#Household Math - Searching for better income and the financial impact of the search...

Question

Let's say someone is earning $18/hr, working 40 hours per week. That person really wants to earn $20/hr but is unable to get that raise with their current employer. If the person quits work to seek out a $20/hr position, how many hours will have to be worked at the $20/hr job to make up for the lost $18/hr?

Answer

The answer depends on the time unemployed. It takes 9 hours at the higher wage to make up for every hour of being unemployed, 9 days for each day unemployed, 9 months for each month, etc...

Analysis

This question hinges on the time the person is out of work looking for a higher paying job. We can find an expression that will give us that relation.

Let's first look at the money being lost by looking for a new job. That can be expressed as 18N, where N is the number of working hours you aren't working (you are uNemployed).

Each day, where N = 8, you lose $18 X 8 = $144

Ok, so now to the amount of money you'll be making. We need to see that, once we're working again, we can essentially look at it as earning the $18/hr, plus earning an additional $2/hr that will make up for the unemployed time.

For each hour where that person could have been earning $18/hr, it'll take 9 hours for the $2/hr to make up for it. And so it'll take 9 days for each day of being unemployed.

If it takes a month to find the job, it'll be 9 months.

And so the message here is this - if the job search is liable to drag on, it might be advisable to find alternate means of earning more income.

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Questions and comments always welcome