Question: A and B face the choice of working in a

A and B face the choice of working in a safe mine at $200/wk or an unsafe mine at $300/wk. The wage differential between the two mines reflects the costs of the safety equipment in the safe mine. The only adverse consequence of working in the unsafe mine is that life expectancy is shortened by 10 years. A and B have utility functions of the form Ui [Xi SiR(Xi)] = Xi + Si + R(Xi) for i = A, B, where
X i 5 i’s income per week in dollars,
Si = 200 if i’s mine is safe, 0 if unsafe,
R (Xi) = 200 if Xi > Xj , 0 if Xi = Xj , - 250 if Xi , Xj (i, j = A, B; j ≠ i).

a. If the two choose independently, which mine will they work in? Explain. (Hint: Use the utility function to construct a payoff matrix like the one described in the text.)
b. If they can negotiate binding agreements costlessly with one another, will their choice be the same as in part a? Explain.

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