Bundle: Microeconomic Theory: Basic Principles and Extensions, 12th + MindTap Economics, 1 term (6 months) Printed Access Card
Bundle: Microeconomic Theory: Basic Principles and Extensions, 12th + MindTap Economics, 1 term (6 months) Printed Access Card
12th Edition
ISBN: 9781337198202
Author: NICHOLSON, Walter, Snyder, Christopher M.
Publisher: Cengage Learning
Question
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Chapter 5, Problem 5.1P

a)

To determine

To find: The utility function in term of 0.75 liter containers and 2 liter containers.

a)

Expert Solution
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Explanation of Solution

If both goods are substitute goods, the utility function will be in the following form:

U=αx+βy

Therfore, from the question, the value of Alpha will be 0.75 and the value of Beta will be 2.

Thus, the utility function is:

U = 0.75x + 2y

b)

To determine

To find: Person E’s demand function.

b)

Expert Solution
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Explanation of Solution

MUx=dUdxMUx=d(0.75x+2y)dx=0.75MUy=d(0.75x+2y)dy=2

In the case of substitute goods, consumer will spend all income on x if ratio of prices Px/Py is less than the marginal utility’s ratio. If it will not be less than the ratio of marginal utility, it will buy zero quantity.

Quantityofx=IPxRatioofprices,PxPy0.752Px38Py

Thus, demand function is:

x={IPxwhenPx38Py0whenPx>38Py

c)

To determine

To find: Demand curve for good x.

c)

Expert Solution
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Explanation of Solution

Demand curve is represented by red line.

Bundle: Microeconomic Theory: Basic Principles and Extensions, 12th + MindTap Economics, 1 term (6 months) Printed Access Card, Chapter 5, Problem 5.1P

d)

To determine

To find: Reason to the shift in demand curve for x.

d)

Expert Solution
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Explanation of Solution

In the diagram, it can be seen that demand curve have two potion that is touched with x axis and other is overlapped on vertical axis. So, the portion that is touched with x axis will shift the curve rightwards.

e)

To determine

To find: The compensated demand curve.

e)

Expert Solution
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Explanation of Solution

The compensated demand curve occurs in the case of substitution effect and not in the case of income effect. Moreover, in the following case, the substitution effect exists so the shape of demand curve will be same as the demand curve of part “d”.

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