ECON 323 HW #2 TAMU
Consider the utility function given by U(x,y)=min{x,y}. Someone who has this utility function is indifferent between consuming 4 units of x and 2 units of y and which of the following?
2 units of x 2 units of y
Suppose a cup of coffee at the campus coffee shop is $2.50 and a cup of hot tea is $1.25. Suppose a student's beverage budget is $20 per week. What is the algebraic expression of his/her budget constraint (denote cups of coffee by C and cups of tea by T)?
2.5C + 1.25T=20
Consider the utility function U(x,y)=2x+3y. The marginal rate of substitution of good x for good y (at some pair (x,y)) is given by:
2/3
Charlie consumes apples and bananas. Charlie's utility function is U(A,B)=A*B where A is the number of apples and B is the number of bananas. Charlie has 40 apples and 5 bananas. Which of the following bundles would Charlie prefer to his?
20 apples, 10 bananas
Ronald consumes apples and bananas. The value that Ronald's utility assigns to a bundle of one apple and one banana is U(1,1)=-100. Is it necessarily true that Ronald prefers zero apples and zero bananas, i.e., (0,0) to (1,1)?
False
Natalia and her sister, Gina, have the following utility functions on the number of slices of pizza (x) and cans of soda (y) they consume in the semester. Natalia's is U(x,y)=3x+2y and Gina's is V(x,y)=4x+2y. If we plot their indifference curves with x measured in the horizontal axis and y measured in the vertical axis, we find that:
Gina's indifference curves are steeper than Natalia's.
A marketing firm is interested in learning about the dynamics of viral video dissemination on the web. In order to do this they show three videos to students at a university and ask them to fill a survey related to the videos. The videos are the epic splits of van Dame (a), the baby (b), and Chuck Norris (c). The survey contains six questions as follows. For each pair of videos, say a and b, they ask the students "is a at least as good as b." In order to make this operational, they provide the students with a picture in which the three videos are depicted as circles with their description next to it. The students are asked to draw arrows between the videos whenever the answer to a question is affirmative. That is, if a student finds video a is at least as good as video b, the student is asked to draw an arrow from the circle with label a to the circle with label b. (No question of the type, "is a at least as good as a" was asked; assume that the answer to each of these trivial questions is affirmative.) In what follows we write a->b when the student draw an arrow from a to b, and so on. The following are the answers to the survey of five different students. Which student has complete preferences?
a-> b, b->c, c->a.
Alexandra is maximizing her utility over goods x and y subject to her budget constraint. Her preferences are smooth (maximizers are always interior). At her optimal consumption bundle, her MRS of goof y for good x is equal to 1. The price of good x is $4. What is the price of good y?
$4
Natalia and her sister, Gina, have the following utility functions on the number of slices of pizza (x) and cans of soda (y) they consume in the semester. Natalia's is U(x,y)=3x+2y and Gina's is V(x,y)=4x+2y. Then, among the bundles that are indifferent to (2,0) for Natalia, the only bundle that gives Gina a utility of 7 is?
(1, 3/2)
Elena consumes bundles of food and transportation. In order to understand her behavior we use a graph of her consumption space in which we draw two axes. We measure food in the horizontal axis and transportation in the vertical axis. Which of the following bundles has the largest amount of food (if the bundles are written consistently with the way we graph consumption)?
(100,80)
Chuck's utility function on the number of cookies he eats, denoted by c, and the number of glasses of milk he drinks, denoted by m, is given by: U(c,m)=min{2c,3m}. What is the point that is most to the south-west in Chuck's indifference curve that passes through (2,8)?
(2,4/3)
Jane's utility function on bundles of two commotities (x,y) is given by: U(x,y)=4x2y3. What is the value of MRSxy(x,y) when x=2 and y=1?
1/3
Jane's utility function on bundles of two commotities (x,y) is given by: U(x,y)=4x2y3. What is the expression for MUy(x,y)?
12x2y2
Consider the utility function U(x,y)=2x+3y. The marginal utility of good x is given by:
2
Jane consumes bundles of apples and pears. In order to understand her behavior we use a graph of her consumption space in which we draw two axes. We measure apples in the horizontal axis and pears in the vertical axis. We write (x,y) to represent a bundle of x apples and y pears. Consider the following list of consumption bundles: (1,2); (1,3); (2,6); (1/2,1/3); and (3,7). Which of these bundles is located the most to the north east in our graph?
(3/7)
Otis consumes two goods: x and y. If the price of x is $2 and the price of y is $5, then the marginal rate of transformation of y into x is:
-2/5
Linda consumes two goods: x and y, has preferences that are smooth and maximizers are always interior, and income W=$150. If px=$25 and py=$5, what is the marginal rate of transformation of y into x (MRTxy) at her optimal bundle?
-5
Linda has an income of $100, which she spends completely on two goods: x and y. The price of x is $20 and the price of y is $12. Which of the following is the slope of her budget constraint (in a graph where x is measured in the horizontal axis and y in the vertical axis)?
-5/3
Consider the utility function U(x,y)=4x+2y. Someone who has this utility function is indifferent between consuming 4 units of x and 0 units of y and which of the following?
0 units of x and 8 units of y
Charlie consumes apples and bananas. Charlie's utility function is U(A,B)=A*B where A is the number of applies and B is the number of bananas. Which of the following bundles would lie on the same indifference curve as the bundle 40 apples and 5 bananas?
20 apples, 11 bananas
Juno has preferences that are represented by the utility function U(x,y)=x1/2y1/2 (this preference is smooth, which implies that maximizers are interior). If Juno has income W=$1000 and px=$50 and py=$25, what is Juno's consumption of good x (assuming Juno maximizes her utility given her budget constraint?)
20 units
Juno has preferences that are represented by the utility function U(x,y)=x1/2y1/2 (this preference is smooth, which implies that maximizers are interior). If Juno has income W=$1000 and px=$50 and py=$25, what is Juno's consumption of good y (assuming Juno maximizes her utility given her budget constraint?)
20 units
What is the horizontal (x) intercept for the following budget constraint: 2x+3y=25?
25/2
Jane's utility function on bundles of two commotities (x,y) is given by: U(x,y)=4x2y3. What is the expression for MRSxy(x,y)?
2Y/3X
Suppose the price of good x is $10, the price of good y is $15, and Katrina's income is $30. What is the equation of Katrina's budget constraint?
2x + 3y = 6
Consider the utility function U(x,y)=4x+2y. An agent who has this utility function prefers which of the following baskets:
3 units of x and 1 unit of y
Suppose that initially the price of good x is $10, the price of good y is $15, and Ellie's income is $30. Budget cuts at work reduce Ellie's income to $25. What is the new vertical (y) intercept of Ellie's budget constraint?
5/3
Jane's utility function on bundles of two commotities (x,y) is given by: U(x,y)=4x2y3. What is the value of MUx(x,y) when x=1 and y=2?
64
Jane's utility function on bundles of two commotities (x,y) is given by: U(x,y)=4x2y3. What is the expression for MUx(x,y)?
8xy3
A preference is complete if:
Between any two alternatives a and b, at least one of the following holds: a is at least as good as b, or b is at least as good as a.
Victor is the manager of a local bank branch in College Station where he consumes bundles of two commodities x and y. Prices in College Station are px=1 and py=5. He is offered a transfer to Dallas where prices are px=2 and py=8; Victor is guaranteed a salary in Dallas with which he would be able to buy exactly what he buys in College Station. Victor's utility function is U(x,y)=xy and his income in College Station is $5000. What happens to Victor's utility if he accepts the change (Victor's utility maximization is always characterized by the tangency rule)?
Increases 1.25%
Jane is the manager of a local bank branch in College Station where he consumes bundles of two commodities x and y. Prices in College Station are px=1 and py=5. He is offered a transfer to Dallas where prices are px=4 and py=5; Jane is guaranteed a salary in Dallas with which he would be able to buy exactly what he buys in College Station. Jane's utility function is U(x,y)=xy2 and his income in College Station is $6000. What happens to Janes's utility if she accepts the transfer (Jane's utility maximization is always characterized by the tangency rule)?
Increases 100%
A decreasing MRS of x for y means:
It is more and more difficult to substitute x for y as the consumption of x is higher
Jon has complete and transitive preferences on bundles of sodas and pizza. Jon finds one soda and two slices of pizza at least as good as two sodas and a slice of pizza. Moreover, two sodas and a slice of pizza is not at least as good as one soda and two slices of pizza. Then, we know that:
Jon prefers one soda and two slices of pizza to two sodas and one slice of pizza.
Phillip's utility function is given by U(x,y)=min{x,2y}. Then his indifference curves are:
L Shaped Curve
Natalia and her sister, Gina, have the following utility functions on the number of slices of pizza (x) and cans of soda (y) they consume in the semester. Natalia's is U(x,y)=3x+2y and Gina's is V(x,y)=4x+2y. If we plot their indifference curves with x measured in the horizontal axis and y measured in the vertical axis, we find that:
Natalia's indifference curves are steeper than Gina's.
Leon has complete and transitive preferences on greek sweets. He finds a piece of Bougatsa is at least as good as a portion of Melomakarona, and he prefers a portion of Melomakarona to a piece of Halva. Can the utility of a piece of Halva be greater than the utility of a piece of Bougatsa?
No
Jane has complete and transitive preferences. Then:
She can rank any pair of alternatives
A marketing firm is interested in eliciting Silvia's tastes on a set of ten automobiles. In order to do this they ask Silvia, for each pair of alternatives (x,y), whether she finds x at least as good as y. Silvia is interested in both the reliability of the car and its safety record. She answers that an alternative x is at least as good as y if and only if x is at least as reliable as y and x has at least the safety ranking as y. Then,
Silvia's answers may violate completeness.
A marketing firm is interested in eliciting Silvia's tastes on a set of ten automobiles. In order to do this they ask Silvia, for each pair of alternatives (x,y), whether she finds x at least as good as y. Silvia is interested in both the reliability of the car and its safety record. She looks at the ratings of both reliability and safety and constructs a combined index by taking the average of the ratings. She answers that an alternative x is at least as good as y if and only if the average index of x is greater than or equal than the average index of y.
Silvia's answers necessarily satisfy completeness.
A marketing firm is interested in eliciting Silvia's tastes on a set of ten automobiles. In order to do this they ask Silvia, for each pair of alternatives (x,y), whether she finds x at least as good as y. Silvia is interested in both the reliability of the car and its safety record. She answers that an alternative x is at least as good as y if and only if x is at least as reliable as y and x has at least the safety ranking as y. Then,
Silvia's answers will always violate completeness
Linda's utility function is given by U(x,y)=2x+y. Then Linda's indifference curves are:
Straight Downward sloping
Suppose that initially the prices of x and y are the same. If the price of good x doubles and the price of good y triples, while income is held constant, the budget line (x is measured in the horizontal axis and y in the vertical axis):
Suppose that initially the prices of x and y are the same. If the price of good x doubles and the price of good y triples, while income is held constant, the budget line (x is measured in the horizontal axis and y in the vertical axis):
The following figure shows the budget constraint and one indifference curve of an agent whose preferences satisfy more is better. It is a two axis graph in which the horizontal axis measures x and the vertical axis measures y. The budget constraint is a line of negative slope. It passes through the points (1,7/3) and (8/3,1). The indifference curve, in red, is a downward sloping curve that touches the budget constraint at (1,7/3) and (8/3,1). No other point in this indifference curve is on or to the south west of the budget constraint. Then,
The agent maximizes utility, given her budget, at both (1,7/3) and (8/3,1).
The following figure shows the consumption space of an agent who consumes two goods, x and y. Good x is measured in the horizontal axis and good y in the vertical axis. The figure shows two budget constraints. These are two straight lines with negative slope. They have different slope. They cross at a single point, labeled B. This point is in the interior of the consumption space. The y intercept of the budget constraint that is flatter, is labeled A and the x intercept of the other budget constraint is labeled C. Suppose that the agent consumes bundle B when her budget constraint is the budget line that passes through B and C. Suppose also that this agents' preferences satisfy more is better. Then,
The agent will never consume a bundle to the left of B when her budget constraint is the line that passes through A and B.
A marketing firm is interested in learning about millennials' preferences on learning experiences. In order to do this they survey students at a university. They ask them six questions as follows. They consider the following leaning experiences: a traditional class, a flipped course (half of the content is delivered online), and an online class. For each pair of these alternatives, say a and b, they ask the students "is a at least as good as b." In order to make this operational, they provide the students with a picture in which the three alternatives are depicted as circles with their description next to it. The students are asked to draw arrows between the alternatives whenever the answer to a question is affirmative. That is, if a student finds alternative a is at least as good as alternative b, the student is asked to draw an arrow from the circle with label a to the circle with label b. (No question is a at least as good as a was asked; assume that the answer to each of these trivial questions is affirmative.) Suppose that a student's answers are as follows: one arrow from the traditional class to the online class, one arrow from the traditional class to the flipped course, one arrow from the online class to the flipped course, and no more arrows.
The student's statements satisfy completeness and transitivity.
Jane prefers a to b, b to c, and c to a. Based on this information, what properties are violated by Jane's preferences (only one answer is correct)?
Transitivity
Michael eats hamburgers and smores. If Michael eats two hamburgers and one smore, he would give up half hamburger in order to eat one smore more (his welfare remaining constant). When he eats smores, he wants more and more. Indeed, he would give up one hamburger more for eating his third smore (his welfare remaining constant). Because of this, we can say that Michael's MRS of smores for hamburgers is not decreasing.
True
Suppose a utility function assigns 3 to bundle a, 2 to bundle b, and 1 to bundle c. Which of the following utility functions represent the same preferences?
U(a)=-1, U(b)=-2, U(c)=-3
Roman loves corn bread. He buys corn meal and wheat flour in order to make corn bread. His recipe calls for two cups of corn meal and one cup of flour for each batch that he bakes. More corn bread is better for Roman. He can bake fractions of a batch, but has no use for corn meal or flour that is left over. What of the following is Roman's utility function on cups of corn meal, denoted by c, and cups of flour, denoted by f?
U(c,f)=min{c,2f}
James consumes slices of pizza, denoted by x, and sodas, denoted by y. The prices are px=4 and py=2, respectively. Jame's income for the semester is $100. Consider the consumption bundle in which Jame buys 20 slices of pizza and 10 sodas. Is this bundle to the north-west of some bundle in Jame's budget constraint when we graph x in the horizontal axis?
Yes
The manager of the local branch of a bank in College Station is offered a transfer to Austin. This person is guaranteed a salary that is able to buy the goods and services that he/she was consuming in College Station. Assume that the welfare of this agent depends only on her consumption, and that the goods in College Station and Austin are comparable. Then, the manager:
can be better off with the transfer but cannot be worse off.
Jane consumes bundles of apples and pears. In order to understand her behavior we use a graph of her consumption space in which we draw a two axes. We measure apples in the horizontal axis and pears in the vertical axis. We write (x,y) to represent a bundle of x apples and y pears. What of the following bundles is to the north-east of (2,4) in our graph? (Read the choices carefully)
five pears and three apples
If the prices of both goods increase by 50% while income remains constant:
the slope of the budget constraint will stay the same.
