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# Pretty sure my professor was wrong but didn't want to start an argument watch

1. "The owner of a firm knows that its profits depend on the (good or bad) state of the economy. If good economy, profit = 400. If bad economy, profit = 200. The economy is good or bad with equal probability, 0.5.

What is the firm's expected profits (after bonus payment) if a bonus to the manager is given by the formula: Bonus = 0.20 x (Profit - 300)."
2. (Original post by voran)
"The owner of a firm knows that its profits depend on the (good or bad) state of the economy. If good economy, profit = 400. If bad economy, profit = 200. The economy is good or bad with equal probability, 0.5.

What is the firm's expected profits (after bonus payment) if a bonus to the manager is given by the formula: Bonus = 0.20 x (Profit - 300)."

This is a very simple question except for one little snag. Obviously the expected profit after bonus payment is 200+100-(Cost of bonus). Here's what I wrote:

Expected profit = 0.5x400 + 0.5x200 - 0.5[0.20x(400-300)] = 290

However, this is the professor's answer:

Espected profit = 0.5x400 + 0.5x200 - 0.5[0.20x(400-300)] - 0.5[0.20x(200-300) = 300

I believe that the professor's answer is wrong/dubious, because by including the final term, it assumes that the manager pays the firm a "negative" bonus if the firm makes 200 profit. I.e. if the economy does badly (=200 profit), then the bonus =0.2(200-300)=-20. But that is surely not true.

Thoughts?
In the real world, bonuses would only be positive normally, so I agree with you, not the prof.

But then again - some people think economics has little to do with the real world
3. You know, you didn't have to start an argument. It isn't considered bad form to discuss the question and in particular, clarify the assumptions.

I mean, you don't have to shout out "Hey ********, you're wrong!"

You could just say "The answer assumes that a negative bonus is paid in the event of a poor economy. Wouldn't it be more realistic to interpret the bonus as being zero when the formula produces a negative amount?" etc.
4. I feel we should bare in mind here the vast gulf between GAAP and economics where either answers possible.
5. Not enough information in the question really. Your prof has assumed that bonus is in ℝ, whereas you've assumed more realistically, that it's in [0,∞).

But since it's not specified in the question and presumably the context of the course is to work in real numbers, assuming bonus is in ℝ is probably the more correct assumption here. It's definitely a little ambiguous though.
6. (Original post by Mark85)
You know, you didn't have to start an argument. It isn't considered bad form to discuss the question and in particular, clarify the assumptions.

I mean, you don't have to shout out "Hey ********, you're wrong!"

You could just say "The answer assumes that a negative bonus is paid in the event of a poor economy. Wouldn't it be more realistic to interpret the bonus as being zero when the formula produces a negative amount?" etc.
Actually I did ask/raise the issue, but was offered an explanation that was not satisfactory. I'm not going to be the smartass ******** who argues with the prof.
7. (Original post by voran)
Actually I did ask/raise the issue, but was offered an explanation that was not satisfactory. I'm not going to be the smartass ******** who argues with the prof.
What was the explanation? I mean the explanation specifically about why you would want to assume a bonus system where employees pay money back?
8. (Original post by Mark85)
What was the explanation? I mean the explanation specifically about why you would want to assume a bonus system where employees pay money back?
They said that my formula was wrong and had no meaning. They said that the expected profit for the firm is given by

0.5x400 + 0.5x200 - [0.2(0.5(400) + 0.5(200) -300] = 300
9. (Original post by voran)
They said that my formula was wrong and had no meaning. They said that the expected profit for the firm is given by

0.5x400 + 0.5x200 - [0.2(0.5(400) + 0.5(200) -300] = 300
You should have asked more specifically about the assumption in the question.

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