7), that is, 2 cookies and 7 glasses of milk. Tommy's mother's indifference curve that passes through the point (c, m) = (5, 4) also passes through
the points (2, 1), (8, 7), and (5, 10).
Suppose there are two goods, the prices of both goods are positive, and a consumer's income is also positive. If the consumer's income doubles and the price of both goods triple,
the slope of the consumer's budget line does not change but the budget line shifts inward toward the origin.
Professor Goodheart's colleague Dr. Kremepuff gives 3 midterm exams. He drops the lowest score and gives each student her average score on the other two exams. Polly Sigh is taking his course and has a 60 on her first exam. Let x2 be her score on the second exam and x3 be her score on the third exam. If we draw her indifference curves for scores on the second and third exams with x2 represented by the horizontal axis and x3 represented by the vertical axis, then her indifference curve through the point (x2, x3) = (50, 70) is
three line segments, one vertical, one horizontal, and one running from (70, 60) to (60, 70).
If you have an income of $40 to spend, commodity 1 costs $4 per unit, and commodity 2 costs $8 per unit, then the equation for your budget line can be written
x1+2x2=10
If you have an income of $40 to spend, commodity 1 costs $2 per unit, and commodity 2 costs $10 per unit, then the equation for your budget line can be written
x1+5x2=20
Deadly Serious, II, studying for his M.B.A., consumes only two goods, Wheaties and pens. Each pen costs $1. Each box of Wheaties costs $2 but has a free pen inside. Pens can be discarded at no cost. If we draw Serious's budget set with pens plotted on the horizontal axis, then his budget set will be bounded by two line segments with slopes
zero and -1
