Several questions about Economics and Industrial Organization.
In part C, the equation for joint surplus has two w terms. The first w term has an H subscript, but the second w has no subscript. The second w should have a J subscript. The expression in parentheses on the right hand side of equation (5) is the firm’s profit on the efforts of H and J: the revenue that H and J generate, r, minus the compensation paid to each, w_H and w_J.
In part B, it says current effort = 1. Please ignore this, as it is wrong. Current effort, in answer to part A, is 0.816 (or the square root of 2/3). Please show how you arrive at this answer in part A, and use this answer as you solve part B.
Also, in part E, there is no mention of a change in wages. This is deliberate, but I now want to give you a hint. In answering whether the monitoring scheme could increase firm profits (above zero, currently), you have to consider both whether the firm can earn higher profits and whether the workers are willing to work at the higher effort levels e* from your answer to part C. Put differently, is there enough of an increase in revenues from high effort (minus the monitoring cost) to make both the firm and each worker better off in the monitoring scheme than initially?
In part G, to be clear the revenue r* is the outcome of the optimal effort levels e* from your answer to part C. The bonus b must be large enough that the workers accept this scheme instead of their outside optionQ
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