4. Consider an investor whose utility function over money is u(w)= 2w?. The investor can invest...

  

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4. Consider an investor whose utility function over money is u(w)= 2w?. The investor can invest in a riskless asset that returns 1 (gross return per ¥1 invested) for sure, or a risky asset that returns 1.4 with probability and 0.8 with probability . (a) Suppose the investor's initial wealth is ¥1000. Letting x denote the amount invested in the risky asset, write the investor's expected utility as a func- tion of x. (b) Find the optimal amount to invest in the risky asset. 4. Consider an investor whose utility function over money is u(w)= 2w?. The investor can invest in a riskless asset that returns 1 (gross return per ¥1 invested) for sure, or a risky asset that returns 1.4 with probability and 0.8 with probability . (a) Suppose the investor's initial wealth is ¥1000. Letting x denote the amount invested in the risky asset, write the investor's expected utility as a func- tion of x. (b) Find the optimal amount to invest in the risky asset.