Econ 101: Welfare Measures

Again, assume a typical consumer whose preference is rational, continuous, and locally non-satiated (I know it’s been a while, so please help yourself: refreshment is on the sidebar). We are interested in the following question: suppose there is a change in price level (say, due to a change in tax policy). Is an average consumer better off or worse off? We say he is better off if his utility now is higher than that before the change. He is worse off otherwise. Meet equivalent- and compensating variation.

Equivalent variation (EV) is the amount of money that you are indifferent to accept given that the alternative is to experience the price change. (Or, quality change – everything can be priced). Compensating variation (CV) is the money equivalent a planner (e.g. the government) compensates you with after the price change, so as to bring you back to your initial utility level. Think about Jakarta’s plan to build monorail in the city.

Suppose that you would like it if Jakarta has a monorail system. Then imagine that somebody is offering you money if you want to give up the monorail. First, you ignore the offer. Then that somebody increases the offer. Again, you refuse. He increases it again, until you become indifferent (here, if he increases it yet again, even by Rp 1, you would take the money and forget about the monorail). Then this amount of money (that makes you indifferent) is the equivalent variation. (If you hate the monorail, your EV is negative).

Now, suppose as the monorail project is completed, Governor Sutiyoso is to take you back to your initial situation, i.e. to your utility level before the realization of the monorail. The natural question here would be: why in the world would he take us back to the lower utility? Don’t worry, this is hypothetical. We just want to imagine that there is an amount of money as net revenue of Governor Sutiyoso the planner. It is like a money equivalent of his success to make you happier, by providing the monorail. This is the compensating variation. (Again, if you dislike the monorail, the CV would be negative).

Why do we need these measures? We might not really need them. But the government sure does. If the government is planning to impose a policy (new tax, subsidy, etc.), then it needs to be able to anticipate the effect. Think about compensation scheme like cash transfer, raskin, etc. These measures help figure out, say, the right level of compensation.

But why two measures? Because in reality you can’t really know the exact level of compensation. The EV and CV give a range where the true measure might be. Can the two be the same, though? Yes, if the change induced by the policy does not affect your wealth. In such a case, the EV is equivalent to CV, and they both are equivalent to another measure, namely the change in consumer’s surplus. The latter is defined as the change in the difference between the total amount you are willing to pay and the total amount you actually end up paying.

Note: EV and CV are due to Hicks (1939), consumer’s surplus is due to Marshall (1920).