Return to the story of Monica and Nancy from Exercise S10. After some additional professional…

Return to the story of Monica and Nancy from Exercise
S10. After some additional professional training, Monica is more productive on
the job, so that the joint profits of their company are now given by 5m 1 4n 1
mn, in tens of thousands of dollars. Again, m is the amount of effort put into
the business by Monica, n is the amount of effort put in by Nancy, and the
costs are m2 and n2 to Monica and Nancy respectively (in
tens of thousands of dollars).

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The terms of their partnership still require that the
joint profits be split equally, despite the fact that Monica is more
productive. Assume that their effort decisions are made simultaneously.

(a) What is Monica’s best response if she expects Nancy
to put in an effort of  

(b) What is the Nash equilibrium to this game?

(c) Compared to the old Nash equilibrium found in
Exercise S10, part (c), does Monica now put in more, less, or the same amount
of effort? What about Nancy?

(d) What are the final payoffs to Monica and Nancy in the
new Nash equilibrium (after splitting the joint profits and accounting for
their costs of effort)? How do they compare to the payoffs to each of them
under the old Nash equilibrium? In the end, who receives more benefit from
Monica’s additional training?

 

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