ISyE3025_Spring_11_HW4Soln

# ISyE3025_Spring_11_HW4Soln - Page 1 of 5 ISyE 3025 Spring...

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Unformatted text preview: Page 1 of 5 ISyE 3025 Spring 2011, Practice HW 4 Solutions This homework is intended for Learning Cycle 4. 2. Maintenance expenses for production department XYZ were \$235,000 in 1999. You are benchmarking various departments, and using 2007 dollars for the comparisons. However, data for XYZ for 2007 are not available, so you will use the 1999 data and adjust the value for inflation. The price index values for your industry are as follows: 1983 1999 2000 2001 2002 2003 2004 2005 2006 2007 100 187.6 193.2 202.9 211.0 218.4 228.2 232.8 239.2 244.8 Determine the value of the maintenance expenses in 1999 but expressed in 2007 dollars. Solution: Apply ratio of index values, 235,000(244.8/187.6) = 235,000(1.305) = 306,652 The graph shows the rise in the price index over time [not needed for answer, but presented here for explanation]. Price index 180 200 220 240 260 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 3. In 1975 John Doe earned \$45,500 after taxes (income tax, payroll tax, etc.) Expenses for necessities were: Category of necessity Expenses in 1975 rent and utilities 8,000 groceries 7,500 clothing 2,000 transportation 3,900 medical 3,400 In 2002 his daughter Mary Doe earned \$98,000 after taxes. The consumer price index (CPI, a general measure of inflation) increased by an average of 3.2% per year from 1975 to 2002. a. How much discretionary income (for things besides necessities, such as entertainment, vacation, investment, etc.) did John Doe have in 1975? Solution: Obtain sum of expenses 24,800 and subtract from 45,500 to obtain discretionary income of 20,700. b. Assume that the quality and quantity of the necessities consumed by both John and Mary were the same. Assume the CPI rate in this example applies to all types of consumer expenditures. Estimate the expenditures by Mary Doe in 2002 for each category of necessity. Solution : Obtain inflation multiplier of (1.032)^(2002-1975) = (1.032)^27 = 2.3407. Then apply this multiplier to each expense category. Category of necessity Expenses in 2002 rent and utilities 18,726 groceries 17,555 clothing 4,681 transportation 9,129 medical 7,958 c. Which one was better off, John or Mary, in terms of having more discretionary income? Solution : Obtain sum of expenses 58,050 and subtract from 98,000 to obtain discretionary income of 39,950. Then convert this amount to 1975 dollars, in the amount of 17,067. This is Mary’s discretionary income measured in 1975 dollars, so her father John was better off in 1975. Note that the comparison could also be made using 2002 dollars: convert John’s discretionary income of 20,700 and apply inflation multiplier of 2.3407 to obtain 48,453, which can be compared to Mary’s 39,950. The ratio in favor of John is the same, no matter which dollars we use: 48,453/39,950 = 20,700/17,067 = 1.213....
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ISyE3025_Spring_11_HW4Soln - Page 1 of 5 ISyE 3025 Spring...

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