A 1. Sensitivity Analysis Consider the following three alternatives (A,B,C) and three possible states of nature (S: economy shrinks, G: economy grows slightly, R: economy grows rapidly, each with a 1/3 probability). The numbers are the net benefits, which are to be maximized. Alternative State of Nature: S G R 1 1 5 B 1 4 4 C 0 4 1 (a) Assume that R has probability 1/3, but the probability of S and G are unknown. Do a 1 dimensional sensitivity analysis showing the EMV of each of the three alternatives as a function of P(S). For what values of P(S) is A best? B best? C best? At what value of P(S) is the value of A and B equal? (Notice that this is NOT a two dimensional sensitivity analysis, since if you know P(S), you then know P(G).) (b) Assume the probabilities of S,G,R are unknown. Draw a two-dimensional sensitivity analysis diagram (with regards to the probabilities of G and R) showing which alternatives are preferred in which regions of the P(G) vs P(R) plot.. For what probabilities of G and R would the EMV of B would be the same as A? (Be sure you can solve for the boundaries between the regions where each alternative is best. At the boundary, the EMV of two alternatives is equal, that gives you an equation.) 2. Be sure to understand how to construct a tornado diagram, and 1 and 2 sensitivity plots A 1. Sensitivity Analysis Consider the following three alternatives (A,B,C) and three possible states of nature (S: economy shrinks, G: economy grows slightly, R: economy grows rapidly, each with a 1/3 probability). The numbers are the net benefits, which are to be maximized. Alternative State of Nature: S G R 1 1 5 B 1 4 4 C 0 4 1 (a) Assume that R has probability 1/3, but the probability of S and G are unknown. Do a 1 dimensional sensitivity analysis showing the EMV of each of the three alternatives as a function of P(S). For what values of P(S) is A best? B best? C best? At what value of P(S) is the value of A and B equal? (Notice that this is NOT a two dimensional sensitivity analysis, since if you know P(S), you then know P(G).) (b) Assume the probabilities of S,G,R are unknown. Draw a two-dimensional sensitivity analysis diagram (with regards to the probabilities of G and R) showing which alternatives are preferred in which regions of the P(G) vs P(R) plot.. For what probabilities of G and R would the EMV of B would be the same as A? (Be sure you can solve for the boundaries between the regions where each alternative is best. At the boundary, the EMV of two alternatives is equal, that gives you an equation.) 2. Be sure to understand how to construct a tornado diagram, and 1 and 2 sensitivity plots