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:

UxxU2 y 2 2UxyUxUy 1 UyyU2 x , 0.

Use this condition to check the convexity of the indifference curves for each of the utility functions in Problem 3.1

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Describe the precise relationship between diminishing marginal utility and quasi-concavity for each case.