Sam is a small business owner. He operates a specialty coffee shop, serving fancy espresso drinks...

 

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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 em- ploys 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. 1. Set up a contingency table for this problem. (see slides) 2. Calculate the surplus for Sam in good and bad times. What is the expected surplus? 3. Calculate Sam's income variance with and without the program. Is this a risk-reducing or risk-increasing policy? 4. Assume U(x) = loga. Calculate expected utility with and without the program. Derive an expression for the expected utility when paying option price 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? 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 em- ploys 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. 1. Set up a contingency table for this problem. (see slides) 2. Calculate the surplus for Sam in good and bad times. What is the expected surplus? 3. Calculate Sam's income variance with and without the program. Is this a risk-reducing or risk-increasing policy? 4. Assume U(x) = loga. Calculate expected utility with and without the program. Derive an expression for the expected utility when paying option price 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?

Answer rating: 100% (QA)

1 Contingency Table Good TimesBad Times Income20001250 Stimulus0300 Total Income20001550 2 Surplus i... View the full answer