A firm's revenue R is stochastically related to the effort exerted by its employee. Effort is a continuous variable. The employee can choose any level of effort e E [0, o0). The choice of effort affects revenue so that: E(R|e) = e and Var(R|e) = 1 where E(R|e) and V ar(R|e) denote the expected value and variance, respectively, of rev- enue when the employee exerts effort level e. The employer cannot observe the level of effort exerted by the employee. The employer wants to design a wage contract w based on the revenue and considers only contracts of the form: w = a + BR, and so the employee is guaranteed a payment a and then a bonus payment ßR which de- pends on revenue. The employee is a risk-averse expected utility maximiser. A contract w gives expected utility: 1 Eu(w\e) = E(w\e) - eV ar(w\e) – c(e) where E(wle) and Var(w\e) denote the expected value and variance of the contract, re- spectively, conditional on effort e, p is a parameter of risk aversion, and c(e) denotes the disutility of effort. For this employee, c(e) = ;e². If the employee rejects the contract, they receive reservation utility of zero. Explain how the employer can implement a level of effort ē.
A firm's revenue R is stochastically related to the effort exerted by its employee. Effort is a continuous variable. The employee can choose any level of effort e E [0, o0). The choice of effort affects revenue so that: E(R|e) = e and Var(R|e) = 1 where E(R|e) and V ar(R|e) denote the expected value and variance, respectively, of rev- enue when the employee exerts effort level e. The employer cannot observe the level of effort exerted by the employee. The employer wants to design a wage contract w based on the revenue and considers only contracts of the form: w = a + BR, and so the employee is guaranteed a payment a and then a bonus payment ßR which de- pends on revenue. The employee is a risk-averse expected utility maximiser. A contract w gives expected utility: 1 Eu(w\e) = E(w\e) - eV ar(w\e) – c(e) where E(wle) and Var(w\e) denote the expected value and variance of the contract, re- spectively, conditional on effort e, p is a parameter of risk aversion, and c(e) denotes the disutility of effort. For this employee, c(e) = ;e². If the employee rejects the contract, they receive reservation utility of zero. Explain how the employer can implement a level of effort ē.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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![A firm's revenue R is stochastically related to the effort exerted
by its employee. Effort is a continuous variable. The employee can choose any level of
effort e E [0, ). The choice of effort affects revenue so that:
E(R|e) = e and Var(R|e) = 1
%3D
where E(R|e) and V ar(R|e) denote the expected value and variance, respectively, of rev-
enue when the employee exerts effort level e. The employer cannot observe the level of
effort exerted by the employee. The employer wants to design a wage contract w based on
the revenue and considers only contracts of the form:
w-α+ βR
and so the employee is guaranteed a payment a and then a bonus payment ßR which de-
pends on revenue. The employee is a risk-averse expected utility maximiser. A contract w
gives expected utility:
Eu(w\e) = E(w\e)-eV ar(w]e) – c(e)
where E(wle) and Var(wle) denote the expected value and variance of the contract, re-
spectively, conditional on effort e, p is a parameter of risk aversion, and c(e) denotes the
disutility of effort. For this employee, c(e) = ;e². If the employee rejects the contract, they
receive reservation utility of zero.
Explain how the employer can implement a level of effort ē.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F85963db8-918e-4b79-bdc4-775d0c35cd44%2Fca2134e1-e1f5-4453-ad83-97dffb09552f%2Fohjjj6_processed.png&w=3840&q=75)
Transcribed Image Text:A firm's revenue R is stochastically related to the effort exerted
by its employee. Effort is a continuous variable. The employee can choose any level of
effort e E [0, ). The choice of effort affects revenue so that:
E(R|e) = e and Var(R|e) = 1
%3D
where E(R|e) and V ar(R|e) denote the expected value and variance, respectively, of rev-
enue when the employee exerts effort level e. The employer cannot observe the level of
effort exerted by the employee. The employer wants to design a wage contract w based on
the revenue and considers only contracts of the form:
w-α+ βR
and so the employee is guaranteed a payment a and then a bonus payment ßR which de-
pends on revenue. The employee is a risk-averse expected utility maximiser. A contract w
gives expected utility:
Eu(w\e) = E(w\e)-eV ar(w]e) – c(e)
where E(wle) and Var(wle) denote the expected value and variance of the contract, re-
spectively, conditional on effort e, p is a parameter of risk aversion, and c(e) denotes the
disutility of effort. For this employee, c(e) = ;e². If the employee rejects the contract, they
receive reservation utility of zero.
Explain how the employer can implement a level of effort ē.
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