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Question 2. For each of the following utility functions: (i) u1(x1,T2) = 2x2. (a) Graph the...
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)...
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...
Indifference curves and utility: Consider the utility function ? (?1, ?2) = 6?1^1/2 + ?2 that...
Indifference curves and utility: Consider the utility function ? (?1, ?2) = 6?1^1/2 + ?2 that describes Moe’spreferences. For the following, think of q1 as the variable you would graph on the horizontal axis. a. Derive an expression for his marginal utility (U1) from a small increase in q1 holding q2 fixed. Also, find U2. b. What is Moe’s marginal rate of substitution (MRS)? Give a brief (2 sentences maximum) intuitive description of what MRS represents. c. Given your answer...
carefully 1. Carefully sketch the indifference curves corresponding to the utility functions and the utility levels...
carefully
1. Carefully sketch the indifference curves corresponding to the utility functions and the utility levels given below (a) u1 2 and ug 8. (b) ulxi,x) x u8 and ug 512. (c) 2 ules,)InIns u1 0.6931 and ug 2.0794. 4 1. Carefully sketch the indifference curves corresponding to the utility functions and the utility levels given below. (a) u(x1,x2) xx u1 2 and u2 = 8. (b) u(x1,x2) x1x; u1 8 and u2 =512. (c) 2 u(x1,x2)=Inx1 +Inx2; u1 0.6931...
For the following utility functions, a. Find the marginal rate of substitution. b. Derive the equation...
For the following utility functions, a. Find the marginal rate of substitution. b. Derive the equation for the indifference curve where utility is equal to a value of 100. c. Plot the indifference curve where utility is equal to a value of 100. (1) u(x1, x2) = x1x2; (2) u(x1, x2) = x1x2 + 10x2; (3) u(x1, x2) = x12 + x2
Treat Bob and Joe as having the same utility function as provided at the beginning of...
Treat Bob and Joe as having the same utility function as
provided at the beginning of the question
Indifference curves and utility: Consider the utility function U (qi,%)-2q1/2 + q2 that describes Joe's preferences. For the following, think of q1 as the variable you would graph on the horizontal axis. 3. a. Derive an expression for his marginal utility (U) from a small increase in qi holding q2 fixed. Also, find b. What is Joe's marginal rate of substitution (MRS)?...
Treat Bob and Joe as the same individual and having the same utility function as provided...
Treat Bob and Joe as the same individual and having the same
utility function as provided at the beginning of the question.
Looking for the solutions to part e and f.
Indifference curves and utility: Consider the utility function U (qi,%)-2q1/2 + q2 that describes Joe's preferences. For the following, think of q1 as the variable you would graph on the horizontal axis. 3. a. Derive an expression for his marginal utility (U) from a small increase in qi holding...
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...
What are the marginal utilities of x1 and x2 given the following utility functions, then find...
What are the marginal utilities of x1 and x2 given the following utility functions, then find the MRS: U(x1, x2) = 4 x1 + 8 x2 U(x1, x2) = (x1 + 2)(x2 + 1) Example. To find the marginal utility for x1, think about how a 1 unit increase in x1, keeping all else constant, will change the amount of utility U. Once you have the marginal utilities for both, you can calculate the MRS.
For each of the following functions, i) pick three utility levels and draw the precise indifference...
For each of the following functions, i) pick three utility levels and draw the precise indifference curves that are associated with the levels of your choice, ii) label the utility level of the lines -- you cannot just draw random lines and assign arbitrary utility levels, and iii) give the name of preferences they represent (hint: see figures in textbook chapter 3). 1. u(x1, 12) = I1 + 2.12 2. u(21, 22) = min(21, 22) 3. u(x1,22) = 21 4....
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)...
carefully
1. Carefully sketch the indifference curves corresponding to the utility functions and the utility levels given below (a) u1 2 and ug 8. (b) ulxi,x) x u8 and ug 512. (c) 2 ules,)InIns u1 0.6931 and ug 2.0794. 4 1. Carefully sketch the indifference curves corresponding to the utility functions and the utility levels given below. (a) u(x1,x2) xx u1 2 and u2 = 8. (b) u(x1,x2) x1x; u1 8 and u2 =512. (c) 2 u(x1,x2)=Inx1 +Inx2; u1 0.6931...
Treat Bob and Joe as having the same utility function as
provided at the beginning of the question
Indifference curves and utility: Consider the utility function U (qi,%)-2q1/2 + q2 that describes Joe's preferences. For the following, think of q1 as the variable you would graph on the horizontal axis. 3. a. Derive an expression for his marginal utility (U) from a small increase in qi holding q2 fixed. Also, find b. What is Joe's marginal rate of substitution (MRS)?...
Treat Bob and Joe as the same individual and having the same
utility function as provided at the beginning of the question.
Looking for the solutions to part e and f.
Indifference curves and utility: Consider the utility function U (qi,%)-2q1/2 + q2 that describes Joe's preferences. For the following, think of q1 as the variable you would graph on the horizontal axis. 3. a. Derive an expression for his marginal utility (U) from a small increase in qi holding...
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...
For each of the following functions, i) pick three utility levels and draw the precise indifference curves that are associated with the levels of your choice, ii) label the utility level of the lines -- you cannot just draw random lines and assign arbitrary utility levels, and iii) give the name of preferences they represent (hint: see figures in textbook chapter 3). 1. u(x1, 12) = I1 + 2.12 2. u(21, 22) = min(21, 22) 3. u(x1,22) = 21 4....
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