How to Calculate Compensating Variation (CV) and Equivalent Variation (EV)

Compensating Variation (CV)

CV is how much money we would have to give to (or take away from) the consumer to get them back to the same level of utility that they had before prices changed. So to calculated CV, you try to get the consumer to the initial utility level at the new prices by changing income.

The process for calculating CV is generally as follows:

1. Find demand functions

2. Plug demand functions into utility function

3. Solve for utility level achieved at the old income and old prices

4. Set the value found in step 3 equal to the utility function using new prices and unknown new income, and solve for new income

5. Subtract old income from income found in step 4 - that's CV

Equivalent Variation (EV)

EV is how much money the consumer would be willing to give up (or be paid) to prevent prices from changing - it is the change in income that would get them to the same new utility level as the change in price would if it happened. Thus to get EV, we get the consumer to the di erent utility level under old prices by changing income.

The process for calculating EV is generally as follows:

1. Find demand functions

2. Plug demand functions into utility function

3. Solve for utility level achieved at the old income and new prices

4. Set the value found in step 3 equal to the utility function using old prices and unknown new income, and solve for new income

5. Subtract income found in step 4 from old income - that's EV