Question

A​ firm's short-run revenue is given by:

R=10e−e²​, where e is the level of effort by a typical worker​ (all workers are assumed to be​ identical). A worker chooses his level of effort to maximize wage less​ effort, given by ​(w−e​). ​(Note: the​ per-unit cost of effort is assumed to be​ 1).

Determine the level of effort and the level of profit​ (revenue less wage​ paid) for each of the following three wage arrangements. Explain why these different​ principal-agent relationships generate different outcomes

a. w​ =​$22 for e≥​1; otherwise w​ =0. ​(Enter your response rounded to one decimal place.​)

The level of effort is ___ and the profit is $___

In this principle-agent relationship, there is or is not an incentive for the worker to increase his or her effort as the wage is not related to the revenues of the firm.

b. w=R/2

The level of effort is ___ and the profit is $___

In this principle-agent relationship, there is or is not an incentive for the worker to increase his or her effort as the wage is not related to the revenues of the firm.

c. w= R-12.5

The level of effort is ___ and the profit is $___

In this principle-agent relationship, there is or is not an incentive for the worker to increase his or her effort as the wage is not related to the revenues of the firm.

Answer 1

​​​so in first case , there was no incentive for the worker to increase his efforts as the wage was not related to revenue. But in the second and third case , the wages were related to revenue, so worker had the incentive to increase the efforts being put in.

(You can comment in case of any doubts)