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Exercise 4 Letu (c-c1/ 2 and let c. > c.> 0 be given. Leti-T1qt12 C2: where π2-1-n. (i) Sketch the function u and indicate in your sketch the points (ci, u(c)), ,u()), and (cr, u (a)). (i) Draw the line that connects the two points (c1, u(c)) and (c, u(c2)) and represent that line algebraically. [Hint: Find the slope and intercept in terms of the two points. (a,u(c)) and (q, u(c)) .] (iii) Use that algebraic result to show that the point (c, π1u(a) + mou(ca)) is on that line. If so, it follows from your diagram that This inequality holds for any u function that is strietly increasing at a di- minishing rate. Notice that π1ct π2c2 c is the expected value of the random vari- able that takes the value ci with probability π1 and takes the value c2 with probability 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 func tion is such that lu (GJ + 2u (c2-u (C) for all (q, C2), then that is called risk-neutrality

Answer 1