Let basket A be (x, y) = (4, 3). For each of the following utility functions...
Let basket A be (x, y) = (4, 3). For each of the following utility functions (a-d), answer the following questions (iiv):
i) Determine the utility at basket A
ii) Write out the equation for the indifference curve that basket A lies on. (simplify to y equals some function of x)
iii) Find 3 other points that lie on the same indifference curve as A.
iv) Calculate the MRSx,y at basket A and give an economic interpretation of what the means in words.
(a) U (x, y) = 9xy.
(b) U (x, y) = 2x2 + 5y2 .
(c) U (x, y) = 6x1/2 + y.
(d) U (x, y) = 8x + 7y.
Homework Answers
I have answered each parts except (iii) for functions (a-d)
The image below shows it.
Sorry i forgot to add (ii) for (d)
equation for indifference curve is ,
8x + 7y = 53
7y = 53 - 8x
y = (53-8x) / 7
Hope this helps
please comment for doubts
thanks
Add Answer to:
Let basket A be (x, y) = (4, 3). For each of the following
utility functions...
For each of the following utility functions: Calculate MUx, MUy, MRSx,y; determine whether or not the...
For each of the following utility functions: Calculate MUx, MUy, MRSx,y; determine whether or not the property of “more is better” is satisfied for both goods; determine whether or not the marginal utility of x diminishes, remains constant, or increases as the consumer buys more x; determine whether or not the marginal rate of substitution diminishes, remains constant, or increases as the consumer substitutes x for y along an indifference curve; and sketch the graph of a typical indifference curve....
Question 1 For the following utility functions (3 pts each for a, b, and c): •...
Question 1 For the following utility functions (3 pts each for a, b, and c): • Find the marginal utility of each good at the point (5, 5) and at the point (5, 15) • Determine whether the marginal utility decreases as consumption of each good increases (i.e., does the utility function exhibit diminishing marginal utility in each good?) • Find the marginal rate of substitution at the point (5, 5) and at the point (5, 15) • Discuss how...
7. Show that the following functions u(x, y) monic functions v(x, y) and determine f(z) = u(x,y) + iv(x, y) are harmoni...
7. Show that the following functions u(x, y) monic functions v(x, y) and determine f(z) = u(x,y) + iv(x, y) are harmonic, find their conjugate har- as functions of 2. 2x2 2лу — 5х — 22. Зл? — 8ху — Зу? + 2у, (а) и(х, у) (b) и(х, у) (с) и(х, у) (d) u(a, y) 2e cos y 3e" sin y, = 3e-* cos y + 5e-" sin y, = elx cos y - e y sin y, (e) u(x,...
1. Consider the following utility functions (a) For each of these utility functions: i. Find the...
1. Consider the following utility functions (a) For each of these utility functions: i. Find the marginal utility of each good. Are the preferences mono- tone? ii. Find the marginal rate of substitution (MRS) iii. Define an indifference curve. Show that each indifference curve (for some positive level of utility) is decreasing and convex. (b) For the utility function u2(x1, x2), can you find another utility function that represents the same preferences? Find the relevant monotone trans formation f(u) (c)...
For each of the following utility functions (a-d), answer the following questions (i-iv) i) Calculate MUz...
For each of the following utility functions (a-d), answer the following questions (i-iv) i) Calculate MUz and MUy ii) Do the consumer 's preferences exhibit a diminishing marginal utility for each good? iii) Calculate MRSa,y iv) Do the consumer's preferences exhibit a diminishing marginal rate of substitution of x? (al U (x,y) = 3x2/5y3/5 (b) (x,y)= 2x2/3+y (c) (x,y)= 12x3/2y1/2 3
Compute the MRS for the following utility functions. Based on your results, explain the curvature of...
Compute the MRS for the following utility functions. Based on your results, explain the curvature of indifference curve associated with each function. i. (5 marks) U(X,Y) = aln(X) + bln(Y) ii. (5 marks) U(X,Y) = XaYb iii. (5 marks) U(X,Y) = aX + bY
2. Show that each of the following utility functions has a diminishing MRS. Do they exhibit...
2. Show that each of the following utility functions has a diminishing MRS. Do they exhibit constant, increasing, or decreasing marginal utility? Is the shape of the marginal utility function an indicator of the convexity of indifference curve? a. (2) U(X,Y) = XY b. (2) U(X,Y) = x2y2 c. (2) U(X,Y) = In X + In Y
3. Suppose the utility function for two goods, x and y, is: U = U(x,y) =...
3. Suppose the utility function for two goods, x and y, is: U = U(x,y) = xłyż. a. Graph the indifference curve for U = 10. b. If x = 5, what must y equal to be on the U = 10 indifference curve? What is the MRS at this point? c. Derive a general expression for the MRS for this utility function. Show how it can be interpreted as the ratio of the marginal utilities. d. Does this individual...
4. Consider the utility function U(x, y) = x + ln y. (a) Find the marginal...
4. Consider the utility function U(x, y) = x + ln y. (a) Find the marginal rate of substitution, MRS of this function. Interpret the result (b) Find the equation of the indifference curve for this function (c) Compare the marginal utility of x and y. How do you interpret these functions? How might a consumer choose between x and y as she tries to increase utility by, for example, consuming more when their income increases?
For each of these utility functions, b. Compute the MRS. c. Do these tastes have...
For each of these utility functions,
b. Compute the MRS.
c. Do these tastes have diminishing marginal rates of
substitution? Are they convex?
d. Construct an indifference curve for each of these functions
for utility numbers U1 = 10 , U2 = 100 , U3 = 200 .
e. Do these utility functions represent different preference
orderings?
1. Consider the following utility functions: (i) U(x,y)- 6xy, (ii) U(x,y)=(1/5)xy, MU,--y and MU,--x ii) U(x,y)-(2xy)M 8xy2 and MUy -8x2y MU,-6y and...
7. Show that the following functions u(x, y) monic functions v(x, y) and determine f(z) = u(x,y) + iv(x, y) are harmonic, find their conjugate har- as functions of 2. 2x2 2лу — 5х — 22. Зл? — 8ху — Зу? + 2у, (а) и(х, у) (b) и(х, у) (с) и(х, у) (d) u(a, y) 2e cos y 3e" sin y, = 3e-* cos y + 5e-" sin y, = elx cos y - e y sin y, (e) u(x,...
1. Consider the following utility functions (a) For each of these utility functions: i. Find the marginal utility of each good. Are the preferences mono- tone? ii. Find the marginal rate of substitution (MRS) iii. Define an indifference curve. Show that each indifference curve (for some positive level of utility) is decreasing and convex. (b) For the utility function u2(x1, x2), can you find another utility function that represents the same preferences? Find the relevant monotone trans formation f(u) (c)...
For each of the following utility functions (a-d), answer the following questions (i-iv) i) Calculate MUz and MUy ii) Do the consumer 's preferences exhibit a diminishing marginal utility for each good? iii) Calculate MRSa,y iv) Do the consumer's preferences exhibit a diminishing marginal rate of substitution of x? (al U (x,y) = 3x2/5y3/5 (b) (x,y)= 2x2/3+y (c) (x,y)= 12x3/2y1/2 3
2. Show that each of the following utility functions has a diminishing MRS. Do they exhibit constant, increasing, or decreasing marginal utility? Is the shape of the marginal utility function an indicator of the convexity of indifference curve? a. (2) U(X,Y) = XY b. (2) U(X,Y) = x2y2 c. (2) U(X,Y) = In X + In Y
3. Suppose the utility function for two goods, x and y, is: U = U(x,y) = xłyż. a. Graph the indifference curve for U = 10. b. If x = 5, what must y equal to be on the U = 10 indifference curve? What is the MRS at this point? c. Derive a general expression for the MRS for this utility function. Show how it can be interpreted as the ratio of the marginal utilities. d. Does this individual...
4. Consider the utility function U(x, y) = x + ln y. (a) Find the marginal rate of substitution, MRS of this function. Interpret the result (b) Find the equation of the indifference curve for this function (c) Compare the marginal utility of x and y. How do you interpret these functions? How might a consumer choose between x and y as she tries to increase utility by, for example, consuming more when their income increases?
For each of these utility functions,
b. Compute the MRS.
c. Do these tastes have diminishing marginal rates of
substitution? Are they convex?
d. Construct an indifference curve for each of these functions
for utility numbers U1 = 10 , U2 = 100 , U3 = 200 .
e. Do these utility functions represent different preference
orderings?
1. Consider the following utility functions: (i) U(x,y)- 6xy, (ii) U(x,y)=(1/5)xy, MU,--y and MU,--x ii) U(x,y)-(2xy)M 8xy2 and MUy -8x2y MU,-6y and...
Most questions answered within 3 hours.
-
4. Determine the theoretical yield of P2O5, when 3.07 g of P
reacts with 6.09 g...
asked 1 hour ago -
Explain the PEST analysis and how a marketer would use this when
putting together a marketing...
asked 1 hour ago -
S sells property with a $500 basis to B for $450, and B later
sells the...
asked 2 hours ago -
True/False Questions
1.
In interpreting an agreement, courts generally apply a
subjective standard.
2.
If, after...
asked 1 hour ago -
On January 1, 20X7, Green Corp. paid $1,020,000 to acquire Wax
Co. Wax maintained separate incorporation....
asked 2 hours ago -
C++
Write a class Fraction that defines adding, subtracting,
multiplying, and dividing fractions by overloading standard...
asked 3 hours ago -
This java code won't run and I can't figure out the problem with
it. Please help...
asked 4 hours ago -
Trace the following recursive methods:
a) isPal with the string “abccda”
b) isAnBn with the string...
asked 5 hours ago -
1. Which of the following is false about photosynthesis?
A. ATP is the molecule used to...
asked 6 hours ago -
A simple random sample of size n=64 is obtained from a
population with a mean of...
asked 7 hours ago -
(2 dimensions, 1 object, 2 accelerations)
1) A projectile is thrown with a wind. The wind...
asked 8 hours ago -
Brian makes $34,100 per year. How much can Brian expect to
contribute to FICA taxes in...
asked 8 hours ago