Question

Brianna’s preferences can be represented by the utility function u(x,y) = min{x,y}. Initially she faces prices ($2,$1) and her income is $12. If prices change to ($3,$1) then the compensating variation

Select one:

a. There is not enough information to determine which variation is greater.

b. is $2 more than the equivalent variation.

c. is $1 less than the equivalent variation.

d. equals the equivalent variation.

e. is $1 more than the equivalent variation.

Answer 1

Answer: The solution to the above problem can be derived as follows:

The given utility function U(x,y) = min{x,y}, implies perfect competency, which in turn implies that x = y.

Compensating Variation: The amount of money to give to the consumer to completely offset the price change

Now given the budget equation and the initial prices of the products, the budget equation is:

2x + 1y = 12

Since, x = y, we replace y with x in the budget equation and hence I get

2x + 1x = 12

or, x = 4 = y (as x=y)

So the utility function becomes U = min(4,4)

or, U = 4

Now after the price change the total expence becomes M = 4*3 + 4*1 (putting values of x and y and their new prices)

M = 16

So the compensating variation is 16 - 12 = 4

Equivalent Variation: The amount of money taken away from consumer that reduces his/her utility by increasing the price

After the price change the budget is

12 = 3x + 1y

or, 12 = 4x (replacing y with x)

or, x = 3 = y

So the utility becomes U = min(3,3) = 3

To have this utilty before the price chnage, the budget would be before price change

M = 3*2 + 1*2 = 8

So the Equivalent variation is 12 - 8 = 4

Hence we see that the Compensating variation is equal to Equivalent variation. Hence the correct answer is option d