Question

Consider the following 3 utility functions with good x and good y: ? ?(?, ?) = (?^2)*sqrt(?), ? ?(?, ?) = 2? − (1/2)?, ? ? (?, ?) = 4 ln ? + ln ?

a. Find Marginal Utility (MUx and MUy) for each these utility functions.

b. Is assumption that more is better satisfied for both goods in all of these utility functions? If not, specify for which function(s) and for which good(s) it is not satisfied.

c. Does the marginal utility of each good diminish, remain constant, or increase as the consumer buys more for each of these functions?

d. Calculate the MRSx,y for each of these utility functions. e. Which utility functions represent tastes that have linear indifference curves?

e. Which utility functions represent tastes that have linear indifference curves? Explain your reasoning.

f. Which of these utility functions represent the same underlying preferences? Explain your reasoning.

g. Which of these utility functions represent preferences that satisfy the convexity assumption (i.e. convex indifference curves)? Explain your reasoning.

h. For ? ?(?, ?), draw a typical indifference curve on a graph with x on the horizontal axis and y on the vertical axis. (It need not be exactly to scale, but the major points like how slope changes along the curve should be clear). Label this curve U1. Draw a second curve U2 such that U2 > U1.

Answer 1