Which functions if(x) are both constant absolute and constant relative risk-aver

Question

Which functions if(x) are both constant absolute and constant relative risk-aversion utility functions? For further reading, see , for example, the economics text Microeconomic Theroy, by A. Mas-Colell, M. Whinston, and J. Green (Oxford University Press, Oxford, 1995). You want to design a solar collector that will concentrate the sun's rays at a point. By symmetry this surface will have a shape that is a surface of resolution obtained by revolving a curse about an axis Without lost of generality, you can assume that this x-axis and the rays parallel to this axis are focused at the origin (see figure 2.16). To derive the equation for the curst, proceed as follows: The law of reflection says that the angles gamma and delta are equal, Use this and results from geometry to show that beta = 2alpha.

Explanation / Answer

    (180- ) + + = 180

   so    = +

since the sun rays are parallel to the x-axis, ==

therefore = 2

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