Compensating Variation
Compensating variation can be used to calculate the effect of a price change on an
individual's overall welfare. The best way to understand it is to work through it
graphically and go through a numerical example.
Graphical Analysis
Suppose we're interested in the effect of an increase in the price of good X on a
particular person. The price goes from Px1 to Px2, where Px2 is greater than Px1. The
individual has M dollars to allocate between X and Y, where Y represents all other
goods and has price Py. Py and M do not have a subscripts because they will remain
constant throughout the analysis.
Step 1: Find the Initial Equilibrium
Her budget constraint before the price increase is the following:
BC1:
M = Px1*X1 + Py*Y1
Given the budget constraint, she will choose bundle 1 in the diagram below and will
be on indifference curve IC1.
Step 2: Find the New Equilibrium Following Price Increase
When the price of X rises to Px2, the budget constraint changes to the following:
BC2:
M = Px2*X2 + Py*Y2
The new constraint is labeled BC2 in the diagram. She now chooses bundle 2 and is
clearly worse off because IC2 is lower than IC1.
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Step 3: Finding the Compensating Variation
Now imagine giving her some extra money to spend after the price change. We could,
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 Spring '10
 fallahi
 $2, $4, expenditure function

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