Deck 5: Demand

Question 1

When other variables are held fixed, the demand for a Giffen good rises when income increases.

Answer 1

False

Question 2

If consumers spend all of their income, it is impossible for all goods to be inferior goods.

Answer 2

True

Question 3

Donald's utility function is . Currently he is buying some of both goods. If his income rises and prices don't change, he will buy more of both goods.

Answer 3

False

Question 4

A consumer has a utility function given by U = min{x₁, 2x₂}. If good 2 has a price of zero, the consumer will always prefer more of good 2 to less.

Question 5

A good is a luxury good if the income elasticity of demand for it is greater than 1.

Question 6

A rational consumer spends her entire income. If her income doubles and prices do not change, then she will necessarily choose to consume twice as much of every good as she did before.

Question 7

A consumer has the utility function U(x, y) = min{x, 2y}. If the price of good x is zero and the price of good y is p, then the consumer's demand function for good y is .

Question 8

If the demand curve is a downward-sloping straight line, then the price elasticity of demand is constant all along the demand curve.

Question 9

Angela's utility function is . It is possible that if her income is very high, an increase in income will not make her spend more on y.

Question 10

If the price elasticity of demand for a good is -1, then doubling the price of that good will leave total expenditures on that good unchanged.

Question 11

If preferences are quasilinear, then for very high incomes the income offer curve is a straight line parallel to one of the axes.

Question 12

If preferences are homothetic, then the slope of the Engel curve for any good will decrease as income increases.

Question 13

Prudence was maximizing her utility subject to her budget constraint. Then prices changed. After the price change she was better off. Therefore the new bundle costs more at the old prices than the old bundle did.

Question 14

An inferior good is less durable than a normal good.

Question 15

If preferences are homothetic and all prices double while income remains constant, then demand for all goods is halved.

Question 16

In economic theory, the demand for a good must depend only on income and its own price and not on the prices of other goods.

Question 17

An Engel curve is a demand curve with the vertical and horizontal axes reversed.

Question 18

It is impossible for a person to have a demand curve that slopes upward at all prices.

Question 19

If income is doubled and all prices are doubled, then the demand for luxury goods will more than double.

Question 20

If two goods are substitutes, then an increase in the price of one of them will increase the demand for the other.

Question 21

Georgina consumes only grapefruits and pineapples. Her utility function is U(x, y) = x²y⁸, where x is the number of grapefruits consumed and y is the number of pineapples consumed. Georgina's income is $105, and the prices of grapefruits and pineapples are $1 and $3, respectively. How many grapefruits will she consume?

A) 10.5
B) 7
C) 63
D) 21
E) None of the above.

Question 22

Darlene's utility function is U(x, y, z) = x³y⁷z. If her income doubles and prices remain unchanged, her demand for good y will more than double.

Question 23

Natalie consumes only apples and tomatoes. Her utility function is U(x, y) = x²y⁸, where x is the number of apples consumed and y is the number of tomatoes consumed. Natalie's income is $320, and the prices of apples and tomatoes are $4 and $3, respectively. How many apples will she consume?

A) 21.33
B) 16
C) 8
D) 48
E) None of the above.

Question 24

For m > p₂, the demand functions for goods 1 and 2 are given by the equations, - 1 and , where m is income and p₁ and p₂ are prices. Let the horizontal axis represent the quantity of good 1. Let p₁ = 1 and p₂ = 2. Then for m > 2, the income offer curve is

A) a vertical line.
B) a horizontal line.
C) a straight line with slope 2.
D) a straight line with a slope of.
E) None of the above.

Question 25

Quasilinear preferences are homothetic when the optimal amount of one of the goods is not affordable.

Question 26

Mickey is considering buying a tape recorder. His utility function is U(x, y, z) = x + f(y)z^.5, where x is the amount of money he spends on other goods, y is the number of tape recorders he buys, and z is the number of tapes he buys. Let f(y) = 0 if y < 1 and f(y) = 8 if y is greater than or equal to 1. The price of tape recorders is $20, the price of tapes is $1, and Mickey can easily afford to buy a tape recorder and several tapes. Will he buy a tape recorder?

A) He should buy a tape recorder at these prices, but if tapes were any more expensive, it would not pay to buy one.
B) He should not buy a tape recorder.
C) He is indifferent to buying a tape recorder or not.
D) Even if the price of tapes doubled, he should still buy a tape recorder.
E) There is not enough information here for us to be able to tell.

Question 27

Clarissa's utility function is U(r, z) = z + 160r - r², where r is the number of rose plants she has in her garden and z is the number of zinnias. She has 250 square feet to allocate to roses and zinnias. Roses each take up 4 square feet and zinnias each take up 1 square foot. She gets the plants for free from a generous friend. If she acquires another 100 square feet of land for her garden and her utility function remains unchanged, she will plant

A) 100 more zinnias and no more roses.
B) 25 more roses and no more zinnias.
C) max(1, min(99, zdem + 100)) more zinnias and some more roses.
D) 20 more roses and 20 more zinnias.
E) None of the above.

Question 28

Where x is the quantity of good X demanded, the inverse demand function for X

A) expressesas a function of prices and income.
B) expresses the demand for x as a function ofand income, where p_x is the price of x.
C) expresses the demand for x as a function ofand, where m is income.
D) specifiesas a function ofand, where m is income.
E) None of the above.

Question 29

Daisy received a tape recorder as a birthday gift and is not able to return it. Her utility function is U(x, y, z) = x + z f(y), where z is the number of tapes she buys, y is the number of tape recorders she has, and x is the amount of money she has left to spend. f(y) = 0 if y < 1 and f(y) = 24 if y is 1 or greater. The price of tapes is $4 and she can easily afford to buy dozens of tapes. How many tapes will she buy?

A) 9
B) 11
C) 7
D) 13
E) We need to know the price of tape recorders to solve this problem.

Question 30

Mike consumes two commodities, x and y, and his utility function is min{x + 2y, y + 2x}. He chooses to buy 8 units of good x and 16 units of good y. The price of good y is $.50. What is his income?

A) $32
B) $40
C) $24
D) $16
E) Mike's income cannot be found unless the price of x is given too.

Question 31

Daisy received a tape recorder as a birthday gift and is not able to return it. Her utility function is U(x, y, z) = x + z f(y), where z is the number of tapes she buys, y is the number of tape recorders she has, and x is the amount of money she has left to spend. f(y) = 0 if y < 1 and f(y) = 8 if y is 1 or greater. The price of tapes is $1 and she can easily afford to buy dozens of tapes. How many tapes will she buy?

A) 18
B) 14
C) 16
D) 20
E) We need to know the price of tape recorders to solve this problem.

Question 32

Clarissa's utility function is U(r, z) = z + 120r - r², where r is the number of rose plants she has in her garden and z is the number of zinnias. She has 250 square feet to allocate to roses and zinnias. Roses each take up 4 square feet and zinnias each take up 1 square foot. She gets the plants for free from a generous friend. If she acquires another 100 square feet of land for her garden and her utility function remains unchanged, she will plant

A) 99 more zinnias and some more roses.
B) 20 more roses and 20 more zinnias.
C) 25 more roses and no more zinnias.
D) 100 more zinnias and no more roses.
E) None of the above.

Question 33

If there are two goods and if income doubles and the price of good 1 doubles while the price of good 2 stays constant, a consumer's demand for good

A) 1 will increase only if it is a Giffen good for her.
B) 2 will decrease only if it is a Giffen good for her.
C) 2 will increase only if it is an inferior good for her.
D) 2 will decrease only if it is an inferior good for her.
E) None of the above.

Question 34

Madonna buys only two goods. Her utility function is Cobb-Douglas. Her demand functions have which of the following properties?

A) Her demand for one of the two goods does not depend on income.
B) Her demand for neither good depends on income.
C) Her demand for each of the goods depends on income and on the prices of both goods.
D) Her demand for each of the two goods depends only on her income and on the price of that good itself.
E) One of the goods is an inferior good and the other is a normal good.

Question 35

Regardless of his income and regardless of prices, Smedley always spends 25% of his income on housing, 10% on clothing, 30% on food, 15% on transportation, and 20% on recreation. This behavior is consistent with which of the following?

A) All goods are perfect substitutes.
B) Smedley's demands for commodities do not change when their prices change.
C) Smedley consumes all goods in fixed proportions.
D) Smedley has a Cobb-Douglas utility function.
E) More than one of the above.

Question 36

Walt consumes strawberries and cream but only in the fixed ratio of three boxes of strawberries to two cartons of cream. At any other ratio, the excess goods are totally useless to him. The cost of a box of strawberries is $10 and the cost of a carton of cream is $10. Walt's income is $200.

A) Walt demands 10 cartons of cream.
B) Walt demands 10 boxes of strawberries.
C) Walt considers strawberries and cartons of cream to be perfect substitutes.
D) Walt demands 12 boxes of strawberries.
E) None of the above.

Question 37

Fred has a Cobb-Douglas utility function with exponents that sum to 1. Sally consumes the same two goods, but the two goods are perfect substitutes for her. Despite these differences, Fred and Sally have the same price offer curves.

Question 38

Harry has $10 to spend on cans of Coke and Pepsi, which he regards as perfect substitutes, one for one. Pepsi costs $.50 a can and Coke costs $.60 a can. Harry has 20 coupons, each of which can be used to buy 1 can of Coke for $.40. Which of the following bundles will Harry buy?

A) 20 cans of Pepsi and no Coke
B) cans of Coke and no Pepsi
C) 10 cans of Coke and 8 cans of Pepsi
D) 10 cans of Coke and 12 cans of Pepsi
E) None of the above.

Question 39

Darlene's utility function is U(x, y, z) = x⁴y⁸z. If her income doubles and prices remain unchanged, her demand for good y will more than double.

Question 40

Seppo consumes brandy and saunas. Neither is an inferior good. Seppo has a total of $30 a day and 6 hours a day to spend on brandy and saunas. Each brandy costs $2 and takes half an hour to consume. Each sauna costs $1 and takes 1 hour to consume. (It is, unfortunately, impossible to consume a brandy in the sauna.) Seppo suddenly inherits a lot of money and now has $50 a day to spend on brandy and saunas. Since Seppo is a rational consumer, he will

A) increase brandy consumption only.
B) increase sauna consumption only.
C) increase consumption of both.
D) consume the same amounts of both goods as before.
E) We can't tell since we are told nothing about his indifference curves.

Question 41

Mary has homothetic preferences. When her income was $1,000, she bought 40 books and 60 newspapers. When her income increased to $1,500 and prices did not change, she bought

A) 60 books and 90 newspapers.
B) 80 books and 120 newspapers.
C) 60 books and 60 newspapers.
D) 40 books and 120 newspapers.
E) There is not enough information for us to determine what she would buy.

Question 42

Wilma Q. has a utility function U(x₁, x₂) = x²₁ + 1.5x₁x₂ + 30x₂. The prices are p₁ = $1 and p₂ = $1. For incomes between $20 and $60, the Engel curve for good 2 is

A) upward sloping.
B) downward sloping.
C) vertical.
D) upward sloping for incomes between $20 and $40 and downward sloping between $40 and $60.
E) downward sloping for incomes between $20 and $40 and upward sloping between $40 and $60.

Question 43

Fred consumes pork chops and lamb chops and nothing else. When the price of pork chops rises with no change in his income or in the price of lamb chops, Fred buys fewer lamb chops and fewer pork chops.

A) Pork chops are a normal good for Fred.
B) Lamb chops are a normal good for Fred.
C) Pork chops are an inferior good for Fred.
D) Lamb chops are an inferior good for Fred.
E) Fred prefers pork chops to lamb chops.

Question 44

Alfredo lives on apples and bananas only. His utility function is U(a, b) = min{a + b, 2b}. He maximizes his utility subject to his budget constraint and consumes the bundle (a, b) = (4, 4).

A) p_a > p_b.
B) p_a is less than or equal to p_b.
C) p_a = p_b.
D) p_a = 2p_b.
E) None of the above.

Question 45

Miss Muffet insists on consuming 2 units of whey per 1 unit of curds. If the price of curds is $5 and the price of whey is $6, then if Miss Muffet's income is m, her demand for curds will be

Question 46

Ambrose's brother Bartholomew has a utility function , where x₁ is his consumption of nuts and x₂ is his consumption of berries. His income is $115, the price of nuts is $5, and the price of berries is $1. How many units of berries will Bartholomew demand?

A) 35
B) 16
C) 70
D) 22
E) There is not enough information to determine the answer.

Question 47

Will Feckless unexpectedly inherits $10,000 from a rich uncle. He is observed to consume fewer hamburgers than he used to.

A) Hamburgers are a Giffen good for Will.
B) Hamburgers are a normal good for Will.
C) Will's Engel curve for hamburgers is vertical.
D) Will's Engel curve for hamburgers is horizontal.
E) Will's preferences are not homothetic.

Question 48

If Charlie's utility function is X⁵_AX_B, the price of apples is p_A, the price of bananas is p_B, and his income is m, then Charlie's demand for apples will be

Question 49

Ms. Laura Mussel's preferences between golf and tennis are represented by U(g, t) = gt, where g is the number of rounds of golf and t is the number of tennis matches she plays per week. She has $24 per week to spend on these sports. A round of golf and a tennis match each cost $4. She used to maximize her utility subject to this budget. She decided to limit the time she spends on these sports to 16 hours a week. A round of golf takes 4 hours. A tennis match takes 2 hours. As a result of this additional constraint on her choice,

A) she plays 1 less round of golf and 1 more tennis match each week.
B) she plays more golf and less tennis, but can't say how much.
C) her choices and her utility are unchanged.
D) she plays 2 less rounds of golf and 3 more rounds of tennis per week.
E) There is too little information to tell about her choices.

Question 50

Ambrose's brother Sebastian has a utility function , where x₁ is his consumption of nuts and x₂ is his consumption of berries. His income is $128, the price of nuts is $2, and the price of berries is $1. How many units of berries will Sebastian demand?

A) 30
B) 60
C) 55
D) 49
E) There is not enough information to determine the answer.

Question 51

If Charlie's utility function were X⁴_AX_B and if apples cost 30 cents each and bananas cost 10 cents each, Charlie's budget line would be tangent to one of his indifference curves whenever

A) 4X_B = 3X_A.
B) X_B = X_A.
C) X_A = 4X_B.
D) X_B = 4X_A.
E) 30X_A + 10X_B = M.

Question 52

Katie Kwasi's utility function is U(x₁, x₂) = 5(ln x₁) + x₂. Given her current income and the current relative prices, she consumes 10 units of x₁ and 15 units of x₂. If her income doubles, while prices stay constant, how many units of x₁ will she consume after the change in income?

A) 10
B) 15
C) 5
D) 20
E) There is not enough information to determine how many.

Question 53

Robert's utility function is U(x, y) = min{ 4x, 2x + y}. The price of x is $3 and the price of y is $1. Robert's income offer curve is

A) a ray from the origin with a slope of 2.
B) a line parallel to the x axis.
C) a line parallel to the y axis.
D) the same as his Engel curve for x.
E) none of the above.

Question 54

If Charlie's utility function were X⁶_AX_B and if apples cost 40 cents each and bananas cost 10 cents each, Charlie's budget line would be tangent to one of his indifference curves whenever

A) 6X_B = 4X_A.
B) X_A = 6X_B.
C) X_B = X_A.
D) X_B = 6X_A.
E) 40X_A + 10X_B = M.

Question 55

Cecil consumes x₁ and x₂ in fixed proportions. He consumes A units of good 1 with B units of good 2. To solve for his demand functions for goods 1 and 2,

A) setand solve for x₁.
B) solve the following two equations in two unknowns: Ax₁ = Bx₂ and p₁x₁ + p₂x₂ = m.
C) solve the following two equations in two unknowns: Bx₁ = Ax₂ and p₁x₁ + p₂x₂ = m.
D) you only need to use the equation given by his budget line.
E) use the fact that he spends all of his income on good 1 so long as it is the cheaper good.

Question 56

Ambrose's brother Patrick has a utility function U(x₁, x₂) = 16x ₁ + x₂. His income is $82, the price of good 1 (nuts) is $2, and the price of good 2 (berries) is $1. How many units of nuts will Patrick demand?

A) 26
B) 12
C) 14
D) 16
E) 30

Question 57

Ambrose's brother Sebastian has a utility function . His income is $165, the price of good 1 (nuts) is $6, and the price of good 2 (berries) is $1. How many units of nuts will Sebastian demand?

A) 25
B) 23
C) 35
D) 21
E) 48

Question 58

Which of the following utility functions represent preferences of a consumer who does not have homothetic preferences?

A) U(x, y) = xy.
B) U(x, y) = x + 2y.
C) U(x, y) = x + y^.5.
D) U(x, y) = min{x, y}.
E) More than one of the above.

Question 59

Miss Muffet insists on consuming 2 units of whey per 1 unit of curds. If the price of curds is $5 and the price of whey is $3, then if Miss Muffet's income is m, her demand for curds will be

Question 60

Katie Kwasi's utility function is U(x₁, x₂) = 2(ln x₁) + x₂. Given her current income and the current relative prices, she consumes 10 units of x₁ and 15 units of x₂. If her income doubles, while prices stay constant, how many units of x₁ will she consume after the change in income?

A) 20
B) 18
C) 10
D) 5
E) There is not enough information to determine how many.

Question 61

With some services,
a. Write down the budget equation that you would have after you paid the entry fee for each of the two plans.
b. If your utility function is xy, how much y would you choose in each case?
c. Which plan would you prefer? Explain.
e.g., checking accounts, phone service, or pay TV, a consumer is offered a choice of two or more payment plans. One can either pay a high entry fee and get a low price per unit of service or pay a low entry fee and a high price per unit of service. Suppose you have an income of $100. There are two plans. Plan A has an entry fee of $20 with a price of $2 per unit. Plan B has an entry fee of $40 with a price of $1 per unit for using the service. Let x be expenditure on other goods and y be consumption of the service.

Question 62

Marie's utility function is U(x, y) = min{ 3x + 2y, 2x + 5y}, where x is the number of units of sugar she consumes and y is the number of units of spice she consumes. She is currently consuming 12 units of sugar and 40 units of spice and she is spending all of her income.
a. Draw a graph showing her indifference curve through this point.
b. The price of spice is $1. In order for this to be her consumption bundle, what must the price of sugar be and what must her income be?

Question 63

Miss Muffet insists on consuming 2 units of whey per 1 unit of curds. If the price of curds is $3 and the price of whey is $3, then if Miss Muffett's income is m, her demand for curds will be

Question 64

Murphy's utility function is U(x, y) = min{ 4x + y, 2x + 2y, x + 4y}. Murphy is consuming 12 units of x and 6 units of y.
a. Draw the indifference curve through this point. At what points does this indifference curve have kinks?
b. The price of good x is $1. What is the highest possible price for y? What is the lowest possible price for y?

Question 65

Briefly explain in a sentence or two how you could tell
a. whether a good is a normal good or an inferior good.
b. whether a good is a luxury or a necessity.
c. whether two goods are complements or substitutes.

Question 66

Let w be the number of whips and j the number of leather jackets. If Kinko's utility function is U(x, y) = min{ 7w, 4w + 12j}, then if the price of whips is $20 and the price of leather jackets is $40, Kinko will demand

A) 4 times as many whips as leather jackets.
B) 6 times as many whips as leather jackets.
C) 3 times as many whips as leather jackets.
D) 5 times as many leather jackets as whips.
E) only leather jackets.

Question 67

Define each of the following:
a. Inverse demand function
b. Engel curve

Question 68

Martha has the utility function U = min{ 4x, 2y}. Write down her demand function for x as a function of the variables m, p_x, and p_y, where m is income, p_x is the price of x, and p_y is the price of y.

Question 69

Is the following statement true or false? "If consumers spend their entire incomes, it is impossible for the income elasticity of demand for every good to be bigger than 1." Write a brief but convincing explanation of your answer.

Question 70

Carlos consumes only two goods, apples and bananas. His utility function is U(a, b) = min{a, b}. Before trade, his initial endowment is w_a apples and w_b bananas. After he trades to his optimal consumption point at these prices, the relative prices change. Carlos is allowed to make further trades if he wishes.

A) Carlos will definitely be better off after the price change.
B) Carlos will be better off if the price of the good he was selling goes up and worse off if the price of the good he was selling goes down.
C) Unless the price of both goods goes down, we cannot tell if Carlos is better off or worse off.
D) Carlos will be better off if the price of the good he was selling goes down and worse off if the price of the good he was selling goes up.
E) Carlos's utility will not be affected by the change.

Question 71

Wanda Lott's utility function is U(x, y) = max{ 2x, y}. Draw some of Wanda's indifference curves. If the price of x is 1, the price of y is p, and her income is m, how much of y does Wanda demand?

Question 72

Miss Muffet insists on consuming 2 units of whey per 1 unit of curds. If the price of curds is $3 and the price of whey is $3, then if Miss Muffett's income is m, her demand for curds will be

Question 73

John Parker Nosey works for the Internal Revenue Service. He is in charge of auditing income of self-employed people. In any year, people divide their total income between consumption and saving. John cannot determine people's consumptions, but he is able to determine how much people have saved over the course of a year. From years of experience, he has learned that people act as if they are maximizing a utility function of the form U(c, s) = 10,000ln(c) + s, where c is the number of dollars worth of consumption in a year and s is the number of dollars saved.

A) If someone saves at least $1,000, then that person's income is at least $11,000.
B) If someone saves nothing, then that person must earn less than $1,000.
C) If someone saves exactly $1,000, then that person's income must be greater than $1,000 and less than $10,000.
D) If someone saves exactly $10,000, then that person must earn exactly $21,000.
E) If someone saves more than $1,000, then that person's income must be more than $20,000.

Question 74

Between 1990 and 2000, a particular consumer's income increased by 25%, while the price of X and of "all other goods" both increased by 10%. It was observed that the consumer's consumption of X and of all other goods both increased by 15%.

A) The consumer did not regard X and "all other goods" as perfect complements.
B) The consumer's preferences cannot be represented by a Cobb-Douglas utility function.
C) The consumer's preferences can be represented by a Cobb-Douglas utility function.
D) The consumer's preferences cannot be represented by a quasilinear utility function.
E) More than one of the above options is true.

Question 75

Carlos consumes only two goods, apples and bananas. His utility function is U(a, b) = a³b². Before he trades, his initial endowment is w_a apples and w_b bananas. After he trades to his optimal consumption point at these prices, the relative prices change. Carlos is allowed to make further trades if he wishes.

A) Carlos will definitely be better off after the price change.
B) Carlos will be better off if the price of the good he was selling goes up and worse off if the price of the good he was selling goes down.
C) Unless the prices of both goods goes down, we cannot tell if Carlos is better off or worse off.
D) Carlos will be better off if the price of the good he was selling goes down and worse off if the price of the good he was selling goes up.
E) Carlos's utility will not be affected by the change.

Question 76

Casper's utility function is 3x + y, where x is his consumption of cocoa and y is his consumption of cheese. If the total cost of x units of cocoa is x², the price of cheese is $8, and Casper's income is $174, how many units of cocoa will he consume?

A) 9
B) 11
C) 12
D) 23
E) 24

Question 77

Casper's utility function is 3x + y, where x is his consumption of cocoa and y is his consumption of cheese. If the total cost of x units of cocoa is x², the price of cheese is $10, and Casper's income is $260, how many units of cocoa will he consume?

A) 12
B) 15
C) 29
D) 14
E) 30

Question 78

Let w be the number of whips and j the number of leather jackets. If Kinko's utility function is U(x, y) = min{ 7w, 4w + 12j}, then if the price of whips is $20 and the price of leather jackets is $40, Kinko will demand

A) 6 times as many whips as leather jackets.
B) 5 times as many leather jackets as whips.
C) 3 times as many whips as leather jackets.
D) 4 times as many whips as leather jackets.
E) only leather jackets.

Question 79

Ray Starr has the utility function .
a. Does Ray prefer more to less of both goods?
b. Draw a diagram showing Ray's indifference curves corresponding to the utility levels U = , U = 1, and U = 2.
c. How can you describe the set of indifference curves for Ray?
d. If the price of x is $1 and the price of y is $1, find Ray's demand for x as a function of his income and draw a diagram showing his Engel curve for x.