Explain what is meant by compensating variation and equivalent variation?

Answer 1

There are three central measures of welfare in economics:

-Consumer Surplus (using a "marshallian demand function) -Equivalent Variation (using Hicksian demand function) -Compensating Variation (also using Hicksian demand function) Although consumer surplus is the most common measure of welfare it is flawed - it is based on a quasi linear demand function - one in which income has no effect on the demand for the good. However if there are large income effects involved; the demand curve is no longer a simple marginal value curve but one in which the value placed on the additional unit is heavily influenced by the amount spent on prior units. The consumer surplus now has no meaning in the marshallian demand context.

We want to ideally examine the effect of a price change allowing income to alter but maintaining utility at some fixed level. Therefore we must use a Hicksian demand function - one in which a price change will be matched with a corresponding change in income such that utility is maintained at some level. We can now utilise equivalent and compensating variation to examine the changes in welfare of the associated price change.

Equivalent variation is the income that you need to take away from an individual to make him equivalently worse off or better off following a price change.

The Compensating variation on the other hand is the amount of income you need to compensate an individual following a price change so that he remains on the same level of utility. For Equivalent variation we maintain utility at the new price ratio whereas in the case of compensating variation we maintain utility at the old price ratio.

Assuming the income effect is significant enough to disregard consumer surplus as an effective measure of welfare change and also a rise in price of good 1; the hicksian demand function which holds income constant will thus be steeper than the marshallian demand (assuming normal good - if inferior the opposite is true). The hicksian demand function relating to the original price level will be associated with a higher utility than the other hicksian associated with the new and higher price. However we cannot observe utility, hence we are using these functions. The equivalent variation will be smaller than the change in consumer surplus which in turn will be smaller than the compensating variation. The intuition behind this is that for a normal good more income is required to compensate the individual for a rise in price to maintain utility than income to be taken away from an individual such that he lies on a same lower utility.