Chapter 16, Problem 25E

To determine

To find: Each year’s tuition for Colorado residents at the University of Colorado in constant 1985 dollars by using annual average consumer price index (CPI).

Answer to Problem 25E

Solution: The required each year’s tuition in constant 1985 dollars is shown below:

Year	Tuition	CPI	Adjusted Tuition ($)
1985	$1,332	107.6	1332
1987	$1,548	113.6	1406
1989	$1,714	124.0	1535
1991	$1,972	136.2	1686
1993	$2,122	144.5	1789
1995	$2,270	152.4	1887
1997	$2,356	160.5	1987
1999	$2,444	166.6	2062
2001	$2,614	177.1	2192
2003	$3,192	184.0	2278
2005	$4,446	195.3	2418
2007	$5,418	207.3	2566
2009	$6,446	214.5	2655
2011	$7,672	224.9	2784
2013	$8,760	233.0	2884
2015	$9,312	238.7	2955

Explanation of Solution

Given: The tuition for Colorado residents at the University of Colorado is provided and the annual average consumer price index (CPI) is obtained from the table 16.1, for the respective years which are shown below:

Year	Tuition ($)	CPI
1985	1332	107.6
1987	1548	113.6
1989	1714	124.0
1991	1972	136.2
1993	2122	144.5
1995	2270	152.4
1997	2356	160.5
1999	2444	166.6
2001	2614	177.1
2003	3192	184.0
2005	4446	195.3
2007	5418	207.3
2009	6446	214.5
2011	7672	224.9
2013	8760	233.0
2015	9312	238.7

Calculation:

The formula to convert the amount from one period to another period is shown below:

$\text{Dollars at time B}=\text{Dollars at time A}\times \frac{\text{CPI at time B}}{\text{CPI at time A}}$

Here, time B represents the present time and time A represents the base time.

Now, convert 1987 tuition in 1985 dollars as shown below:

$\begin{array}{c}1987\text{ dollars}=1985\text{ dollars}\times \frac{\text{CPI of the year }1987}{\text{CPIof the year }1985}\\ =\$1332\times \frac{113.6}{107.6}\\ =\$1406\end{array}$

Also, convert 1989 tuition in 1985 dollars as shown below:

$\begin{array}{c}1989\text{ dollars}=1985\text{ dollars}\times \frac{\text{CPI of the year }1989}{\text{CPIof the year }1985}\\ =\$1332\times \frac{124.0}{107.6}\\ =\$1535\end{array}$

Similarly, calculated each year’s tuition in constant 1985 dollars is shown below in the tabular manner:

Year	Tuition	CPI	Adjusted Tuition ($)
1985	$1,332	107.6	1332
1987	$1,548	113.6	1406
1989	$1,714	124.0	1535
1991	$1,972	136.2	1686
1993	$2,122	144.5	1789
1995	$2,270	152.4	1887
1997	$2,356	160.5	1987
1999	$2,444	166.6	2062
2001	$2,614	177.1	2192
2003	$3,192	184.0	2278
2005	$4,446	195.3	2418
2007	$5,418	207.3	2566
2009	$6,446	214.5	2655
2011	$7,672	224.9	2784
2013	$8,760	233.0	2884
2015	$9,312	238.7	2955

Interpretation: From the above table, it can be concluded that the adjusted tuition is increased as the CPI increased when the adjustment is done by taking the year 1985 as base.

To graph: The line plot of actual dollar tuition and constant dollars tuition on the same axes for the respective years.

Explanation:

Graph: The value of constant tuition dollar by taking 1985 dollars for the remaining years are obtained in the previous part. With the help of Excel, the two-line plots are obtained for the adjusted minimum wages and the minimum wages in constant dollars as shown below:

Step 1: Enter the data of actual tuition dollar and the constant dollar tuition during the respective years in the spreadsheet of Excel. The data is shown below:

Year	Tuition	Adjusted Tuition ($)
1985	$1,332	$1,332
1987	$1,548	$1,406
1989	$1,714	$1,535
1991	$1,972	$1,686
1993	$2,122	$1,789
1995	$2,270	$1,887
1997	$2,356	$1,987
1999	$2,444	$2,062
2001	$2,614	$2,192
2003	$3,192	$2,278
2005	$4,446	$2,418
2007	$5,418	$2,566
2009	$6,446	$2,655
2011	$7,672	$2,784
2013	$8,760	$2,884
2015	$9,312	$2,955

Step 2: Select the data, click on Insert, and select the Line chart as shown below:

Step 3: The two line plots showing actual tuition dollar, and the constant dollar tuition is obtained as shown below:

Interpretation: From the above two line plots on the same axes, it can be concluded that the constant dollar tuition has risen steadily from the year 1985 to the year 2015 but the actual dollar tuition for these years has increases sharply. So, it can be observed from the graph that the actual dollar tuition is increasing faster than the constant tuition dollar during the period 1985 to 2015.