3) Consider two types individuals in a very large economy who all have an util ity function of 11.01;) = x/E) and initial wealth levels of $100. They face a 50% chance of health expenditures of an amount $19 (low risk type) and $75 (high risk type) respectively. Suppose the insurance company knows that both types of individuals are equally likely, but they cannot identify the types separately. i)What is the maximum that each individual is willing to pay to insure against health costs? ii) If the insurance company is naive, what is the fair insurance price that it sets? Does it make a loss, and why? iii) What is the market solution when the insurance company realizes that not everyone buys insurance at a fair price? What is the aggregate utility? iv) What is the solution where government forced a mandatory enrolment into insurance? What is the aggregate utility