Consider yet another variation on Examples 16.1 through 16.4, where everything remains as…

Consider yet another variation on Examples 16.1 through 16.4, where everything remains as specified except the probabilities. The probabilities are specified below. Determine a value for π(y = g|H) = α such that (1) the monitor is useless and not controllable, (2) useful and allows zero risk premium, (3) useful and implies observing y = g is “good” news and (4) useful and implies observing y = g is “bad” news. Verify each of your claims by solving for the associated optimal contract.

((Example 16.1: Assume the manager’s input can be H or L, with H preferred by the firm. Output can be either x1 or x2 (with x1

As a benchmark, if output itself is the only contractible variable it is routine to verify the optimal pay-for-performance arrangement has respective (low and high output) payments of I ∗ x1 = 0 and I ∗ x2 = 7, 305.66. The firm’s cost is C(H) = 3, 652.83 and the manager’s risk premium is 652.83. (This should be familiar.)

Next (continuing to reprise the earlier example) we introduce an additional performance measure. This measure will report either y = g or y = b. The probabilities are specified in Table 16.1, where you should note that absent the additional measure we are back to the benchmark setting of π(x1|H) = π(x2|H) = .50 and π(x1|L) = 1.

Also notice the new, improved optimal pay-for-performance arrangement displayed in Table 16.1.1 The additional measure is useful, as we have I ∗ x1g > I∗ x1b . Following our earlier definition in Chapter 14, it is also informative, as the conditional likelihood measure of expression (14.10) is a nontrivial function of measure y (when x1 obtains). Overall, the firm’s cost is reduced to C(H) = 3, 148.70, which implies a risk premium for the manager of 148.70

Now check out the new measure’s controllability by the manager. Notice, glancing at the probabilities in Table 16.1, that we have π(g|H) = .75, π(b|H) = .25, π(g|L) = .20 and π(b|L) = .80. The respective unconditional likelihood ratios, using expression (16.1), are LRg = 20/75

((Example 16.4: Finally, consider yet another variation, that in Table 16.4. Here the new measure is not useful, is not informative; but is controllable by the manager.

The competing tests are once again in conflict. The optimal contract ignores the additional information. The new measure fails the informativeness test, but is surely controllable by the manager.

What are we to conclude? Informativeness, as assessed by the conditional likelihood ratio is the gold standard here. And, as evidenced by the four examples, there is no logical connection between controllability and informativeness. In Example 16.1 they are both present, and in Example 16.2 they are both absent. In Example 16.3 we have informativeness and absence of controllability, while in Example 16.4 we have controllability and absence of informativeness. There simply is no logical connection between informativeness and controllability.

The slippage, or error if you want to be less polite, is in how the presence of other information is handled. Controllability asks whether the manager can affect the statistical description of the new measure, regardless of what other information is present. While intuitive and, yes, simple, this ignores what is already being learned from the other information as well as any possible interactions between the existing and the new measures. Informativeness, on the other hand, stresses whether the manager can affect the statistical description of the new measure, conditional on what other information is present.3

Both tests boil down to a nonconstant, well-chosen likelihood ratio. The difference is informativeness looks for new information; it is conditional on the existing information. In this sense, informativeness could be interpreted as conditional controllability, controllability that is conditioned on what is already being learned from other information sources. This, however, is just another way of saying the fundamentals come down to whether the conditional likelihood ratio is nonconstant.4

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.
Don't really see any of sources I provided, but elsewise its great, thank you!
Customer 452697, May 8th, 2021
Thank you
Customer 453087, March 5th, 2022
English 101
Thank you for this excellent analysis of the Alchemist.
Customer 453213, June 15th, 2022
Customer 452591, March 18th, 2021
It was a very long paper, but she followed all the instructions, and she even finished the paper 5 days before the due date. Will write an essay with her again, thanks!
Customer 452967, November 27th, 2021
English 101
great summery in terms of the time given. it lacks a bit of clarity but otherwise perfect.
Customer 452747, June 9th, 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
Customer 453057, May 23rd, 2022
Health Care
awesome work
Customer 452777, October 14th, 2021
The writer was timely and proficient. I had to ask for a revision, but I got it back quickly with no other issues. Would use this essay writing service again
Customer 452441, November 14th, 2021
Emergency Management
Overall, I think it's a great service. I have yet to submit the assignment, so I don't know what kind of grade I'll get. But customer service was excellent. Reviews were made and the assignment proofed for satisfaction.
Customer 453015, December 15th, 2021
Love this writer!!! Great work
Customer 452597, April 5th, 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