U(x) = - PG-, +b). + 6 b>0. 6. (HARAO) The HARA (for hyperbolic absolute risk aversion) class of utility functions is defined by 1-y / ax y (1-y 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 - x? (c) Exponential: U(x) = -- [Try y = - 1 (d) Power: U(X) = 6,7% (e) Logarithmic: U(x) = lnx Try U(.x) = (1 - y)-Y((HY -- 1)/y)] Show that the Arrow--Pratt risk aversion coefficient is of the form 1/(ex + d) U(x) = - PG-, +b). + 6 b>0. 6. (HARAO) The HARA (for hyperbolic absolute risk aversion) class of utility functions is defined by 1-y / ax y (1-y 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 - x? (c) Exponential: U(x) = -- [Try y = - 1 (d) Power: U(X) = 6,7% (e) Logarithmic: U(x) = lnx Try U(.x) = (1 - y)-Y((HY -- 1)/y)] Show that the Arrow--Pratt risk aversion coefficient is of the form 1/(ex + d)