Asked by Alexandria Russell on May 28, 2024
Verified
Ellsworth's utility function is U(x, y) minx, y.Ellsworth has $150 and the price of x and the price of y are both $1.Ellsworth's boss is thinking of sending him to another town where the price of x is $1 and the price of y is $2.The boss offers no raise in pay.Ellsworth, who understands compensating and equivalent variation perfectly, complains bitterly.He says that although he doesn't mind moving for its own sake and the new town is just as pleasant as the old, having to move is as bad as a cut in pay of $A.He also says he wouldn't mind moving if when he moved he got a raise of $B.What are A and B?
A) A 50 and B 50.
B) A 75 and B 75.
C) A 75 and B 100.
D) A 50 and B 75.
E) None of the above.
Compensating Variation
A measure in economics of the amount of money one would need to reach their original utility level after a change in price or income.
Equivalent Variation
An economic measure of the amount of money that leaves an individual equally well off, given changes in prices or utility.
Income
The financial gain received by an individual or entity, typically measured over a certain period, resulting from labor, investments, or other sources.
- Compute and contrast compensating and equivalent variations across various economic situations.
Verified Answer
Compensating variation is the amount of money that must be given to an individual to offset a welfare-reducing change in their circumstances, such as a price increase.
Equivalent variation is the amount of money that must be taken away from an individual to leave them as well off as they were before a welfare-improving change in their circumstances, such as a price decrease.
In this case, Ellsworth's boss is proposing a welfare-reducing change by changing the prices of x and y.
We can start by finding Ellsworth's initial utility level. Since he has $150 and the price of both x and y is $1, he can buy 75 units of x and 75 units of y.
U(75,75) = 75
Now we need to find the utility level that Ellsworth would have in the new town with the new prices. Since the price of x is still $1 in the new town, he can still buy 75 units of x with his $150. However, the price of y is now $2, so he can only buy 75/2 = 37.5 units of y.
U(75,37.5) = 37.5
To find the compensating variation (CV), we need to find the amount of money that would have to be added to Ellsworth's income in the new town to make him as well off as he was before.
CV = U(75,75) - U(75,37.5) = 75 - 37.5 = $37.5
So Ellsworth would need to be given an additional $37.5 in the new town to compensate him for the price change.
To find the equivalent variation (EV), we need to find the amount of money that would have to be taken away from Ellsworth's income in the old town to make him as well off as he would be after the price change.
EV = U(75,75) - U(75,37.5) = 75 - 37.5 = $37.5
So if Ellsworth received a pay cut of $37.5 in the old town, he would be as well off as he would be in the new town with the price change.
Now we can use these values to find A and B.
A = CV = $37.5
B = EV = $37.5 + $37.5 = $75
Therefore, the answer is D, A = $37.5, and B = $75.
Learning Objectives
- Compute and contrast compensating and equivalent variations across various economic situations.
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