This simple agency problem is designed almost entirely for a spreadsheet. Below you will see a printout of a spreadsheet with mostly empty cells. Your goal is to fill in the blank cells. You will be thinking of this firm as experimenting with different values of the commission rate, b, ranging from zero to 1.5, as shown in the first column of the table.
Assume:
Effort = E
Output = Q = dE (d is a "productivity parameter"; higher levels of d correspond to higher productivity)
Disutility of Effort = C(E) = E2
Agent's reward = Y = a + bQ
Agent's Utility = Y- C(E)
In your "base" calculation, let d=20. (But allow the spreadsheet to input alternative values for d).
a) Given the different values of b in column one, fill in the agent's choices of effort, his output, and his total commission income in the next three columns. (By commission income we mean only the part of his income that depends on how much he produces, i.e. bQ).
b) Suppose that, to get the agent to work at this firm at all, he must attain an overall utility level of 20 (this is what he can get at another firm). For each row of the table (i.e. for each different value of b under consideration), calculate the level of a the firm must offer the agent to induce him to come to the firm. Hint: remember that the agent's total income must be at least 20 because he gets disutility from effort too.
Attachment:- #3 and #4.pdf