Saba and Hana own a small hotel. They run the risk of loss due to small kitchen fires. This risk can be mitigated by taking precautions (e.g., purchasing fire extinguishers, installing fire alarms). Assume that the total cost of precautions can be represented by TC= 80F + 4F2, where F is equal to the actions to reduce the risk of a fire. The total benefit of these precautions is TB = 100B – B2.
a) If Saba and Hana do not have any insurance for their restaurant, what is the optimal level of precautions? (Hint: Use MB and MC analysis to find your answer) (10 marks)
b) Suppose Saba and Hana already have insurance for their restaurant that reduces the total benefit of taking precautions to TB = 90B – 2B2. What happens to the optimal level of precautions? Show your work mathematically and explain your result analytically. (13 marks)
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