1) Explain why a bundle of goods cannot be optimal (i.e., why some other bundle must be a better choice) if the marginal rate of substitution (MRS) at this point is not equal to the ratio of the goods’ prices.

2) A consumer has a current income of $60, which can be spent only on goods X and Y. The price of good X is $3, and the price of good Y is $2.

a. i. Graph the consumer’s budget constraint, clearly labeling the intercepts and the slope of the budget line. ii. Suppose that the consumer chooses to purchase 12 units of good X. On the same graph, show the consumer’s utility-maximizing bundle (quantities of X and Y) and the indifference curve through this point.

b. Now the price of good X increases to $4. If X is a normal good and Y is an inferior good, show what the new utility-maximizing bundle might look like on the graph above (including the new budget line and the indifference curve through this point), and explain your reasoning. [You don’t have enough information to determine the exact bundle, but you can determine whether consumption of each good increases or decreases.]