Ellsworth's utility function is U(x, y)= min{x, 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.

Question

Quizplus · Accepted Answer

To find the values of A and B, we need to use the concept of compensating and equivalent variations.

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.

Ellsworth's Utility Function Is U(x, Y)= Min{x, Y}