1 Paycheck Protection Program Sam is a small business owner. He operates a specialty coffee shop, serving fancy espresso drinks and freshly roasted beans for use at home. The coffee shop employs 10 workers. Assume consumption of high-end coffee is pro-cyclical - i.e. it is higher in recessions. Sam's coffee shop makes $2,000 in profit per day in good times, but only $1,250 per day in recessions. Now suppose the government is considering implementing a business stimulus program. In a recession, they will provide small businesses with $300 per day. Under this program, Sam's coffee shop will make $2,100 in good times, and $1,300 per day in bad times, excluding the stimulus. Finally, assume recessions occur 25 percent of the time. 4. Assume U(x)=logx. Calculate expected utility with and without the program. Derive an expression for the expected utility when paying option price z for the program. 5. Calculate the option price, and compare to expected surplus. (Hint: You will need to use Wolfram Alpha.) 6. Suppose the opportunity cost is $170. Assume Sam is the only beneficiary. Would a standard CBA recommend this project? Would you recommend this project