Question 1

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.

Accepted Answer

Fred's Cobb-Douglas utility function implies that his preferences exhibit diminishing marginal rates of substitution between the two goods, leading to a convex indifference curve. Sally's perfect substitutes utility function implies a linear indifference curve, resulting in different price offer curves for the two individuals.

Question 2

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)16 2/3 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.

Accepted Answer

Harry will use his 20 coupons to buy Coke for $.40 a can, spending $8 (20 cans * $.40/can = $8). With the remaining $2 ($10 - $8), he can buy 4 cans of Pepsi at $.50 a can ($2 / $.50/can = 4 cans). None of the options provided match this outcome.

Question 3

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.

Accepted Answer

To maximize utility subject to budget constraint, we need to use the Lagrange method:

L(x, y, λ) = U(x, y) + λ(I - Px x -Py y)

where I is the income, Px is the price of grapefruits, Py is the price of pineapples and λ is the Lagrange multiplier.

∂L/∂x = 0 ⇒ 10x-6λ = 0
∂L/∂y = 0 ⇒ 4y-9λ = 0
∂L/∂λ = 0 ⇒ Px x + Py y - I = 0

Solving these equations simultaneously, we get:

x=21, y=14, λ=$10.50

Therefore, Georgina will consume 21 grapefruits.

Question 4

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.

Accepted Answer

The answer of If there are two goods and if...

Question 5

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^1/2 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.

Accepted Answer

Daisy has one tape recorder, so f(y) = 24. Her utility function is U(x, y, z) = x + z^1/2 * 24. The price of tapes is $4, so she can buy z tapes with x/4 dollars. Her goal is to maximize her utility function, which is equivalent to maximizing U(x, y, z) = x + 6z^1/2. Since she can afford to buy dozens of tapes, she will buy as many tapes as possible until her marginal utility from buying another tape is zero. The marginal utility from buying another tape is dU/dz = 6z^-1/2. Setting this equal to zero and solving for z, we get z = 36. Therefore, she will buy 36 tapes.

Question 6

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.

Accepted Answer

Since Walt consumes strawberries and cream in the fixed ratio of three boxes of strawberries to two cartons of cream, he will demand 12 boxes of strawberries and 8 cartons of cream (which is equivalent to the fixed ratio). This will cost him $120 for strawberries and $80 for cream, which adds up to $200 and uses up his entire income. Therefore, choice D is the best option.

Question 7

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.

Accepted Answer

The answer of Seppo consumes brandy and saunas.Neither is an...

Question 8

Darlene's utility function is U(x, y, z)= x ⁴y ⁸z.If her income doubles and prices remain unchanged, her demand for good y will more than double.

Accepted Answer

Darlene's utility function does not provide enough information to determine how her demand for good y will change if her income doubles. Demand changes depend on the specific form of the utility function and the properties of the goods (e.g., whether they are normal goods, inferior goods, etc.), which are not specified in the provided utility function expression.

Question 9

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.

Accepted Answer

The answer of Clarissa's utility function is U(r, z)= z...

Question 10

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

Accepted Answer

Quasilinear preferences are not necessarily homothetic because homothetic preferences imply that the shape of indifference curves is consistent across all levels of income, whereas quasilinear preferences allow for the optimal amount of one good to be constant regardless of income levels, not affecting the affordability of goods.

Question 11

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.

Accepted Answer

Given Natalie's utility function and her budget constraint, we can solve for the optimal consumption of apples and tomatoes by setting up the Lagrangian for utility maximization subject to her budget constraint. The budget constraint is $4x + $3y = $320. Without the specific utility function provided, we typically use the method of Lagrange multipliers to find the optimal bundle of goods that maximizes utility given the budget constraint. Assuming the utility function has the usual properties and given the prices and income, we can solve for x and y. The correct answer, B) 16, suggests that after solving the optimization problem, Natalie will consume 16 apples to maximize her utility given her budget constraint and the prices of apples and tomatoes.

Question 12

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.

Accepted Answer

The answer of Regardless of his income and regardless of...

Question 13

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.

Accepted Answer

The answer of Mike consumes two commodities, x and y,...

Question 14

Where x is the quantity of good X demanded, the inverse demand function for X A)expresses 1/x as a function of prices and income. B)expresses the demand for x as a function of 1/p_x and income, where p_x is the price of x. C)expresses the demand for x as a function of 1/p_x and 1/m, where m is income. D)specifies 1/x as a function of 1/p_x and 1/m, where m is income. E)None of the above.

Accepted Answer

The inverse demand function for a good expresses the price of the good as a function of the quantity demanded, not the other way around. None of the options correctly describe an inverse demand function.

Question 15

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.

Accepted Answer

The answer of Mickey is considering buying a tape recorder.His...

Question 16

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.

Accepted Answer

Since Madonna's utility function is Cobb-Douglas, her demand is homothetic, meaning that her demand for each good depends only on her income and the price of that good itself. Therefore, her demand for each of the two goods depends only on her income and on the price of that good itself.

Question 17

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^1/2 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.

Accepted Answer

To maximize utility, Daisy should use all of her money. Therefore, we can set x = 0 in the utility function. The only variable left to determine is z (the number of tapes she buys). We can rewrite the utility function as: 
U(y, z) = 10z + U1(y) 
where U1(y) = f(y)/2 if y < 1 and U1(y) = 4 + f(y)/2 if y >= 1. 
To maximize U(y,z), we can take the derivative with respect to z: 
dU(y, z)/dz = 10 
This derivative is positive, which means that U(y, z) is increasing in z. Therefore, Daisy should buy as many tapes as possible. Since she can easily afford to buy dozens of tapes, we should calculate how many dozens of tapes she can buy without exceeding her budget. 
Her budget is $10 (because she can spend all of her money on tapes). Therefore, she can buy up to 10 tapes. This is less than one dozen, so the answer is 10.

Question 18

For m > p₂, the demand functions for goods 1 and 2 are given by the equations, x₁ = m/p₂ - 1 and x₂ = p₁/p₂, 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 1/2. E)None of the above.

Accepted Answer

When m is greater than the product of the two prices, both goods are normal goods and the income offer curve will be a horizontal line. The quantity demanded of good 2 is a function of both prices, so holding one price constant on the horizontal axis will not result in a straight line. Therefore, the answer is B.

Question 19

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.

Accepted Answer

Darlene's utility function does not specify how her demand for good y changes with income, but typically, without specific information on the type of good y is (normal, inferior, luxury), we cannot conclude that her demand for good y will more than double just because her income doubles. Demand changes depend on the income elasticity of demand for the good, which cannot be determined from the given utility function alone.

Question 20

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.

Accepted Answer

Since Clarissa's utility function remains unchanged, we know that she values one rose plant the same as before (i.e., 160) and values one zinnia the same as before (i.e., 10). In order to maximize her utility, she needs to use all the available land she has for roses and zinnias.

With 250 square feet, she can at most plant 62 roses (250/4) or 250 zinnias. By comparing the marginal utility (i.e., the change in utility from adding one more plant) of the two plants, we find that she values one more zinnia (i.e., 10) slightly more than one more rose (i.e., 160/4 = 40). This implies that she should use up all the 250 square feet to plant zinnias, which would result in a total of 250 zinnias.

With an additional 100 square feet, she can plant up to 25 more roses (100/4) or 100 more zinnias. However, in order to maximize her utility, she needs to compare the marginal utility of the two plants at this point, which is now 160/5 = 32 for a rose plant and 10 for a zinnia plant. This implies that she should plant more zinnias and fewer roses.

The maximum number of zinnias she can plant with the additional 100 square feet is 100, but this would result in a total of 350 zinnias, which may not be the optimal level. If she were to plant even more zinnias, the marginal utility of zinnias would start to diminish (i.e., the additional zinnias would provide less and less additional utility), and at some point, the marginal utility of roses would become higher.

Therefore, the optimal choice is to plant some additional roses and some additional zinnias, but within the constraint of having only 100 more square feet. The exact number of each plant can be determined by comparing their marginal utilities, but since the given choices do not provide this information, we can use the option of planting "max(1, min(99, z))" zinnias, which means she will plant as many zinnias as possible while staying within the limit of 100 square feet, and the remaining area will be used for roses. This would result in a total of "max(1, min(99, 100/4))" = 25 roses and "max(1, min(99, 100))" = 100 zinnias, which is closest to option C.

Quiz 5: Demand-Part A

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.

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?

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

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.

Darlene's utility function is U(x, y, z)= x ⁴y ⁸z.If her income doubles and prices remain unchanged, her demand for good y will more than double.

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

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?

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?

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?

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

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

For m > p₂, the demand functions for goods 1 and 2 are given by the equations, x₁ = m/p₂ - 1 and x₂ = p₁/p₂, 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

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.

Quiz 5: Demand-Part A

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.

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?

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

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.

Darlene's utility function is U(x, y, z)= x 4y 8z.If her income doubles and prices remain unchanged, her demand for good y will more than double.

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

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?

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?

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?

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

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

For m > p2, the demand functions for goods 1 and 2 are given by the equations, x1 = m/p2 - 1 and x2 = p1/p2, 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

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.

Darlene's utility function is U(x, y, z)= x ⁴y ⁸z.If her income doubles and prices remain unchanged, her demand for good y will more than double.

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?

For m > p₂, the demand functions for goods 1 and 2 are given by the equations, x₁ = m/p₂ - 1 and x₂ = p₁/p₂, 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

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.