Simon, a self-made millionaire, owns the world’s most extensive collection of artisan garden gnomes. His collection is very attractive to thieves, so Simon takes costly measures to protect his investment. The marginal benefit of these measures is where A represents the quantity of theft prevention actions taken. The marginal cost of these actions is MC = 1,000 + 3A. 

a. If Simon has no insurance, what is the optimal number of precautionary measures for him to take to protect his valuable gnome collection?

b. Suppose Simon insures his collection and the insurance contract covers half of all losses so that the marginal benefit is now MB = 2,500 – 2.5A. What happens to Simon’s optimal level of precautions? Explain why this is the case.

c. What would Simon’s optimal level of precaution be if he insured his collection fully against losses?