Question

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, Si, R(Xi)] = Xi + Si + R(Xi) for i = A, B, where X_i is i’sincome per week in euros, S_iis 200 if the mine is safe and 0 otherwise, and R(X_i) = 200 if X_i > X_j, 0 if X_i = X_j and -250 if X_i < X_j.

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.)
-Safe Mine or Unsafe Mine

b. If they can negotiate binding agreements costlessly with one another, will their choice be the same as in part a? Explain.

-Safe Mine or Unsafe Mine

Answer 1

b. We can see that at Nash they both are getting lower utility than they would get if they both agreed to work at safe mine.

(S,S) is Pareto superio to all the other scenarios as it has maximum combined utility (400+400=800).

Thus, if they can both costlessly negotiate binding agreement, their choice will be (S,S) rather than (U,U)