Joe has a utility function given by u(x, y) = x^ 2 + 2xy + y^...
Joe has a utility function given by u(x, y) = x^ 2 + 2xy + y^ 2
a. Compute Joes marginal rate of substitution, MRS(x, y).
b. Joe’s cousin, Alex, has a utility function v(x, y) = x+y. Compute Alex’s marginal rate of substitution, MRS(x, y).
c. Do u(x, y) and v(x, y) represent the same preferences?
Homework Answers
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...
Suppose utility is given by the following function: u(x, y) = xy3 Use this utility function...
Suppose utility is given by the following function: u(x, y) = xy3 Use this utility function to answer the following questions: (d) What is the marginal rate of substitution implied by this utility function? What does this mean in words? (e) How much of each good would this individual need to have to be willing to trade 1 unit of good x for 1 unit of good y (i.e. for the MRS to be equal to 1)? (f) Suppose we...
ots) Mark has preferences that can be represented by the following utility function: U(x,y)= (18+x)(+1). Sarah's...
ots) Mark has preferences that can be represented by the following utility function: U(x,y)= (18+x)(+1). Sarah's utility function is v) 6x +60 y - 4x + 2xy - 24 y +29: Do Mark and Sarah have the same preferences? You must prove your answer. U (x, y) = 6x+60 y - 4x + 2
Suppose Alex’s preferences are represented by u(x1,x2) = x1x32. The marginal utilities for this utility function...
Suppose Alex’s preferences are represented by u(x1,x2) = x1x32. The marginal utilities for this utility function are MU1 = x23 and MU2 = 3x1x22. (a) Show that Alex’s utility function belongs to a class of functions that are known to be well-behaved and strictly convex. (b) Find the MRS. [Note: find the MRS for the original utility function, not some monotonic transformation of it.] (c) Write down the tangency condition needed to find an optimal consumption bundle for well-behaved preferences....
Hi, please solve . Thank you 7. Shawn has quasi linear preferences, linear in x2. His utility function is given by U...
Hi, please solve . Thank you
7. Shawn has quasi linear preferences, linear in x2. His utility function is given by U (x1, x2) = In(xı) + x2 I (a) Compute his MU, and MUZ (b) Compute Shawn's marginal rate of substitution (MRS) for a bundle (x1, x2). (c) Find his demand function for x, and xz in terms of prices and income (P1, P2, y).
Problem 1 (10pts) Jim's utility function is U (x, y) = xy. Jerry's utility function is...
Problem 1 (10pts) Jim's utility function is U (x, y) = xy. Jerry's utility function is U (x,y) = 1,000xy +2,000. Tammy's utility function is U2, y) = xy(1 - xy). Bob's utility function is U(x,y) = -1/(10+ 2xy). Mark's utility function is U (2,y) = x(y + 1,000). Pat's utility function is U (2,y) = 0.5cy - 10,000. Billy's utility function is U (x,y) = x/y. Francis' utility function is U (x,y) = -ry. a. Who has the same...
4. Assume a utility function described by u(x,y)=2/xy. a. Given the utility function, u(x,y)=2xy, sketch the...
4. Assume a utility function described by u(x,y)=2/xy. a. Given the utility function, u(x,y)=2xy, sketch the indifference curves for u = 50, 72 and 98. e indifference Carved forbise banta un b. Sketch budget constraint of 5x +10y = 30. Label intercepts (where it crosses the axes). 00:0 VE c. Solve for calculate) the optimal bundle (x, y) and sketch the optimal solution.
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?
5. Consider the utility function U(x, y) = 2/x + y. 1) Is the assumption that...
5. Consider the utility function U(x, y) = 2/x + y. 1) Is the assumption that "more is better” satisfied for both goods? 2) What is MRS, for this utility function? 3) Is the marginal rate of substitution diminishing, constant, or increasing in x as the consumer substitutes x for y along an indifference curve? 4) Will the indifference curve corresponding to this utility function be convex to the origin, concave to the origin, or straight lines? Explain.
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...
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...
ots) Mark has preferences that can be represented by the following utility function: U(x,y)= (18+x)(+1). Sarah's utility function is v) 6x +60 y - 4x + 2xy - 24 y +29: Do Mark and Sarah have the same preferences? You must prove your answer. U (x, y) = 6x+60 y - 4x + 2
Hi, please solve . Thank you
7. Shawn has quasi linear preferences, linear in x2. His utility function is given by U (x1, x2) = In(xı) + x2 I (a) Compute his MU, and MUZ (b) Compute Shawn's marginal rate of substitution (MRS) for a bundle (x1, x2). (c) Find his demand function for x, and xz in terms of prices and income (P1, P2, y).
Problem 1 (10pts) Jim's utility function is U (x, y) = xy. Jerry's utility function is U (x,y) = 1,000xy +2,000. Tammy's utility function is U2, y) = xy(1 - xy). Bob's utility function is U(x,y) = -1/(10+ 2xy). Mark's utility function is U (2,y) = x(y + 1,000). Pat's utility function is U (2,y) = 0.5cy - 10,000. Billy's utility function is U (x,y) = x/y. Francis' utility function is U (x,y) = -ry. a. Who has the same...
4. Assume a utility function described by u(x,y)=2/xy. a. Given the utility function, u(x,y)=2xy, sketch the indifference curves for u = 50, 72 and 98. e indifference Carved forbise banta un b. Sketch budget constraint of 5x +10y = 30. Label intercepts (where it crosses the axes). 00:0 VE c. Solve for calculate) the optimal bundle (x, y) and sketch the optimal solution.
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?
5. Consider the utility function U(x, y) = 2/x + y. 1) Is the assumption that "more is better” satisfied for both goods? 2) What is MRS, for this utility function? 3) Is the marginal rate of substitution diminishing, constant, or increasing in x as the consumer substitutes x for y along an indifference curve? 4) Will the indifference curve corresponding to this utility function be convex to the origin, concave to the origin, or straight lines? Explain.
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...
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