Suppose a consumer has the following utility function defined over the 2 goods X and Y:

a. If this consumer originally consumed 10 units of X and 24 units of Y, and if the consumption of X were increased to 15 units, how much Y would be would the consumer be willing to give up and maintain the initial level of satisfaction? That is, how much less Y is needed in exchange for the increase in the consumption of X if the consumer is to be equally satisfied before and after the change occurs?

b. On a carefully constructed graph plot this consumer's indifference curve through the original consumption bundle from part a. (you only need to consider X and Y values up to 50) and indicate the consumer's original consumption position. Plot X on the horizontal axis and Y on the vertical axis. As you can verify (or have already verified), the consumer is indifferent to the points (10,24) and (15,18). If you double the amount of each good in these two consumption bundles, you would have the bundles (20,48) and (30,36). Since the two original bundles are on the same indifference curve, are these two new doubled bundles on the same but higher indifference curve? Why or why not?