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8. Manmohan Singh is a family farmer. He has set aside enough moneyto look after his family for the next 6 months and nds he has (250,000 available to invest. He has three options: (i) Put the money in a Simonth bank deposit that will pay interest of 5% at the end of 6 months. (ii) Buy regular seed for 2200000 and put the remainder of the money in a 67month bank deposit like the one in (it. He would then plant the seed and harvest a crop in 6 months' time. The crop would be valued at $500,000 if the rains are good, but only $50,000 it there is a drought. The probability ofa good rainy season is 0.7 and the probability of a drought is 0.3. (iii) Buy droughtresistant seed for $250,000 and plant that instead. The harvest would again be in 6 months, but the yields with the drought-resistant seed will be worth #400,000 if the rains are good and {350,000 if there is a drought. Singh wants to maximise his expected utility of wealth, which is U(W) = M, where Wis the family' 5 wealth in 6 months' time. (a) Which of the three options will Singh choose? Explain fully. (b) Suppose Singh could buy crop insurance if he plants regular seed. The premium would be due at the time of the harvest and the insurance would pay him 450,000 it there had been a drought. What is the aetuarialiy fair premium for this insurance? What is Singh' 5 maximum willingnessetoepay for it? Explain fully. \f