Chapter 17, Problem 56DE

a.

To determine

Develop and interpret the index using 2000 as the based period.

Answer to Problem 56DE

The index is as given below:

Year	Average Salary	Index
2000	$1,988,034	100
2001	$2,264,403	113.9
2002	$2,383,235	119.88
2003	$2,555,476	128.54
2004	$2,486,609	125.08
2005	$2,632,655	132.43
2006	$2,866,544	144.19
2007	$2,944,556	148.11
2008	$3,154,845	158.69
2009	$3,240,206	162.99
2010	$3,297,828	165.88
2011	$3,305,393	166.26
2012	$3,440,000	173.04

Explanation of Solution

Calculation:

The index using 2000 as the base period is obtained as follows:

Year	Average Salary	$\text{Index}\left(P\right)=\frac{p_t}{p_0}\times 100$
2000	$1,988,034	$\frac{\text{1},\text{988},0\text{34}}{\text{1},\text{988},0\text{34}}\times 100=100$
2001	$2,264,403	$\frac{\text{2},\text{264},\text{4}0\text{3}}{\text{1},\text{988},0\text{34}}\times 100=113.90$
2002	$2,383,235	$\frac{\text{2},\text{383},\text{235}}{\text{1},\text{988},0\text{34}}\times 100=119.88$
2003	$2,555,476	$\frac{\text{2},\text{555},\text{476}}{\text{1},\text{988},0\text{34}}\times 100=128.54$
2004	$2,486,609	$\frac{\text{2},\text{486},\text{6}0\text{9}}{\text{1},\text{988},0\text{34}}\times 100=125.08$
2005	$2,632,655	$\frac{\text{2},\text{632},\text{655}}{\text{1},\text{988},0\text{34}}\times 100=132.43$
2006	$2,866,544	$\frac{\text{2},\text{866},\text{544}}{\text{1},\text{988},0\text{34}}\times 100=144.19$
2007	$2,944,556	$\frac{\text{2},\text{944},\text{556}}{\text{1},\text{988},0\text{34}}\times 100=148.11$
2008	$3,154,845	$\frac{\text{3},\text{154},\text{845}}{\text{1},\text{988},0\text{34}}\times 100=158.69$
2009	$3,240,206	$\frac{\text{3},\text{24}0,\text{2}0\text{6}}{\text{1},\text{988},0\text{34}}\times 100=162.99$
2010	$3,297,828	$\frac{\text{3},\text{297},\text{828}}{\text{1},\text{988},0\text{34}}\times 100=165.88$
2011	$3,305,393	$\frac{\text{3},\text{3}0\text{5},\text{393}}{\text{1},\text{988},0\text{34}}\times 100=166.26$
2012	$3,440,000	$\frac{\text{3},\text{44}0,000}{\text{1},\text{988},0\text{34}}\times 100=173.04$

Interpretation:

The average salary of 2000 and 2012 had increased to 73%.

b.

To determine

Find the average player’s real salaries for those years.

Describe the trend in the deflated salaries.

Compare the results with part (a).

Answer to Problem 56DE

The average player’s real salaries for those years is given below:

Year	Average Salary	CPI	$\begin{array}{l}\text{Real Income}\\ =\frac{\text{Money Income}}{\text{CPI}}\times 100\end{array}$
2001	$2,264,403	177.1	$1,278,601
2003	$2,383,235	184	$1,388,846
2011	$2,555,476	224.94	$1,469,455
2012	$2,486,609	229.594	$1,498,297

Explanation of Solution

Calculation:

The average player’s real salaries for those years is obtained as follows:

Year	Average Salary	CPI	$\begin{array}{l}\text{Real Income}\\ =\frac{\text{Money Income}}{\text{CPI}}\times 100\end{array}$
2001	$2,264,403	177.1	$\frac{\text{2},\text{264},\text{4}0\text{3}}{177.1}\times 100=\$1,278,601$
2003	$2,383,235	184	$\frac{\text{2},\text{555},\text{476}}{184}\times 100=\$\text{1},\text{388},\text{846}$
2011	$2,555,476	224.94	$\frac{\text{3},\text{3}0\text{5},\text{393}}{224.94}\times 100=\$\text{1},\text{469},\text{455}$
2012	$2,486,609	229.594	$\frac{\text{3},\text{44}0,000}{224.94}\times 100=\$\text{1},\text{498},\text{297}$

From the table, it is observed that the real income is increased about 17% over the period. That is, in real terms 1.45% increases per year.