These two ideas of compensation are not very different, but they do give somewhat different answers and slightly different graphs. Compensating according to utility (utility compensation) requires more knowledge in that we have to know exactly what the consumer's indifference curves look like, or we have to know her utility function. However, this method leaves the consumer exactly as well off as before the price change.

Expenditure compensation only requires that we know how much price changed and how much was being consumed prior to the price change. However, as we shall see this leads to "overcompensation."

For completeness we're going to do the analysis both ways. You can choose your preferred method at this point (based on what your prof prefers).
Expenditure Compensation
Utility Compensation

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