Justin is considering majoring in bioinformatics. He is considering three career options: working for a Silicon Valley start-up, working for a large pharmaceutical firm, or working for a university research center. Justin assesses the starting salary and the probability of getting a job in each area as:

Type of job Probability of getting a job Starting salary

Start-up .2 $45,000

Pharmaceutical .4 $80,000

University .3 $60,000

Unemployed .1 0

• Calculate Justin’s expected starting salary.
• Justin is considering hedging his bets by investing additional time and effort into a second major in chemical engineering which means he must spend another year in school. The cost of another year in school is tuition of $12,000 plus the foregone earnings he will have by delaying the start of his career. However, he estimates that the additional major will increase his starting salary in some areas as well as changing the probabilities he will work for any one type of employer and will open up another career path as follows:

Type of job Probability of getting a job Starting salary

Start-up .15 $48,000

Pharmaceutical .35 $84,000

University .20 $63,000

Chemical engineer .28 $90,000

Unemployed .02 0

Calculate Justin’s expected starting salary if he delays graduation by one year (ignore discounting at this time).

• Calculate the expected cost of achieving the extra degree.
• Now, let’s assume that, by taking on the additional course work, Justin must delay graduation by one year. Justin’s discount rate is 0%. Assume that he will work for an additional 25 years after he pursues his new degree and 26 years if he does not pursue the degree. Is the additional degree worth the additional cost (assuming a 0% discount rate and constant earnings for the rest of her career)? Why or why not?

Questions 5 - 7

Joan has two job offers. One is a straight $50,000 per year job. The other job pays $32,000 but comes with stock options. The current stock price is $1.30 and Joan will get 100,000 options which she can exercise in one year. If she does not exercise them at that time, they become worthless. If she does exercise them, she will buy the stock at a price of $1.30 and will sell it immediately if she can make a profit on the transaction. If she can’t make a profit, she will let them expire. Joan is considering what the future value of the stock will be and her thinking is:

Future Stock Price Probability

$.60 .2

$1.00 .2

$2.00 .4

$8.00 .2

• What is the expected price of the stock price in one year?
• Assume that Joan will only exercise the stock option if she can make a profit by doing so. Assume further that she considers her salary in the job with the stock option to consist of the base salary plus any amount she might gain from exercising the stock option. What is Joan’s expected income if she takes the job with the stock options?
• What is the probability that Joan can make at least $100,000 on the job with the stock options?

Questions 8 - 10

Jason plans on going on to get an MBA. He owns 20,000 shares of XYZ that are currently valued at $3.00 per share. Jason must sell the stock in one year to fund his MBA. He has a probability distribution around the price of the stock in one year when he must sell it that looks like:

Price per share Probability

$2.00 .2

$3.50 .4

$4.00 .2

$7.00 .2

• What is the expected price of the stock in one year?
• What is Jason’s expected gain on the sale of the stock in one year?
• Jason can buy a put option that will allow him to sell the stock in one year at a price of $2.70 per share. The cost of the option is $.15 per share. What is Jason’s expected gain on the sale of the stock in one year if he decides to buy the put option?

Questions 11 – 12

The total market demand for labor can be written as: Ld = 1,000 – 50w where L is labor demand and w is the hourly wage rate.

1. What is the equilibrium wage and quantity of labor employed if the labor supply function is: L = -800 + 100w? How much producer surplus is received?
2. Suppose the government imposes a minimum wage of $16 per hour. What is the new level of employment? How much producer surplus is now received?

Questions 13 - 17

John is currently working for a temp agency. He always gets some kind of job, sometimes working doing inventory, sometimes as a bartender and sometimes as a parking valet. The daily pay for each job and the probability of getting each job over a two day period is shown below:

Prday1 Prday2

Parking valet ($60) .4 .4

Bartender ($90) .3 .2

Inventory ($120) .3 .4

• Calculate the probability that John does the same job on each day.
• Given that John does the same job on each day, calculate his expected earnings over the two day period.
• Calculate the probability that John will earn less than $200 over the two day period.
• Given that John will earn less than $200 over the two day period, calculate the probability that he is a parking valet both days.
• What is John’s expected earnings over the two day period?

Questions 18 - 19

A monopsonist has the following demand for labor: L = 40 - .004w. The supply of labor to the monopsonist can be written as: w = 5 + .01L. The marginal cost of hiring another worker is thus: MC = 5 + .02L.

• How many workers will be hired and what wage will be paid by the monopsonist?
• Now suppose a union negotiates a wage rate of $25 for however many workers want to work for the firm at that wage. How many workers will now be hired?

Questions 20 – 21

The demand for workers can be written as: L = 24,000 – 30w. The supply of workers can be written as: L = -200 + 20w.

• Calculate the equilibrium wage rate and level of employment. Calculate the consumer and producer surplus.
• Now suppose that a payroll tax of $50 is imposed. What is the new gross wage (before tax) and the new number of workers hired? What is the new net wage (after tax). What is the new consumer surplus? Producer surpluss? Revenue raised by the tax? Deadweight loss from the tax?

Questions 22 - 24

Franco lives in Italy and earns $57,000 per year. He is considering a job offer in the U.S. that pays $64,000 per year for the next four years after which Franco will return to Italy to go to college. Franco estimates that the cost of moving is about $18,000 and he has a discount rate of 3%.

• What is the present discounted value of the move (do not discount the cost of the move but discount each year of earnings after the move?
• If Franco’s discount rate increased to 9%, what would be the present discounted value of the move?
• Now assume that the there is a 10% chance that the US job will fall through and that, if Franco makes the move, he will end up unemployed. In that case, what is the present discounted value of his earnings in the US if he makes the move?

Questions 25 - 26

Ricardo wants to go to school in Italy next year. He has $60,000 in savings for college and is trying to decide whether to convert the money into euros and invest them in an Italian bank that pays 8% interest or leave the money in the US in which case he earns 5%. The euro is currently trading at 1 euro = $1.30. His tuition must be paid in euros. He must take the money out in one year.

• Assume that, at the end of the year the euro is trading at 1 Euro = $1.45 and that Ricardo has left her money in a US bank and changed it into euros at the end of the year. How many euros will he have available to pay for school? How many euros would he have available if he had changed his dollars at the start of the year and put them in an Italian bank to begin with?
• Assume that, at the end of the year the euro is trading at 1 euro= $1.10. If Ricardo had left his money in the US bank and changed it into euros at the end of the year, how many euros would he have for school? How many euros would he have had if he had changed his $ into euros at the start of the year?

Questions 27 - 30

Pharma Medical is trying to decide which of two medical tests to use in testing for a specific disease. The two tests are described below in terms of their true positive, true negative, false positive and false negative rates. Test one costs $500 to administer and test 2 costs $2,000 to administer. Under each test, anyone who tests positive receives surgery at a cost of $70,000 per surgery. 60% of the true positives who receive surgery are saved and the remaining 40% die.

Outcome Test 1 Test 2

True positive .040 .042

True Negative .870 .880 .

False Positive .045 .035

False Negative .045 .043

Assume the test is to be administered on 1,000 people.

• Calculate the false positive rate for each test. (What % of the positives are false positives and what % of the negatives are false negatives?)
• Calculate the false negative rate for each test (What % of the negatives are false negatives?)
• Calculate the total cost of conducting each testing scenario (total cost of testing plus surgery for 1,000 people)
• Calculate the cost per life saved under each testing scenario.