Economics Alex is a. retail worker making $15 per hour. Suppose she lives in a state where there is no unemployment insurance {U1} system. To protect herself in the event ofjoh loss in a recession, she saves part of her salary. During an economic expansion, she has $12 to spend; in a recession she has $3. Now suppose her state decide: to introduce a UI program, with a replacement rate of ll percent. Now, she can consume $15 in expansions, and $9 in recessions. The economy is in a recession onethird of the time. From this, we can assemble the following contingency table: 1. Calculate the surplus for Alex in good and bad times. What is the ex pected surplus? 2. Calculate Alex's income variance with and without the UI program. Is this a. risk-reducing or risk-increasing program? 3. Assume [ILL-fl = logs. Calculate expected utility with and without the UT program. Derive an exprmsion Jfor the expected utility when paying option price a for the program. 4. Calculate the option prise, and compare to expected surplus. (Hint: You will need to use Wolfram Alpha} 5. Suppose the opportunity cost is $4.5D. Assume Alex is the only beneciary. 1ii'vfould a standard CBA recomeIId this project? Would you recommend this project