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(a)
If,
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Answer to Problem 5.20P
The consumer's optimal basketis 15 units of x and 60 units ofy.
Explanation of Solution
Budget constraint/line shows all possible combinations of two goods that can be purchased, given the level of income of the consumer and the market prices of both goods.
Indifference curve (IC) shows all possible combination of two goods that gives the same level of satisfaction to the consumer.
At the point of tangency of the budget line and the indifference curve, the consumption bundle is optimal. The slope of the IC and the budget line is equal at this point.
A consumer has utility function:
X represents pizza and y represents other goods.
Given that −
Income = $120
The budget line of the consumer is:
First find the values that satisfy the tangency condition, which is the requirement by putting
From Equ (1) and Equ (2), then −
Now the put the value of x form Equ (3) in Equ (1) to calculate the value of y −
Hencethe consumer's optimal basket consist 15 units of x and 60 units of Y.
(b)
If the price of food reduced to $3, then income and substitution effect of consumer is to be calculated.
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Answer to Problem 5.20P
The consumer's substitution effect is 2.7.
Explanation of Solution
Substitution effect: Substitution effect is the term used in economics to change in the relative prices of products on the basis of consumption pattern.
To calculate the consumer's income and substitution effect of a decreases in the price x to 3.
Use the new tangency conditions equation for this price.
It is given by the equation
The new budget constraints-
Put y =3x in Equ (1), to calculate the value of x.
Put the value of x in Equ (1) to calculate the value of y −
Since the consumer's utility is
is given:
Thus, the consumer's optimal basket when
The consumer's substitution effect is
(c)
The compensating variation of price change is to be calculated.
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Answer to Problem 5.20P
The consumer's compensating variation of the price change is 16.2.
Explanation of Solution
Compensating variation is the quantity of earning of the consumer able to give after a price alteration to be just well of as before the price variation.
The consumers compensating variation of the amountalteration is equal to the difference between the consumers earning 120 the income requires to buy the decomposition basket.
The decomposition basket can be taken for hence the consumers compensating variation of the price change is
The decomposition basket can be calculated as −
Put the values of x and y in above equation −
Compensation variation =
Compensation variation = 120 − 103.8 = 16.2
(d)
The equivalent variation of price change is to be calculated.
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Answer to Problem 5.20P
The compensating variation of the price change
Explanation of Solution
Equivalent variation is the volume of income the consumer would need before a price change to be just as well off after the price change.
The consumer's equivalent variation of the price change is equal to the amount needed to achieve the utility after the price change which is
If
This basket can be brought for
Hence, the consumer's equivalent variation of the price change is
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Chapter 5 Solutions
EBK MICROECONOMICS
- Economics (MindTap Course List)EconomicsISBN:9781337617383Author:Roger A. ArnoldPublisher:Cengage Learning
- Principles of MicroeconomicsEconomicsISBN:9781305156050Author:N. Gregory MankiwPublisher:Cengage Learning
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