1. Pretty easy: Consider the problem of costly signaling through education, that was in the book and that I went over in class.  Suppose that a "Challenged" student felt that taking a Tough Course was the equivalent of a loss of $13,000 a year in future salary.  (In the version I discussed, it was $9,000 a year.)  As before, an Able student sees a Tough Course as the equivalent of a loss of $6,000.  What's the minimum number of courses could an employer for the $150,000 salary?  Briefly explain your reasoning.

 

2.  Costly signaling, sort of from the te Suppose electricians come in two types: competent and incompetent. Both types can get certified by taking a training course, but for the incompetent types, certification takes extra time and effort. Competent ones have to spend C months preparing for a certification exam: incompetent ones take twice as long. Certified electricians can earn $100,000 when they work for licensed contractors. Uncertified electricians can only earn $25,000 each year for freelance.  Each type of electrician gets a payoff of (Yearly Salary)/2000 - (Months to Get Certified).  What is the lowest value of C for which a competent electrician will choose to signal by getting certified, but an incompetent one will not?  

 

(This sounds complicated, but it is exactly parallel to the education example in the book.  Follow what the book does for taking courses, and just switch it over to this case.)

 

3. From the text quoting a review of a book by Michael Lewis who also wrote Moneyball and The Big Short, "Mr. Robinson (the MBA-graduate author of the book) pretty much concludes that business schools are a sifting device - MBA degrees are union cards for yuppies. 'But perhaps the important fact about the Stanford business school is that all meaningful sifting occurs before the first class begins. No messy weeding out is done within the walls. They don't want you to flunk. They want you to become a rich alum who'll give a lot of money to the school.' But one wonders if corporations are abdicating to the Stanford admissions office the responsibility for selecting young managers, why don't they simply replace their personnel departments with Stanford admissions officers, and eliminate the spurious education? Does the very act of throwing away a lot of money and two years of one's life demonstrate a commitment to business that employers find appealing?"

 

How would you answer Lewis's question, in two or three sentences? 

 

4. Snake handling in certain religions, hazing in past fraternities - choose one and say in a sentence or two why it is a costly signal?   You might answer: What is the cost?  Who is signaling to who?

 

 

 

 

 

 

 

5. (a) The Republican South Carolina primary is this Sunday, Feb 20.  Let's assume that there are only four Republican voters in all of South Carolina.  The four citizens rank the four Republican candidates starting from their favorite on the left to their least favorite on the right.  

Using T for Trump, R - Rubio, C- Cruz, B - Bush,

 

Citizen 1.   T, R, C, B             (most preferred to least preferred)

Citizen 2.   B, T, C, R

Citizen 3.   B, T, R, C

Citizen 4.   C, T, R, B

 

Which candidates are Pareto efficient for these four citizens?  If anyone is not Pareto efficient say why.  

 

(b) Suppose there were 4004 voters, in groups with the following sizes and preference rankings as shown.:

Group 1 (size 4 voters )        T, R, C, B

Group 2 (size 1000 voters)   B, R, C, T

Group 3 (size 2000 voters)   R, B, C, T

Group 4 (size 1000 voters)   C, R, B, T

 

Which candidates are Pareto-efficient for these 4004 voters?  (You should be able to look at this and give the answer in a second.)

 

(c) Assume again that there are only 4 Republican citizens and they have these preferences

 

Citizen 1. T, R, C, B

Citizen 2. B, R, C, T

Citizen 3. B, R, T, C

Citizen 4. C, T, R, B

 

Who would win by a majority vote?  (That means that candidate with the most first place votes wins.)

 

Here's a topic that hasn't come up in class yet but it's not difficult and you should be able to do it before the lecture.  The Center for World Control, which runs elections, decides to change the voting system.  It's no longer majority vote.  The new one works as follows: a candidate gets 4 points for being a voter's first choice, 3 for being a voter's second, 2 for third and 1 for fourth. Each candidate's points are summed over each of the four voters.  For example, in this case T would get 4+1+2+3 = 10 points total.  This is called the Borda method.  The candidate with the highest total wins.  Who would win?   

 

(d) This is a little harder, but not terrible.  If some candidate is not Pareto efficient for the voters, could that candidate ever win by the Borda method?  Say in a sentence why or why not.

 

 

Question A on my homework is to solve each of these sub-questions, but I don't understand this section of the course. I've tried to figure it out, but it's due by midnight on 10/24 and I'm out of guesses.  Can you help me? 

1. Joanne sells silk-screened t-shirts at a community festival. Her marginal cost to produce
one t-shirt is $3.50. Her total cost to produce 60 t-shirts is $300, and she sells them for
$7 each. Use Python to graph this information and determine the number of t-shirts
Joanne must produce and sell to break even.

2. A Rent-A-Truck company plans to spend $14 million on 280 new vehicles. Each
commercial van will cost $55,000, each small truck $20,000, and each large truck
$70,000. Past experience shows that they will need twice as many vans as small trucks.
How many of each vehicle can they buy?

3. A pharmacist mixes together three types of vitamin tablets. Each tablet A contains,
among other things, 13 mg of niacin and 11 IU of vitamin E. The amounts for a tablet B
are 18 mg and 14 IU, and for a tablet C are 23 mg and 36 IU. Use Python to determine
how many of each tablet there are if there are 225 total tablets, 4300 mg of niacin, and
5200 IU of vitamin E.

4. A pension fund manager decides to invest a total of at most $35 million in US Treasury
bonds paying 5% annual interest and mutual funds paying 8% annual interest. He plans
to invest at least $5 million in bonds and at least $10 million in mutual funds. Bonds
have an initial fee of $100 per million dollars, while the fee for mutual funds is $200 per
million. The fund manager is allowed to spend no more than $6000 on fees. How much
should be invested in each to maximize annual interest? What is the maximum annual
interest?

5. Jayla is raising money for the homeless and discovers each church group requires 2 hours
of letter writing and 1 hour of follow-up calls, while each labor union needs 2 hours of
letter writing and 3 hours of follow-up. She can raise $100 from each church group and
$175 from each union. She has a maximum of 20 hours of letter writing and 14 hours of
follow-up available each month. Determine the most profitable mixture of groups she
should contact and the most money she can raise in a month.

6.Recreate the following graph using Python. Be sure to replace 'Red Line' and 'Blue Line
with the correct inequalities. (See attachment for graph.)

7. Francesca wants to start exercising to burn at least 1200 extra calories per week, but she
does no have much spare time for exercise. According to a website, she can burn an
average of 2.5 calories per minute walking, 4 calories per minute cycling, and 8 calories
per minute swimming. She would like her total time walking and cycling to be at least 3
times as long as she spends swimming. Show would also like to walk at least 20 minutes
per week. How much time should she spend on each activity not only to meet her goals,
but also to minimize her total exercise time per week?

8. A plant food is made from three chemicals, labeled I, II, and III. In each batch of the
plant food, the amounts of chemicals II and III must be in the ratio of 5 to 3. The amount
of nitrogen must be at least 29 kg. The percent of nitrogen in the three chemicals is 8%,
4%, and 5%, respectively. If the three chemicals cost $1.03, $0.83, and $0.68 per
kilogram, respectively, how much of each should be used to minimize the cost of
producing at least 650 kg of the plant food?

9. Among uses of automated teller machines (ATMs), 93% use ATMs to withdraw cash and
32% use them to check their account balance. Suppose that 96% use ATMs to either
withdraw cash or check their account balance (or both). Given someone who uses an
ATM to check his or her balance, what is the probability that this person also uses an
ATM to withdraw cash?

10. A study showed that in 1990, 49% of all those involved in a fatal car crash wore seat
belts. Of those in a fatal crash who wore seat belts, 46% were injured and 27% were
killed. For those not wearing seat belts, the comparable figures were 41% and 52%,
respectively. Find the probability that a randomly selected person who was unharmed in
a fatal crash was not wearing a seat belt.

 

Attachments:

• 1492657014-MBA 6300 week 1 homework questions.docx