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Mathematics & Economics
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Math Problem
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Piecework & Working for the minimum wage. Problem solving paper

Math Problem Instructions:

solve problem in excel
1.Piecework (Exercise 4.7.8 from the textbook)
In the 1880s many young women in large cities worked at home sewing clothing. They were paid by the piece, hence the name “piecework” for this type of labor. A pants stitcher would finish a pair of pants, putting in canvas for the pockets and waistband linings, and would receive 12.5 cents per pair of pants finished. She could generally finish 16 pairs of pants a week, working from 8 am until dark. [You can read more about this on the web at historymatters.gmu.edu/d/5753/ ]
What was her hourly rate of pay in 1880? What assumptions did you make about working hours per week: How many hours per day? How many days per week?
Convert her 1880 wages to current (2019) wages.
Compare her hourly rate to the current minimum wage.
2.Working for the minimum wage (Exercise 4.7.22 from the textbook, plus commentary) 

Figure out the annual income in 2019 dollars for someone who worked at a minimum wage job 40 hours/week for 50 weeks in 1975.
Compare that income to the annual income of someone working the same hours and weeks at the minimum wage in 2019.
What do you think is a fair minimum wage? Should it be different for different states or cities, reflecting their cost of living?
EXTRA: Which of the states, counties, cities, or companies in the US do you think have a fair minimum wage, based on information presented at https://www(dot)businessinsider(dot)com/minimum-wage-2019-state-map-2018-12 ? How reliable is this source?
EXTRA: Which states/counties do you think pay teachers fairly? What do you think constitutes fair pay? How did the in-class exercise and discussion “Budgeting and Cost of Living” affect your conclusions about this?
Resources:
Inflation calculator http://www(dot)bls(dot)gov/data/inflation_calculator.htm
CPI http://inflationdata(dot)com/inflation/consumer_price_index/historicalcpi.aspx?reloaded=true
Cost of living calculator http://inflationdata(dot)com/inflation/Cost_of_Living/Cost_of_Living_Calculator.asp
Minimum wage in US http://www(dot)dol(dot)gov/whd/minwage/chart.htm
Minimum wage to afford rent https://reports(dot)nlihc(dot)org/sites/default/files/oor/2BDR_HOUSING_WAGE-MAP.pdf
Teachers can’t afford to buy a house http://www(dot)pbs(dot)org/newshour/rundown/report-finds-home-ownership-reach-many-teachers-nationwide/?utm_source=facebook&utm_medium=pbsofficial&utm_campaign=newshour

Math Problem Sample Content Preview:
1 Piecework (Exercise 4.7.8 from the textbook)
In the 1880s many young women in large cities worked at home sewing clothing. They were paid by the piece, hence the name “piecework” for this type of labor. A pants stitcher would finish a pair of pants, putting in canvas for the pockets and waistband linings, and would receive 12.5 cents per pair of pants finished. She could generally finish 16 pairs of pants a week, working from 8 am until dark. [You can read more about this on the web at historymatters.gmu.edu/d/5753/ ]
What was her hourly rate of pay in 1880? What assumptions did you make about working hours per week: How many hours per day? How many days per week? The total pay in a week was 16 pairs of pants a week*12.5 cents per pair= 200 cents. The 1880’s generation are thought to have been religious with strict observance of the Sabbath day. Assuming she worked for 6 days a week with exception of Sunday, her daily pay per pant was 200 cents/ 6 days= 33.33 cents. Working from 8 a.m. till dark, presumably ‘dark’ translates to 8 p.m. in winter, there would be exhaustingly 12 hours working hours daily utmost. Therefore, her hourly rate of pay, might have been 33.33 cents/12 hours=2.78 cents per hour.
Convert her 1880 wages to current (2019) wages.
The conversion of cents into dollars first using today’s exchange rate gives the following figures of her then wages:
* Pay per pant(12.5 cents)=$0.125
* 16 pairs per week(200 cents)=$2
* Daily pay(33.33 cents)=$0.3333
* Hourly rate of pay(2.78 cents)=$0.0278
In August 2019 her current wages considering the 3.14 inflation rate since 1913 are as follows:
* Pay per pant(12.5 cents)=$ 3.27
* 16 pairs per week(200 cents)=$52.36
* Daily pay(33.33 cents)=$8.73
* Hourly rate of pay(2.78 cents)=$0.73
Compare her hourly rate to the current minimum wage.
Her hourly rate earnings were $0.0278. The current minimum hourly wage is $7.25. The difference between the two wages is $7.222.
2 Working for the minimum wage (Exercise 4.7.22 from the textbook, plus commentary) 

Figure out the annual income in 2019 dollars for someone who worked at a minimum wage job 40 hours/week for 50 weeks in 1975. In 1975, the minimum hourly wage was $1.80 for farm workers and $2.10 for nonfarm workers. Using the lesser figure between the two minimum hourly wages, for 40 hours per week, the worker earned $1.80*40= $72 whereas in 50 weeks, annual income was $72*50=$3,600. The wages in 2019 would be:
* Hourly pay($1.80)=$8.86
Updated on
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