M23 A grocery store owner's utility of income 3,: is represented by the utility function U(y) : ln{y). She earns 100000 per year. but there is a 10% chance of the store catching re, in which case she stands to lose 50 000 in terms of merchandise destroyed and repair to the store. (a.} Show that the certainty equivalent of the grocer is equal to 93 303 and determine the corresponding risk-premium. T'l'i-"ould the risk-premium of the 50 000 loss be higher or lower if the original earnings would have 200 000 instead of 100 000? Determine the maximum premium the grocery's owner is willing to pay for a full insurance. {ll} Provide real-world examples in which there is only partial cover in insurance contracts. {c} This part is more difcult and aims to give one reason why partial cover is frequently observed in the real world. Suppose the insurance company offers a exible policy with a premium of 0.120 per 1 of loss. As a consequence. the owner decides to insure herself for a cover of almost 28 000. Verify this. and explain why the owner takes only partial cover at this premium