Suppose a consumer's preferences for two goods can be represented by the Cobb-Douglas utility function U = Axαyβ , where A, α, and β are positive constants. The marginal utilities are MUx = αAxα−1yβ and MUy = βAxαyβ−1. Answer all parts of Problem 15 for this utility function.
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.