6. (HARA) The HARA (for hyperbolic absolute risk aversion) class of utility functions is defined by U(x)=- ax +b b> 0 The functions are defined for those values of x where the term in parentheses is nonnegative. Show how the parameters y,

a, and b can be chosen to obtain the following special cases (or an equivalent form)

(a) Linear or risk neutral: U(x) = x

(b) Quadratic: U(x)=x-cx2

(c) Exponential: U(x) = -e

(d) Power: U(x) = cx

(e) Logarithmic: U(x) = Inx [Try y=- y = -] [Try U(x) = (1-y)-((x 1)/v)] Show that the Arrow-Pratt risk aversion coefficient is of the form 1/(cx + d)