Question

Indifference curves and utility: Consider the utility function ? (?1, ?2) = 6?1^1/2 + ?2 that describes Moe’spreferences. For the following, think of q1 as the variable you would graph on the horizontal axis.

a. Derive an expression for his marginal utility (U1) from a small increase in q1 holding q2 fixed. Also, find U2.

b. What is Moe’s marginal rate of substitution (MRS)? Give a brief (2 sentences maximum) intuitive description of what MRS represents.

c. Given your answer in part (b), find Moe’s MRS when q1 = 9 and q2 = 8. If one unit of good 1 was taken from Moe, how much of good 2 would he need in compensation to maintain his original level of utility? Fractional units of each good are possible.

d. Graph Moe’s indifference curve for a utility level of 60. At a minimum, use the 3 bundles of the goods that have the following levels of good 2 (0, 24, & 60) to plot the indifference curve. Does Moe have a diminishing marginal utility for good one? How about for good two?

e. Is the fact that Moe’s indifference curve intersects with the q1 axis a violation of any of the 5 properties of indifference curves? Briefly support your answer.

f. After considering the preferences represented by this utility function, provide an example of goods that might be reasonably represented by q1 and q2 (Hint: think about how the utility Moe derives from consuming good 2 differs from that of good 1).

Answer 1

As per HOMEWORKLIB RULES first four subparts are to be answered in case of multiple subparts

Kindly ask rest of the questions in a separate post