4. You are planning on investing your 401k money and are deciding between stocks and bonds. If you invest in stocks, your returns are dependent upon the economy. If the economy is good, you will earn a total of 40% return on your investment for the next 10 years (so, if you invest x, you'll have 1.4x at the end of 10 years). If the economy is bad, you will lose 20% of your initial investment over the next 10 years. You estimate that there is an 80% chance that the economy will be good over the next 10 years. If you choose to invest in a 10-year savings bond, you will earn a 10% return by the end of 10 years guaranteed. If you plan to retire in 10 years and have 1 million dollars total to invest in the two options, how much should you invest in each option in order to maximize expected utility? Assume that your utility function is U(x) = ln(x), and that you do not want to borrow money. 4. You are planning on investing your 401k money and are deciding between stocks and bonds. If you invest in stocks, your returns are dependent upon the economy. If the economy is good, you will earn a total of 40% return on your investment for the next 10 years (so, if you invest x, you'll have 1.4x at the end of 10 years). If the economy is bad, you will lose 20% of your initial investment over the next 10 years. You estimate that there is an 80% chance that the economy will be good over the next 10 years. If you choose to invest in a 10-year savings bond, you will earn a 10% return by the end of 10 years guaranteed. If you plan to retire in 10 years and have 1 million dollars total to invest in the two options, how much should you invest in each option in order to maximize expected utility? Assume that your utility function is U(x) = ln(x), and that you do not want to borrow money