(Solved): 4. (50 points) A consumer's utility function is given by u(xy) = 4xX@y2/3, what is this consumer's ...

4. (50 points) A consumer's utility function is given by u(xy) = 4xX@y2/3, what is this consumer's marginal rate of substitution between goods x and y. Suppose you also know that good x costs $4, good y costs $8 and the consumer has an income of $120. A) What is this consumer's optimal combination of x and y? B) Does this consumer find goods x and y to be substitutes or compliments? Explain with math and words how you know this. Using the consumer's preferences, find 3 points on their demand curve for good y.