Finance-Based Question

solomonflow

Hey guys,

I have a repeat examination coming up soon and I'm having a particular problem with the the following kind of scenario. I'm not really sure how to calculate the answers to the following types of questions. Obviously, what follows isn't an actual exam question but it's the kind of area where I'm a little confused.
If any of you guys could provide solutions (with some sort of explanation/workings) to any of the following questions, it'd be very much appreciated.

Thanks guys!:o

The hypothetical scenario is as follows:

Consider the information below:
For Group K the cost of attaining an educational level y is C(K)=2000y

and for Group M the cost of attaining that level is C(K) =4000y

Employees will be offered $30,000 if they have y < y*, where y* is an education threshold determined by the employer.

They will be offered $90,000 if they have y>y*.


7. Refer to the Scenario above. The highest level of y* that can be set and still have the high-productivity people choose to meet it is
a. 90.
b. 60.
c. 30.
d. 22.5.
e. 15.

8. The lowest level of y* that can be set and have only the high-productivity people meet it is
a. 90.
b. 60.
c. 30.
d. 22.5.
e. 15.

9. If the threshold educational level y* is set at 45,
a. only individuals in Group K will attain it.
b. only individuals in Group M will attain it.
c. individuals in both groups will attain it.
d. no individuals will attain it.
e. some fraction of individuals in each group will attain it.

10. Refer to Scenario 2. If the threshold educational level y* is set at 13 1/3,
a. only individuals in Group K will attain it.
b. only individuals in Group M will attain it.
c. individuals in both groups will attain it.
d. no individuals will attain it.
e. some fraction of individuals in each group will attain it.

11. If the threshold educational level y* is set at 20,
a. only individuals in Group K will attain it.
b. only individuals in Group M will attain it.
c. individuals in both groups will attain it.
d. no individuals will attain it.
e. some fraction of individuals in each group will attain it.

12. An employer who only wants to hire those people who find learning less costly can do so by choosing y* to be anywhere between
a. 15 and 45.
b. 15 and 30.
c. 13 1/3 and 30.
d. 8 and 20.
e. None of the above.

Time Magazine

Hi solomonflow,

First of all this is not finance, it's microeconomics. Don't insult us microeconomists by suggesting we do finance :pac:

These questions are simple once you really understand the two equations:

For Group K the cost of attaining an educational level y is C(K)=2000y
For Group M the cost of attaining that level is C(M) =4000y

For argument's sake, imagine that y=3. Then the cost to Group K is 2000*3 = $6,000. The cost to Group M is 4000*3 = $12,000. So the cost is much higher for Group M than Group K. Specifically, it's twice as high.

If somebody is going to choose to do something, the benefits must be greater than (or equal to) the costs. So imagine a job is offered that requires three years of education (i.e. y=3) and the wage is $10,000. Only Group K will obtain the education necessary for the job because the costs to them of $6,000 are less than the benefits of $10,000. (Group M's will be "losing" $2,000 because the costs to them of $12,000 are less than the benefits of $10,000.)

Once you understand this logic, you can answer the questions above by yourself.

(I'll grant you imaginary bonus point if you spend a few minutes thinking about why this might explain why so few people do postgrads, even though they would offered a place.)

solomonflow

Hi Time Magazine,

Thanks a million for the response! I really do appreciate it.
Yeah, it was part of a microeconomics module, but somebody else insisted it was finance. Still though, my bad.:o

Oh, right. That's pretty straight forward then.

7. Answer: C (when e* = 30)
30*2,000 = 60,000
90,000-60,000 = 30,000 (30,000 = 30,000, so Group K is indifferent and so attain education at e* = 30)

8. Answer: D (when e* = 22.5)
22.5*2,000 = 45,000
90,000-45,000 = 45,000 (45,000 > 30,000, so Group K attain education at e* = 22.5)

22.5*4,000 = 90,000
90,000-90,000 = 0 (0 < 30,000, so Group M don't attain education at e* = 22.5)
At e* = 15, Group M would have been indifferent, and thus attained education.

9. Answer D (when e* = 45, neither group will attain education)
45*2,000 = 90,000
90,000-90,000 = 0 (0 < 30,000, so Group K will not attain education at e* = 45)

45*4,000 = 180,000
90,000 - 180,000 = -90,000 (-90,000 < 30,000, so Group M will not attain education at e* = 45)

10. Answer: C (when e* = 13 1/3, both groups will attain education)
13 1/3*2,000 = 26,660
90,000-26,660 = 63,340 (63,340 > 30,000, so Group K will attain education at e* = 13 1/3)

13 1/3*4,000 = 53,320
90,000-53,320 = 36,680 (36,680 > 30,000, so Group M will attain education at e* = 13 1/3)

11. Answer: A (when e* = 20, only Group K will attain education)
20*2,000 = 40,000
90,000-40,000 = 50,000 (50,000 > 30,000, so Group K will attain education at e* = 20)

20*4,000 = 80,000
80,000-90,000 = 10,000 (10,000 < 30,000, so Group M will not attain education at e* = 20)

12. Answer: e (none of the above)
Any of the above values for e* will either exclude or include both groups.

I hope the above are correctly answered.

In response to the postgrad question, I guess it's because some of these individuals' productivity wouldn't be high enough to justify the cost of the education. (i.e. For these individuals, the costs of this type of education would be greater than the benefits they could hope to enjoy upon graduation.)

Thanks a million again!
Your assistance is greatly appreciated!;)

solomonflow

Hi again,

Just wondering if anybody could help me with another micro-related question (though this one definitely has a finance premise):

There is a box. It has either €250 with a probability of 40% or €50 in it with a probability of 60%. We assume one would like to maximise expected value.

There is an individual who can tell you what is inside the box without opening it. What is the maximum fee one would pay to gain this information?

Thanks again.:o

Anonymous1987

Calculate the expected value of either occurrence
i.e. €250 with a probability of 40% or €50 in it with a probability of 60% os its: €250*0.6 + €250*0.4 = €130
Therefore you would not pay over the expected value €130. I'm not certain on this so better to wait on confirmation from other posters.

Économiste Monétaire

I look at this way. Assuming the agent is risk neutral (i.e., linear utility of wealth (w)),

E(w) = 250*0.4 + 0.6*50 = 130

or

w* = 250 (with certainty).

You're willing to pay for information up to 250 - 130 = 120

Économiste Monétaire

Actually, my answer looks wrong. Did you write out the whole question? Usually you're given a gamble and another amount with certainty. Is there a second option?

solomonflow

Hey guys,

Thanks a million for your responses.

In reply to Économiste Monétaire, yeah, there is a certain offer from a previous part:
Another individual offers him/her €140 for the box. The question pertaining to that part is: Would one accept this offer, given that he/she cannot be sure what is inside the box?
As you guys have mentioned, you can use the expected value to determine whether or not one should accept this offer.
i.e. (.4)250 + (.6)50 = 130 -- 140 > 130, so accept the offer.

However, I'm still unsure as to how to attain the maximum fee one should pay.

Thanks again!

Économiste Monétaire

That's the important part . What are you willing to pay to make that inequality (140 > 130) a strict equality? (i.e., so you will be indifferent between 140 for certain and the gamble.) Think of a cost of information, p,

[latex]\displaystyle 140 - p \geq 130 [/latex]

[latex]\displaystyle p \leq 10 [/latex]

Slippers 2

What about looking at the expected value of paying the fee?

There is a .6 chance that you find out that it's €50 and you are down the fee.
There is a .4 chance that you find out that it's €250, don't sell it, are up €110 and down the fee.

E(paying the fee) = .6(-f) + .4(110-f)

= - .6f + 44 - .4f

= 44 - f

As long as you pay less that €44 you will increase your expected value.

Does that look right?

Économiste Monétaire

That might be right. Another way to get that answer would be,

E(u(w)|p) = 0.6*(140) + 0.4*(250) = 184.

184 - 140 = 44

The value of information is 44. Hmm..