1. How much is a consumer hurt by an increase in price (like a tax)?
Three Methods to measure this:
Change Consumer Surplus.
Compensating Variation
The amount of income that must be given to restore old utility.
Equivalent Variation
The amount of income that must be taken away from before to give new utility.

2. Simple Compensation
Ari lives in London and has utility min{x1,x2}, p1=p2=1,income=12.
Suddenly, the p1 doubles.
The government wants to return Ari to his old utility by giving him free x2. How many should they give to him?
The government decides that this is too expensive and instead decides to tax Todd who lives in Exeter who has the same utility as Ari but didn't have a price increase.
How much do they need to tax Todd so that he has the same utility as Ari without any government help?

3. Example.
In Springfield there are two goods: Pork chops x and Coca-Cola y.
The utility function for the typical resident is
u(x,y)=
In 2000, px=py=1 and income is 100.
In 2001, foot and mouth disease hits and px goes up to 4 (and income is still 100).
The Blair decides to try to compensate Springfield’s poor citizens. What should he do?

4. Consumer Surplus Method
CS is the area under the demand curve.
Change of CS is change of this area.
Demand for x is
So change in area is going to be

5. CV and EV methods Utility= In 2000, px=py=1, so utility =
Remember CV is how much m to add to 2001.
EV is how much m to take away in 2000.

6. Comments on compensation.
These 3 method are only the same when utility is quasi-linear. (This is due to income effects).
The CS method is always going to yield results between the two other methods.