2. An employer’s health plan offers to employees the opportunity to put money, before tax, into a health account the employee can draw upon to pay for health-related expenditures.

Any funds not used in the account by the end of the year are forfeited. Suppose the employee’s probability distribution for his health-related expenditures over the coming year has density f(θ). Suppose also that his marginal tax rate is α, 0 < α < 1, and that he wishes to maximize his expected after-tax income. How much money,

d, should he contribute to the health account?