A consumer purchases two goods, X and Y, which are perfect complements. In other words, the goods are only beneficial when consumed together. (For example, think of X as left shoes and Y as right shoes.) Therefore the consumer gains no extra benefit from additional units of X in excess of the number of units of Y he has (and vice versa). As such, the consumer's indifference curves look like this:

a. The consumer has $120 to spend, the price of a unit of X is $5, and the price of a unit of Y is $10. How many units of X and Y does the consumer purchase?Since the two goods are only beneficial when consumed together (any unit of X that does not have an accompanying unit of Y is useless to the consumer, and vice-versa), the consumer will only buy the goods in pairs.

b. The price of X increases to $10. How many units of X and Y does the consumer purchase now? How much additional income would the consumer need to reach the prior level of utility at the new prices? How much income could the consumer sacrifice to hold the old prices constant, while reaching the same utility as at the new prices?The compensating variation for a policy is the amount of money the consumer could pay and still be as well off after the price increase as he was before (i.e., the amount he would be willing to pay as compensation for having the policy enacted). How much less money does he need to be able to buy 8 pairs (his initial consumption) but at the new price ($20 per pair)?