Question

Exercise 4 Leta(c) = c1/2 and let c! > cı > 0 be given. Letc= π1c1+12c2, where 1- () Sketch the function u and indicate in your sketch the points (ci,u), u()), and (c,u()). (ii) Draw the line that connects the two points (q, u(c) and (c2,น(e)) and represent that line algebraically, [Hint Find the slope and intercept in terms of the two points, (c,a(c) and e, u()).1 (i) Use that algebraic result to show that the point (č, mu(G)+ π2u(c)) is on that line. If so, it follows from your diagram that This inequality holds for any u function that is strictly increasing at a di minishing rate. Notice that π1cı + π2c2-i is the expected value of the random vari- able that takes the value c1 with probability π1 and takes the value c2 with probability π2- Inequality (5) says that the expected utility of that random variable is less than the utility of getting the expected value of that random variable with probability one. That is called risk aversion. If the u fune- tion is such that π1a(c)+12u(c) = u(E) for all (q, c), then that is called risk-neutrality

Answer 1