Economics of Risk Suppose that an individual faces uncertainty regarding the return to a financial asset. The individual invests $1, 000 in the financial asset. With a probability equal to p = 1/3, the return is a relatively low rate equal to R1 = 1.1. On the other hand, the individual receives a high rate of return equal to R2 = 1.3 with probability (1 - p) = 2/3. Write down an expression for an individual's expected income. Then, write down an expression for an individual's expected utility. Assuming that people obtain diminishing returns from income, draw a graph to show the amount of utility an individual would obtain at both possible rates of return. In addition, use your graph to reflect an individual's expected utility.How do individuals perceive the interest rate risk that they encounter? For example, suppose that individuals could make a choice between always earning their expected rate of return or facing interest rate risk. Which option would they prefer? Use detailed graphical analysis with economic interpretation to support your answer. Bank Runs Suppose that a bank has 100 depositors. Each depositor has $30,000 and is considering a savings decision. The bank has access to investment opportunities which pay a 20% rate of return (R2 = 1.2) if an individual leaves the funds in for two periods. Alternatively, if an individual is forced to liquidate early, she only gets her deposit hack (R1 = 1). Suppose that there is a 30% chance that the individual will have to withdraw her funds early (after one period). The nancial institution offers the following return on the funds: (Impatient) If you leave your deposits in the bank for one period, you will earn a 5% rate of return (r1 = 1.05). (Patient) If you leave your deposits in the bank for two periods, you will earn a return of m. 1. The rate of return that the bank will offer to depositors who withdraw their fluids after two periods will be r2: 2. Suppose that 75 depositors have chosen to withdraw their funds from the bank early. The bank's total earnings will be 3. Assuming that a patient depositor would be able to obtain funds from the bank, how much would he or she receive