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6.  Optimal Pregnancy
Suppose that you and your partner have decided to have a baby, and that the ideal time for the birth is 3 years from today.  Relative to this ideal, there is a constant loss of utility for each month early and a constant utility loss per month late, but the loss per month late is twice as large as the loss per month early.  Let the probability that you will succeed at conceiving in any month that you try by .
Assume that babies are born exactly 9 months after conception, that there is no risk of miscarriage, that there is no change over time in your probability of conceiving, and that there is no discounting.   (NOTE: Using a spreadsheet is not recommended for this problem.  A brute-force answer from a spreadsheet will receive only partial credit).
a.For what range of  values should you start trying to conceive immediately? Does your answer confirm what you said in part (a)? [Hint:  When setting up this problem, think about the expected utility loss in different periods.]
b.Suppose you know for sure that  = .35.  In what month should you start trying?
c.Now assume you do not know the value of Pi for sure because of heterogeneity in population.  In the population of couples of which you and your partner are a member, half are “high-probability” couples, meaning that they have  = .6; the other half are low-probability couples, with Pi = .1 (note that the mean probability is still.35). You do not know to which group you belong. When should you start trying? If your answer is different from your answer to part (c), give an intuitive explanation for why this is the case.
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mmdadan

现在还可以，回复吗？我看到迟了