a)
To know:
Impact on quantity of goat’s milk due to increase in price.
a)
Explanation of Solution
Given:
Utility function:
m denotes goat’s milk and s denotes strudel.
Lagrange multiplier is used to find consumer’s equilibrium.
Budget constraint:
Substitute utility function and budget constraint in Lagrange multiplier:
Taking first order condition:
Solving the above equations:
Ratio of given equations are as follows:
Substitution of M value in above budget constraint:
As value is 0, it shows no impact on quantity due to increase in price of milk.
Introduction:
Expected utility is the satisfaction that will be achieved after the consumption of certain goods and services. It is an estimated utility.
b)
To prove:
b)
Explanation of Solution
The lagragian function for the given problem is shown below:
Taking first order derivative, the following result is obtained which is shown below:
By using above function, the following result is obtained which is shown below:
Taking ratio of above equations, the following result is shown below:
Substitute the M value in budget constraint:
Thus, from above value of M, the following result is obtained which is shown below:
The above result shows that increase in the price of strudel does not affect the quantity of goat’s milk.
Introduction:
Expected utility is the satisfaction that will be achieved after the consumption of certain goods and services. It is an estimated utility.
c)
To show: Income effect in above parts is identical.
c)
Explanation of Solution
If a two goods case is considered, then the income and substitution effects that arise due to the change in the price of one good on the
Slutsky equation:
Uncompensated demand =
Compensated demand =
To generate
The Hickson demand function is obtained by taking the derivative of expenditure function with respect to their prices as shown below:
Now taking the derivative of
Since,
It shows that
Hence proved.
Introduction:
Expected utility is the satisfaction that will be achieved after the consumption of certain goods and services. It is an estimated utility.
d)
To show:
Marshallian demand function
d)
Explanation of Solution
The Marshallian demand function shows changes in the price of y do not affect x purchases.
That is,
Thus, by using this following result is obtained.
Hence proved.
Introduction:
Expected utility is the satisfaction that will be achieved after the consumption of certain goods and services. It is an estimated utility.
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Chapter 6 Solutions
Microeconomic Theory
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- Economics (MindTap Course List)EconomicsISBN:9781337617383Author:Roger A. ArnoldPublisher:Cengage Learning