Sample Question #75 (economics – utility function)

Let *U(x) *be an investor’s utility function over some *x. *For example, *x *could be wealth level or total returns from her asset holdings.

Write the mathematical expression that describes an investor who prefers more of *x* to less.

Write the mathematical expression that describes an investor who is risk-averse with regard to *x*.

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ANSWER

Preferring more of x to less means the utility function must be increasing in x. So U'(x) > 0, where the prime symbol indicates first derivative.

Risk aversion means the investor, when facing uncertainty over changes in x, gets more disutility from losing some amount of x than utility from getting that same amount. In other words, the utility of getting extra x is decreasing in x. Mathematically, this is just U"(x) < 0.