Question

1.The Indiana State budget was $35.9 billion for the 2001-2003 biennium and 68.1 billion for the 2017-2019 biennium. The price deflator was 0.83 for the the 2001-2003 period and 1.16 for the 2017-2019 period, with a base year of 2009.

What was the average annual rate of increase in nominal spending between the 2001-2003 biennium and the 2017-2019 biennium? The number of years between the two time periods is 14; i.e., consider the time between the end of one biennium to the beginning of the next.

2.The Indiana State budget was $35.9 billion for the 2001-2003 biennium and 68.1 billion for the 2017-2019 biennium. The price deflator was 0.83 for the the 2001-2003 period and 1.16 for the 2017-2019 period, with a base year of 2009.

The average annual rate of increase in real spending is 2.21%. Why is average annual rate of increase in real spending so different from the average annual rate of increase nominal spending that you calculated in the previous question?

Please show work if you can, so that I can try to understand the problem!

Answer 1

1.

We want to calculate the compounded annual growth rate over here i.e. by what rate, compounded annually, should the 2001-2003 figure increase to get to the 2017-19 figure.

Algebraically, the above statement can be written as:

Where,

• i is the annual growth rate
• 14 is the no. of years between the two periods

or i = 4.68%

2.

Now, the budget figures given in the question are nominal figures meaning that they are not adjusted for inflation. Real values on the other hand adjust the nominal values for inflation.

Why adjust for inflation? Let's say you earn a salary of $100,000. After a year you get a hike of 10% and it becomes $110,000. This is a nominal increase. In reality prices may have increased too, because of inflation. So your real rate of growth of salary is actually less than 10%. This is because the $110,000 would no longer buy the same amount of goods and services as it would have bought a year ago.

Now, the price deflator given in the question is a measure of change in prices. The real value is calculated using the formula:

So real value of budgeted figures is:

And the real growth rate is:

or i = 2.21%

So, it is because the price level has increased, the real growth rate of budgeted figures is less than the nominal growth rate.