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intro
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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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YOUR NAME HERE
Problem 1.
Suppose someone gets paid for overtime and doubleovertime 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.
I'm deliberately not spacing the X values (hours) equally, to make sure
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This note was uploaded on 01/23/2012 for the course MATH 110 taught by Professor Blair during the Winter '08 term at Eastern Michigan University.
 Winter '08
 BLAIR

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