Answer all parts of Problem 3.15 for the utility function U = √x + 2√y. The marginal utilities for x and y are, respectively, MUx = 1/(2√x ) and MUy = 1/√y .
In problem 15
a) Is the assumption that more is better satisfied for both goods?
b) Does the marginal utility of x diminish, remain constant, or increase as the consumer buys more x? Explain.
c) What is MRSx, y?
d) Is MRSx, y diminishing, constant, or increasing as the consumer substitutes x for y along an indifference curve?
e) On a graph with x on the horizontal axis and y on the vertical axis, draw a typical indifference curve (it need not be exactly to scale, but it needs to reflect accurately whether there is a diminishing MRSx, y). Also indicate on your graph whether the indifference curve will intersect either or both axes. Label the curve U1.
f) On the same graph draw a second indifference curve U2, with U2 > U1.