Suppose your utility lIlCthIl is U =1n(I/10,000). If your utility falls below 0, you die. a. Show that this utility function exhibits a positive but diminishing marginal utility of income. b. Suppose you purchase a $150 Ninja Professional Blender. (I just bought one it is awesome!) If you estimate that the chance your blender is destroyed in a terrible pia colada accident is l in 10 for any given year. What would be the actuarially fair cost of an insurance plan that pays for your blender to be replaced in the case of a beverage-related disaster? 0. If your income is $20,000, what is the maximum amount you would pay for an insurance plan that would replace your blender in the event of a beverage-related disaster? d. If your income is $100,000, what is the maximum amount you would pay for an insurance plan that would replace your blender in the event of a beverage-related disaster? e. Suppose both Dollar Tree and Macy's sell the Ninja Professional blender and both stores offer extended warranties. Which store is likely to charge more for the extended warranty and why? f. Suppose the chance a natural disaster destroys your house is l in 100 and that the replacement cost of your house is $500,000. What would be the actuarially fair cost of an insurance plan that pays for your house to be rebuilt in the case of a natural disaster