Question

Penny is considering a sales position at a risk-neutral company. If she works hard, there's a 90% chance of earning $1 million and a 10% chance of earning $500,000. Alternatively, if she pays no effort, the chances change to 40% for $1 million and 60% for $500,000. Penny currently earns $30,000 a year at a restaurant with no effort. What is Penny's total expected income (including her restaurant job) if she takes the sales job and works hard?

a) $1,030,000

b) $1,000,000

c) $800,000

d) $900,000

Answer 1

After calculating the expected income from the sales job by summing the probabilities of the outcomes multiplied by their respective incomes, and adding Penny's current income, the result is $980,000. However, this answer is not reflected in the options provided, indicating a possible error in the question or the options.

Step-by-step explanation:

To calculate Penny's total expected income (including her restaurant job) if she takes the sales job and works hard, we need to first find the expected income from the sales position. The expected income from working hard in the sales job can be calculated through the expected value formula:

Expected income = (Probability of outcome 1 x Income from outcome 1) + (Probability of outcome 2 x Income from outcome 2)

In this case:

Expected income = (0.90 x $1,000,000) + (0.10 x $500,000)

Expected income = ($900,000) + ($50,000)

Expected income = $950,000

Now, we add Penny's current job income to this expected income from the sales position:

Total expected income = Expected income from sales job + Current job income

Total expected income = $950,000 + $30,000

Total expected income = $980,000

However, none of the given options matches this calculated value. It seems there might be a mistake either in the question or the answer choices provided. Penny's total expected income (including her current restaurant job) if she takes the sales position and works hard is $980,000.