Question

As you probably know, there is still a difference in wages for men vs. women in this country. Besides straight-up

discrimination and bias (which has been lessening over the decades), people point to many other factors that continue
to keep the average amount earned by a full-time, year-round female employee lower than males, on average (like
women taking more time off for maternity than men do for paternity, career selection, etc.).
Every ten years as part of the census, data is collected that gives the median income of "full-time year-round workers."
In 2010 the median income of FTYR workers was $42,800 for men, compared to $34,700 for women. In 1960, if you
adjust the wages to 2009 dollars, wages were $38,907 for men and $23,606 for women.
Based on this data, when might we predict women's wages might catch up to men's? Show all work you did to get
your answer. AND NO LINKS TO FILES OR ANYTHING LIKE THAT.

Answer 1

9514 1404 393

Answer:

year 2066

Explanation:

In order to do this, we need to make some assumptions. We'll assume that the 2010 wages are also in 2009 dollars. (If not, there's an inflation factor that needs to be accounted for.) We also need to assume the form of the change in wages over time. The simplest assumption there is that wages change linearly.

Then we can write equations for men's and women's wages as follows:

Using the 2-point form of the equation for a line, we have ...

y = (y2 -y1)/(x2 -x1)(x -x1) +y1

Men's wages

y = (42800 -38907)/(2010-1960)(x -1960) +38907

y = 77.86(x -1960) +38907

y = 77.86x -113,698.6 . . . . . where x is the year

Women's wages

y = (34700 -23606)/(2010 -1960)(x -1960) +23606

y = 221.88x -411,278

These values are equal when ...

77.86x -113,698.6 = 221.88x -411,278

297,580.2 = 144.02x . . . . . . . add 411278 -77.86x

2066.2 = x . . . . . . . divide by the coefficient of x

Based on this data we predict women's wages might catch up to men's in the year 2066, about 56 years from 2010.

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Alternate solution

In the 50 years from 1960 to 2010, the fraction of men's wages that women receive has increased from 23606/38907 ≈ 0.606729 to 34700/42800 ≈ 0.810748. That is a change of about 0.204 of men's wages in 50 years. The remaining fraction of 1-0.810748 = 0.189 might be expected to be wiped out in another (0.189/0.204)(50 years) = 46.4 years. That would be the year 2056.

The different results come from different assumptions. For the second solution, we assumed that the fraction improved linearly. Under the first assumption, that wages improved linearly, the fractional improvement is non-linear, and decreases over time.

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Additional comment

The usual assumption regarding things financial is that they change exponentially over time. If we use an exponential model, instead of a linear one, wage parity is reached in about 2046.