Return to Example 15.2, but now assume the second variable has a variance of s 2 = 5, 000….

Return to Example 15.2, but now assume the second variable has a variance of σ 2 = 5, 000. Determine an optimal (linear) contract. Explain the difference between this contract and that in the original setting.

((Example 15.2 To illustrate, stay with the setting in Example 15.1 and assume the new information variable is structured precisely as the original one. So we have x = a1 + .7a2 + ε and y = a1 + .7a2 + ε along with σ 2 = σ 2 = 10, 000. Think of this as a random sample of size two. In any event, solving program (15.12) provides β ∗ 1 = β ∗ 2 = .10, ω ∗ = −30 and a cost to the firm of C(H) = 70. This cost is less than the original example’s cost of C(H) = 80. To provide the intuition, notice that for any contract described by (15.9), the manager’s risk premium will be

We know from our earlier work that the manager will allocate all of his input to the first task. His certainty equivalent if H is supplied is therefore

Motivating H requires CEH ≥ CEL, or β1 + β2 ≥ cH H−L = 60 500−200 = .20. This reflects the fact here that the sum of the piece rates is the source of the incentive. With this observation, it is clear we want to minimize the manager’s risk premium while simultaneously ensuring the two piece rates sum to .20. With the additional information, this means we want to minimize 500[β 2 1 + β 2 2 ] subject to β1 + β2 ≥ .20. And we thus have β1 = β2 = .10. From here, setting CEH = 0 provides ω = −30. But the central observation is the fact the second variable allows us to diversify the noise in the original performance measure, thereby creating a (modest) portfolio of performance measures that, in total, lowers the performance assessment noise and thus the manager’s risk premium.

Example 15.2, then, is a case where an additional performance measure is useful. And this returns us to the informativeness criterion. Is variable y in the example informative in the presence of measure x? Definitely. With independence between the two error terms (ε and ε), we readily conclude the conditional likelihood ratio (expression (14.10) to be precise) in this case is

With independent error terms, knowledge of measure x has no effect on our assessment of variable y’s likelihood ratio. The new information is an independent assessment, unaffected by what we have learned from the first measure. And this likelihood ratio surely suggests variable y informs us about the manager’s behavior.10

Notice, however, that the control problem is well isolated here. It centers on the choice between L and H, because we assume the firm wants the input used exclusively on the first task and the performance measures more heavily weight that first task. Given this, the additional performance measure speaks precisely to the control problem of motivating choice of H over choice of L.

Calculate the price
Make an order in advance and get the best price
Pages (550 words)
*Price with a welcome 15% discount applied.
Pro tip: If you want to save more money and pay the lowest price, you need to set a more extended deadline.
We know how difficult it is to be a student these days. That's why our prices are one of the most affordable on the market, and there are no hidden fees.

Instead, we offer bonuses, discounts, and free services to make your experience outstanding.
How it works
Receive a 100% original paper that will pass Turnitin from a top essay writing service
step 1
Upload your instructions
Fill out the order form and provide paper details. You can even attach screenshots or add additional instructions later. If something is not clear or missing, the writer will contact you for clarification.
Pro service tips
How to get the most out of your experience with Online Academic Experts
One writer throughout the entire course
If you like the writer, you can hire them again. Just copy & paste their ID on the order form ("Preferred Writer's ID" field). This way, your vocabulary will be uniform, and the writer will be aware of your needs.
The same paper from different writers
You can order essay or any other work from two different writers to choose the best one or give another version to a friend. This can be done through the add-on "Same paper from another writer."
Copy of sources used by the writer
Our college essay writers work with ScienceDirect and other databases. They can send you articles or materials used in PDF or through screenshots. Just tick the "Copy of sources" field on the order form.
See why 20k+ students have chosen us as their sole writing assistance provider
Check out the latest reviews and opinions submitted by real customers worldwide and make an informed decision.
Social Work and Human Services
Although it took 2 revisions I am satisfied but I did receive it late because of that.
Customer 452603, March 25th, 2021
Human Resources Management (HRM)
Very well written and very impressed with this service!
Customer 453077, February 16th, 2022
Very fast response and did a excellent job.
Customer 453201, May 31st, 2022
Thank you!
Customer 452545, February 6th, 2021
Nice work
Customer 453185, May 21st, 2022
Social Work and Human Services
Great work I would love to continue working with this writer thought out the 11 week course.
Customer 452667, May 30th, 2021
IT, Web
Awesome paper in such a short amount of time. Was in a jam with another service who didn't deliver, but Theresa did the job correctly. I will use her again to do my essays for sure!
Customer 452967, November 27th, 2021
Human Resources Management (HRM)
I finished the first deliverable of a project presentation but had no time to finish my second deliverable. The writer revamped my first deliverable and made it much more appealing! Not only was I impressed with the content but I was so grateful for the time they took to redo the background. I have been under a lot of pressure at work and at home so this has been a great service when I have had little time! I appreciate the detail and help! Always on time and always exceeding expectations!
Customer 453077, April 5th, 2022
Classic English Literature
It was my first time using such a service. Essay was good and nicely formatted.
Customer 452441, February 16th, 2022
Business Studies
First of all, the writer made sure that he completely understood my assignment and all the guidelines before he began writing. My paper was finished very fast and well before the specified deadline. I thought it was written excellently. He definitely completely grasped the topic. Overall, he is a great writer and I couldn't have asked for better.
Customer 452441, November 29th, 2021
Human Resources Management (HRM)
My son and I have been sick for two weeks, of course at the end of my semester. I am so grateful that myhomeworkgeeks were able to help! Both papers got A's and I couldn't be more thrilled! Thank you so much and don't forget to tip your writer!
Customer 453077, February 22nd, 2022
English 101
great summery in terms of the time given. it lacks a bit of clarity but otherwise perfect.
Customer 452747, June 9th, 2021
Customer reviews in total
Current satisfaction rate
3 pages
Average paper length
Customers referred by a friend
15% OFF your first order
Use a coupon FIRST15 and enjoy expert help with any task at the most affordable price.
Claim my 15% OFF Order in Chat
Live ChatWhatsApp