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?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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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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