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 demand for another good work in opposite directions. The substitution has a positive effect whereas income has a negative effect.
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
- Economics (MindTap Course List)EconomicsISBN:9781337617383Author:Roger A. ArnoldPublisher:Cengage Learning