Suppose that each person is characterized by the accident probability α ∈ [0, 1]. If the person’s Bernoulli utility function is √ x, and if the income is 400 Dollars and the accident causes a loss of 400 Dollars, then one can check that a person of type α is willing to pay at most p = 800α − 400α 2 for insurance — if we write this equation as a function of p then we get α = 1 − 0.05 p 400 − p. Clearly, the expected cost of providing insurance to a person of type α is 400α. Finally, suppose that the types α are uniformly distributed on [0, 1], i.e., the fraction of types [0, α¯] in the whole population [0, 1] is exactly 1/α¯. (a) First, suppose that by law everyone must have insurance. Determine the insurance premium p at which the insurance company breaks even (i.e., makes zero profits).The insurance premium is?