Mas Ibas has funds amounting to Rp. 10 billion rupiah to be invested in shares. Coincidentally 2 months ago PT. Krakatau Steel sells IPO (Initial Public Offering) to the public at a very sexy price, namely only Rp. 850,- per share. From information from consultant Mas Ibas, there are several situations that could occur in the next year as follows: If the future prospects for the share price are as follows: PT Krakatau Steel performs well and is profitable, then it is possible for the share price to increase by 40% from the initial IPO purchase price. However, if PT Krakatau Steel does not perform well and actually loses because the government's industrial policy does not support the development of the national steel industry by allowing foreign steel products to enter without import duties, then PT's share price will decline. Krakatau Steel will drop to only Rp. 50,- per share. Apart from that, consultant Mas Ibas also informed that if the business performance of PT. Krakatau Steel remains as it was during the first IPO sale, so the future share price will only increase by 10%. Other information conveyed to Mas Ibas is that the possibility of PT Krakatau Steel losing money is 20% and apart from that 50% is its current performance. Based on this situation, financial consultant Mas Ibas provided another investment alternative in the form of buying bonds from the government which would give a return of 8% per year.

a) Try to calculate the investment expectations for purchasing PT's IPO. Krakatau Steel in the next 1 year?

b) If it is assumed that the utility function of the income obtained from Mas Ibas from the investment of funds owned is U(p) = p ² (where each p value of ownership of funds has a benefit of pxp) which investment will be chosen? ? And what is the equivalent utility value of the selected investment?

c) The question is the same as in b) when the utility function from the income obtained by mas Ibas U(p) = p ^1/2 ?