3. (11 points) Violet's utility function is given as U (x, y) price of good y is q, and Violet has m dollars in her pocket. A. Find Violet's ordinary demand for each good. B. Find the inverse demand function for good x. C. Find the equation for the Engel curve for good x. D. Is the Engel curve for good x a straight line? Why or why not? E. Is good x a normal or inferior good? Why? F. Is good y a normal or inferior good? Why? G. Are good x and y complements, substitutes, or have no relation with each other? Why? H. Suppose that p = 8, q = 5, and m = 140. What is the maximum level of utility that Violet can achieve? How many units of each good will maximize Violet's utility? 1. What is the maximum level of utility that Violet can achieve? = = x² + 2xy. Suppose that the price of good x is p, the J. Draw the budget line, the indifference curve with the maximum utility level that Violet can achieve, and mark the point where these two "touch" each other (i.e., the point of tangency between the budget line and the indifference curve). Label the x and y coordinates for this point. [Hint: To see how the indifference curve might look like, set the equation for the utility function equal to the maximum utility level that you found in part (H). Then use an online math tool to see what the function might look like in a graph. Wolfram Alpha does an excellent job in this, but you can use other tools of your choice. Keep in mind that Wolfram Alpha plots the whole function, with both positive and negative values for x and y. However, in this case, both x and y should be greater or equal to zero (because they are quantity of goods), so only the part of the graph inside the first quadrant is relevant; you can ignore the rest of the graph.]
3. (11 points) Violet's utility function is given as U (x, y) price of good y is q, and Violet has m dollars in her pocket. A. Find Violet's ordinary demand for each good. B. Find the inverse demand function for good x. C. Find the equation for the Engel curve for good x. D. Is the Engel curve for good x a straight line? Why or why not? E. Is good x a normal or inferior good? Why? F. Is good y a normal or inferior good? Why? G. Are good x and y complements, substitutes, or have no relation with each other? Why? H. Suppose that p = 8, q = 5, and m = 140. What is the maximum level of utility that Violet can achieve? How many units of each good will maximize Violet's utility? 1. What is the maximum level of utility that Violet can achieve? = = x² + 2xy. Suppose that the price of good x is p, the J. Draw the budget line, the indifference curve with the maximum utility level that Violet can achieve, and mark the point where these two "touch" each other (i.e., the point of tangency between the budget line and the indifference curve). Label the x and y coordinates for this point. [Hint: To see how the indifference curve might look like, set the equation for the utility function equal to the maximum utility level that you found in part (H). Then use an online math tool to see what the function might look like in a graph. Wolfram Alpha does an excellent job in this, but you can use other tools of your choice. Keep in mind that Wolfram Alpha plots the whole function, with both positive and negative values for x and y. However, in this case, both x and y should be greater or equal to zero (because they are quantity of goods), so only the part of the graph inside the first quadrant is relevant; you can ignore the rest of the graph.]
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
![3. (11 points) Violet's utility function is given as U (x, y)
price of good y is q, and Violet has m dollars in her pocket.
A. Find Violet's ordinary demand for each good.
B. Find the inverse demand function for good x.
C. Find the equation for the Engel curve for good x.
D. Is the Engel curve for good x a straight line? Why or why not?
E. Is good x a normal or inferior good? Why?
F. Is good y a normal or inferior good? Why?
G. Are good x and y complements, substitutes, or have no relation with each other? Why?
H. Suppose that p = 8, q = 5, and m
=
140. What is the maximum level of utility that Violet can achieve? How
many units of each good will maximize Violet's utility?
1. What is the maximum level of utility that Violet can achieve?
=
= x² + 2xy. Suppose that the price of good x is p, the
J. Draw the budget line, the indifference curve with the maximum utility level that Violet can achieve, and mark
the point where these two "touch" each other (i.e., the point of tangency between the budget line and the
indifference curve). Label the x and y coordinates for this point. [Hint: To see how the indifference curve might
look like, set the equation for the utility function equal to the maximum utility level that you found in part (H).
Then use an online math tool to see what the function might look like in a graph. Wolfram Alpha does an
excellent job in this, but you can use other tools of your choice. Keep in mind that Wolfram Alpha plots the
whole function, with both positive and negative values for x and y. However, in this case, both x and y should
be greater or equal to zero (because they are quantity of goods), so only the part of the graph inside the first
quadrant is relevant; you can ignore the rest of the graph.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc4e3d5c7-de25-4f60-a4d1-89725a885bce%2F17cb321c-26a2-41ab-aba8-fa6fc7c6e14e%2Ffv47abs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. (11 points) Violet's utility function is given as U (x, y)
price of good y is q, and Violet has m dollars in her pocket.
A. Find Violet's ordinary demand for each good.
B. Find the inverse demand function for good x.
C. Find the equation for the Engel curve for good x.
D. Is the Engel curve for good x a straight line? Why or why not?
E. Is good x a normal or inferior good? Why?
F. Is good y a normal or inferior good? Why?
G. Are good x and y complements, substitutes, or have no relation with each other? Why?
H. Suppose that p = 8, q = 5, and m
=
140. What is the maximum level of utility that Violet can achieve? How
many units of each good will maximize Violet's utility?
1. What is the maximum level of utility that Violet can achieve?
=
= x² + 2xy. Suppose that the price of good x is p, the
J. Draw the budget line, the indifference curve with the maximum utility level that Violet can achieve, and mark
the point where these two "touch" each other (i.e., the point of tangency between the budget line and the
indifference curve). Label the x and y coordinates for this point. [Hint: To see how the indifference curve might
look like, set the equation for the utility function equal to the maximum utility level that you found in part (H).
Then use an online math tool to see what the function might look like in a graph. Wolfram Alpha does an
excellent job in this, but you can use other tools of your choice. Keep in mind that Wolfram Alpha plots the
whole function, with both positive and negative values for x and y. However, in this case, both x and y should
be greater or equal to zero (because they are quantity of goods), so only the part of the graph inside the first
quadrant is relevant; you can ignore the rest of the graph.]
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