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m110-chapter-3-4-extra

# m110-chapter-3-4-extra - intro YOUR NAME HERE Piecewise...

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intro Page 1 YOUR NAME HERE Piecewise Linear homework One problem per sheet, but this first sheet is a demonstration rather than a problem. The current (2010 or so) Social Security payroll tax works like this: From To Tax rate Bracket 1: 0 \$106,000.00 4.20% Bracket 2: \$106,000.00 infinity 0.00% So we can find the x and y values of the breakpoints: (take a look at these formulas in light yellow) x y 0 \$0.00 \$106,000.00 \$4,452.00 This is a regressive tax (the marginal rate gets lower as income goes up), so we use the “min” function instead of the “max” function. Income TaxAmt. Comment \$0 \$0.00 \$15,080 \$633.36 roughly minimum wage for a year's worth of work \$35,000 \$1,470.00 roughly the median US personal income (not household) \$106,000 \$4,452.00 The bracket boundary \$150,000 \$4,452.00 \$200,000 \$4,452.00 I'm deliberately not spacing the X values (Income) equally, to make sure our formula works well in that case. \$0 \$100,000 \$200,000 \$300,000 \$0 \$1,000 \$2,000 \$3,000 \$4,000 \$5,000 Social Security Payroll Tax Person's Yearly income Tax Amount

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Sheet1 Page 2 YOUR NAME HERE Problem 1. Suppose someone gets paid for overtime and double-overtime as follows (the 40 and 60 are hours worked in a week) From To Hourly Wage Bracket 1: 0 40 \$14.00 Bracket 2: 40 60 \$21.00 Bracket 2: 60 infinity \$28.00 So we can find the x and y values of the breakpoints: (fill in the formula as needed) x (hrs per week) y 0 \$0.00 40 60 Does this represent economies of scale, or diseconomies of scale, for the worker? Type your answer and explanation here: So should you use “min” or “max”? Write your full formula in B23 and then fill it down to do all the computations. Hours TotalPay Comment 0 5 10 20 40 A bracket boundary 41 50 60 A bracket boundary 61 70 80 and then graph your results, please.
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