In footnote 7 we showed that for a utility function for two goods to have a strictly diminishing MRS (i.e., to be strictly quasi-concave), the following condition must hold:

UxxU 2

x − 2UxyUxUy + UyyU 2

y < 0 Use this condition to check the convexity of the indiffer ence curves for each of the utility functions in Problem 3.1.
Describe the precise relationship between diminishing marginal utility and quasi-concavity for each case.