A consumer's preferences are represented by the following utility function:u(x, y) = 2 T+ Vỹ +71. Recall that for any two bundles A =(TA, YA) and B(TB, YB) the following equivalencethen holdsAEB 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 convexpreferences. Also remember that preferences are strictly convex when for any three bundlesA, 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 theMRS at the point (x3, Y3) = (7,6)?4. Derive an equation for the indifference curve through the bundle (x2,Y2) = (4,9). With anequation it is meant: y as a function of x, y(x), such that (x, y(x)) lies on the indifferencecurve passing through bundle (4,9).

A consumer's preferences are represented by the following utility function: u(r, y) = 2/T+ v+7 1. Recall that for any two bundles A = (xA, YA) and B = then holds (xB, YB) the following equivalence A- B u(A) > u (B) Which of the two bundles (r1,y1) = (9, 4) or (r2, Y2) = (4,9) does the consumer prefer?

A consumer's preferences are represented by the following utility function: u(r, y) = 2/T+ v+7 1. Recall that for any two bundles A = (xA, YA) and B = then holds (xB, YB) the following equivalence A- B u(A) > u (B) Which of the two bundles (r1,y1) = (9, 4) or (r2, Y2) = (4,9) does the consumer prefer?

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter10: Consumer Choice Theory

Section: Chapter Questions

Problem 9P

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