Q9 There are four people (Ellie, Fred, Grant, Hugh) each with different utility functions: uE(x)=x0.4uF(x)=x0.8uG(x)=xuH(x)=x1.2 Everyone has 100, which they can either keep in a Bank account (money is safe but there is no interest) or invest in a (100) bond of a small (risky) company "Alphapharma". If they choose the bond, there are two equally likely outcomes: They either get 0 (i.e. lose the money if the company fails), or get 200 (i.e. make 100 profit). a) Explain which individuals would invest in Alphapharma. Now assume that the government has decided that small companies like Alphapharma would benefit from more investment, so introduce an incentive scheme. The details are as follows: - The government instantly gives the investor 25% of the amount invested. Assume this cannot be re-invested. Under this new scheme: b) Write down how much money an investor would have in each of the two outcomes if they chose the bond c) Carefully explain if Alphapharma would attract any additional investment? (when compared to (a) above) Now assume that the government introduces an even more generous scheme. In addition to the above: - If the company fails, the government gives the investor p% back of the total amount invested. Under this more generous scheme: d) Write down how much money an investor would have in each of the outcomes if they chose the bond (as a function of p ) e) Calculate how large p would need to be to ensure all four individuals invested. Q9 There are four people (Ellie, Fred, Grant, Hugh) each with different utility functions: uE(x)=x0.4uF(x)=x0.8uG(x)=xuH(x)=x1.2 Everyone has 100, which they can either keep in a Bank account (money is safe but there is no interest) or invest in a (100) bond of a small (risky) company "Alphapharma". If they choose the bond, there are two equally likely outcomes: They either get 0 (i.e. lose the money if the company fails), or get 200 (i.e. make 100 profit). a) Explain which individuals would invest in Alphapharma. Now assume that the government has decided that small companies like Alphapharma would benefit from more investment, so introduce an incentive scheme. The details are as follows: - The government instantly gives the investor 25% of the amount invested. Assume this cannot be re-invested. Under this new scheme: b) Write down how much money an investor would have in each of the two outcomes if they chose the bond c) Carefully explain if Alphapharma would attract any additional investment? (when compared to (a) above) Now assume that the government introduces an even more generous scheme. In addition to the above: - If the company fails, the government gives the investor p% back of the total amount invested. Under this more generous scheme: d) Write down how much money an investor would have in each of the outcomes if they chose the bond (as a function of p ) e) Calculate how large p would need to be to ensure all four individuals invested