46. The utility function of an individual is as given here

(a) The individual in question is invited to participate in a contract which can result in a gain of Rs 2 lac or a loss of half this amount with equal probabilities. Show that he would not accept this contract.
Now, suppose that there are four individuals, each with utility functions like the above, who are deciding whether to enter this contract as a group, sharing profits or losses equally. Should they accept it?

(b) Reconsider the utility function. The individual involved is asked to choose one or none of the two contracts C 1 and C2• Contract C 1 is likely to involve a loss of Rs 40 thousand with a probability of0.40 and profit of Rs 70 thousand with a probability of0.60. Contract C2 is composed of two contracts each of which promises a profit of Rs 35 thousand with a probability of0.60 and a loss of Rs 20,000 with a probability of0.40. The outcomes of each of these two contracts making up C2 are independent.
Should the individual accept the contract C1? C2? None?

Amount ('000 of Rs) : 400 200 100 70 50 15 0 Utility Index : 1 0.90 .83. .80 .78 .73 .70 Amount ('000 of Rs) -25 -40 - -50 -60 - - 100 -200 Utility Index : .64 .60 .58 .50 .40 .00