Question 3 (40 points) Ben has an ice cream shop. On sunny days he earns $1000, and on cloudy days his income is $400. Let's assume that those two are only states of nature and probability of having a sunny day is 0.8. His utility function for consumption in those two states of nature is U(c,-,., cc) = 0.8ln(c,.) + 0.2ln(cc), where 0,. and cc are values of his consumption when it is sunny and cloudy, respectively. One of Ben's neighbors, John, is an insurance agent. Knowing what kind of business line Ben is in, he advise Ben to purchase \"cloudy day\" coupons to insure his income on cloudy days. The \"cloudy day\" coupon would pay $2 on cloudy day for every coupon purchased. Each coupon costs $1. Should Ben listen to John's advice and if yes, how many coupons would he buy