Suppose that in 2015 a typical US student attending a state

Suppose that in 2015, a typical U.S. student attending a state supported college bought 8 textbooks at a price of $90 per book and enrolled in 28 credit hours of coursework at a price of $400 per credit hour. In 2016, the typical student continued to purchase 8 textbooks and enroll in 28 credit hours, but the price of a textbook rose to $100 per book, and the tuition price increased to $440 per credit hour. The base year for computing a \"student price index\" using this info is 2015. The price index for any base year is 100. The value of the student price index in 2015 is

Solution

The value of the student price index in 2015 should be 100.

In the question it is given that we have to take 2015 as the base year for calculation of student price index (SPI).

and the value of any price index in the base year is given to be 100 (also as given in the question itself).

More formally , it can be shown as below:

For the year 2015:

1. calculate the cost of basket of goods

Here our basket of goods contain: a) cost of textbooks b) tuition fees

cost = (90$ * 8 ) + (28 * 400$ ) =720$ + 11200$ = 11920$

To calculate the SPI for the year 2015, following is the formulae =

(cost of basket of goods in the year of interest / cost of the basket of goods in the base year ) * 100

Here our cost of basket of goods in the year of interest pertains to 2015 year.And our base year is also 2015.

Thus:

(11920/11920) * 100 =100

Thus the SPI for 2015 is 100.

If it was asked to calculate the student price index of 2016 then the calculation would be as follows:

For the year 2016:

1. calculate the cost of basket of goods

basket of goods contain a) textbooks b) tuition fees

Cost= (100$ * 8) + (28 * 440$ ) = 800$ + 12320$ = 13120$

SPI = (13120/ 11920 ) * 100 = 110.06 = 110 approx.

We see that that the prices have risen as SPI of 2016 > SPI of 2015