library(exams)
exams_skeleton(markup = "markdown", encoding = "UTF-8",
  writer = c("exams2html", "exams2pdf", "exams2moodle"))
options(scipen=999)

Question

You just graduated from university with a BA diploma in Business Analytics. You were searching for Data Scientist positions and found 2 options. One of them is in another country, but more profitable. Another vacancy is in your hometown, but it is just an internship with a probability to be promoted.

You were offered 2 positions: - to work for \(81000 NOK\) per annum in another country. Cost of re-allocation (visa, transportation) is \(10 NOK\) and housing will cost you \(24000 NOK\) per year. - to work as an intern for \(81000 NOK\) per annum in your hometown, with a \(0.1 %\) probability to get full-time DS position (\(170100 NOK\)) at the end of every year of employment. If you stay in the hometown you are living with parents and donโ€™t pay for the housing. However, there is a \(0.4\) probability that they will kick you out at the end of the first year of employment and you will have to pay \(72900 NOK\) per year for a new flat for the rest 2 years.

  1. Calculate expected utility (after 3 years of employment) for each option and chose the optimal one
  2. Consider another option. If you work in your hometown, you can start paying \(8000 NOK\) to your parents for the flat from the very beginning. It will lower the probability to be kicked out to \(0.2\) . Is it a better choice?

Solution

For the work in the another country we have:

\[ \begin{aligned} option1 &= salary1 * 3 years - visa - house * 3years \\ &= 81000 * 3 - 10 - 24000 * 3 \\ &= 170990. \end{aligned} \]

Fort the stay home as intern we need to take into account conditional probabilities, because some events are mutually exclusive:

\[ \begin{aligned} earnings &= salary2 + probProm * salary3 * 2 + (1-probProm) * salary2 + (1-probProm) * probProm * salary3 + (1-probProm)*(1-probProm)*salary2 \\ &= 81000 + 0.1 * 170100 * 2 + (1 - 0.1) * 81000 + (1 - 0.1) * 0.1 * 170100 + (1 - 0.1) * (1 - 0.1)*81000 \\ &= 268839. \\ \\ spendings &= - probKick * flat * 2 \\ &= - 0.4 * 72900 * 2 \\ &= option2_spe.\\ \\ optoion2 &= earnings - spendings \\ &= 268839 - 58320 \\ &= 210519. \end{aligned} \]

and finaly, option #3:

\[ \begin{aligned} option3 &= 218879 \end{aligned} \]

Meta-information

extype: num exsolution: 170990.00 exname: essay1 extol: 0.01