Suppose that two persons, A and B, can each earn a high income(H) or a low income (L). The following table describes the probability of each of the four events. Make sure that you understand what each cell means: in particular, you should note that q + s + 2r = 1.

(a) If each person expects H with probability p, and this is independent of what happens to the other person, describe q, r, and s in terms of p.

(b) Now assume that the fortunes of the two persons are correlated. Using the variables in the table, how would you capture the idea that the incomes of A and B might be positively correlated? Negatively correlated? How would the extremes of perfect correlation be expressed?

(c) Which of these cases do you find most conducive for mutual insurance between A and B?

Transcribed Image Text:

H for B L for B H for A 9 P L for A Y S