Question

For each of the utility functions below, compute the Arrow-Pratt coefficients of risk-aversion. Say whether the utility functions have constant absolute risk aversion, increasing absolute risk aversion, or decreasing absolute risk aversion. (a) u(w) = a + Bw where B > 0. (b) u(w) = w2. (c) u(w) = w1/2 (d) u(w) = wl-/(1-0) where o € (0,1). (e) u(w) =1-e-aw where a > 0.

Answer 1

Arrow - Przett mecell.cle of abscute pusk av mecum.cle of abscute bäsk avercior * given by = -_U"cue whese. "W) and U'(c) die the "Cua) . lira e. and lernative of the ' ਪuicity uਪਹੈ। @ MW) = x+ Bw, pon "W) = ß M"(w) - ó reas As R(W)=0 uch) = 2 R(W) = 0 the function . or risk-neutral. 6 Ulica) = 2 Qw RCW) - as we, Roc) <o. is tisk loving The function ③ Maw) = wolle e'(W) = 1 T R () = 4 wall . w'a tayo ID 13121 Que fired) = - WILO as wo so, deeneasing absdecke SASK-a version

@ uw) = - اون l'(a) = to 15 .5ECO,1) (1-o) wo owaty 00-(+9 9 = R(W)= weg A WC li" (W) = -6 wool so w ..AS O ECO,1), RCW)>o. R'rw)= - so, decreasing absdite Bisk aversion 4W) = t-e-aw, a> M'(W) = -(-x) e-aw R(W)= 030-0W d e u"(W) = d.(-de-ow constant absolute risk anession xo-aw sa