Type II Diabetes is a costly and potentially debilitating disease. The total costs incurred over a lifetime by a person with Type 2 diabetes were recently estimated to be $85,000 - from treating the disease directly, and complications like nerve damage, amputations, and stroke.

Consider a simplified model of the market for health insurance, where diabetes is the only future health risk people face. Assume that there are 1,000 people classified as "normal weight" and 1,000 people classified as "overweight." Normal weight people face a 20% chance of developing Type II diabetes in their lifetime, and overweight people a 30% chance.

Assume an individual can expect to earn $2,000,000 over the course of their lifetime. Additionally, assume individuals spend all their money on consumption, andu(c)=c^(1/2). Ignore any intertemporal considerations of interest rates, inflation or discount factors, i.e.r=0.

What is the amount,x, that each type of individual would be willing to pay for an insurance contract that fully insures them against the lifetime costs of developing diabetes?