Part 4 only 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).

The graphical showcasing of consumers choices of two given goods which will provide the consumer…

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).

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).

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Concept explainers

Marginal Rate of Technical Substitution

MRTS reaches a manufacturer when a part of the product is lowered to sustain the manufacturing level when the other part is extended. It is the level of the quantity that is lowered when one extra volume is used, and the output is unchanged.

Preferences and Utility Analysis

Before understanding what is preference and utility analysis, it is very important to understand the terms preference and utility separately.

Question

Part 4 only

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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