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A consumer's preferences are represented by the following utility function: u(x, y) = 2/T + v+7 1. Recall that for any two bundles A = (TA, YA) and B = (*B, YB) the following equivalence then holds A- B + u(A) > u (B) Which of the two bundles (r1, Y1) = (9, 4) or (x2, Y2) = (4,9) does the consumer prefer? %3D 2. Take as given for now that this utility function represents a consumer with strictly convex preferences. Also remember that preferences are strictly conver when for any three bundles A, B, and C, if B > A and CE A then aB + (1 – a)C > A for any a E (0, 1). Use this information and your answer to part (1) to determine which of the two bundles (x3, Y3) = (7,6) or (x2, Y2) = (4, 9) the consumer prefers. Verify your answer. 3. Derive an expression for the marginal rate of substitution. Interpret the MRS. What is the MRS at the point (r3, y3) = (7,6)?

A consumer's preferences are represented by the following utility function: u(x, y) = 2/T + v+7 1. Recall that for any two bundles A = (TA, YA) and B = (*B, YB) the following equivalence then holds A- B + u(A) > u (B) Which of the two bundles (r1, Y1) = (9, 4) or (x2, Y2) = (4,9) does the consumer prefer? %3D 2. Take as given for now that this utility function represents a consumer with strictly convex preferences. Also remember that preferences are strictly conver when for any three bundles A, B, and C, if B > A and CE A then aB + (1 – a)C > A for any a E (0, 1). Use this information and your answer to part (1) to determine which of the two bundles (x3, Y3) = (7,6) or (x2, Y2) = (4, 9) the consumer prefers. Verify your answer. 3. Derive an expression for the marginal rate of substitution. Interpret the MRS. What is the MRS at the point (r3, y3) = (7,6)?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A consumer's preferences are represented by the following utility function: u(x, y) = 2 T+ Vỹ +7 1. Recall that for any two bundles A = (TA, YA) and B (TB, YB) the following equivalence then holds AEB u(A)> u (B) Which of the two bundles (x1,Yı) = (9,4) or (x2, Y2) = (4,9) does the consumer prefer? 2. Take as given for now that this utility function represents a consumer with strictly convex preferences. Also remember that preferences are strictly convex when for any three bundles A, B, and C, if B E A and C E A then aB +(1 – a)C > A for any a E (0, 1). Use this information and your answer to (1) to determine which of the two bundles (03, Y3) = (7,6) or (x2, Y2) = (4, 9) the consumer prefers. Verify your answer. 3. Derive an expression for the marginal rate of substitution. Interpret the MRS. What is the MRS at the point (x3, Y3) = (7,6)? 4. Derive an equation for the indifference curve through the bundle (x2,Y2) = (4,9). With an equation it is meant: y as a function of x, y(x), such that (x, y(x)) lies on the indifference curve passing through bundle (4,9).
Transcribed Image Text:A consumer's preferences are represented by the following utility function: u(x, y) = 2 T+ Vỹ +7 1. Recall that for any two bundles A = (TA, YA) and B (TB, YB) the following equivalence then holds AEB u(A)> u (B) Which of the two bundles (x1,Yı) = (9,4) or (x2, Y2) = (4,9) does the consumer prefer? 2. Take as given for now that this utility function represents a consumer with strictly convex preferences. Also remember that preferences are strictly convex when for any three bundles A, B, and C, if B E A and C E A then aB +(1 – a)C > A for any a E (0, 1). Use this information and your answer to (1) to determine which of the two bundles (03, Y3) = (7,6) or (x2, Y2) = (4, 9) the consumer prefers. Verify your answer. 3. Derive an expression for the marginal rate of substitution. Interpret the MRS. What is the MRS at the point (x3, Y3) = (7,6)? 4. Derive an equation for the indifference curve through the bundle (x2,Y2) = (4,9). With an equation it is meant: y as a function of x, y(x), such that (x, y(x)) lies on the indifference curve passing through bundle (4,9).
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