Question

In 1949, Sycamore, Illinois built a hospital for about $500,000. In 1987, the county restored the courthouse for about $2.4 million. A price index for nonresidential construction was 14 in 1949, 92 in 1987, and 114.5 in 2000. According to these numbers, the hospital cost about a. $4.1 million in 2000 dollars, which is more than the cost of the courthouse restoration in 2000 dollars. b. $4.1 million in 2000 dollars, which is less than the cost of the courthouse restoration in 2000 dollars. c. $3.6 million in 2000 dollars, which is more than the cost of the courthouse restoration in 2000 dollars. d. $3.6 million in 2000 dollars, which is less than the cost of the courthouse restoration in 2000 dollars.

Answer 1

Using price index adjustments, the 1949 cost of the hospital in 2000 dollars is approximately $4.1 million, which exceeds the adjusted $2.98 million cost of the 1987 courthouse restoration. The correct option is 'a', indicating the hospital cost is more.

Step-by-step explanation:

The student's question involves adjusting historical costs to reflect inflation or changes in price level over time using a given price index for nonresidential construction. To compare the costs of the hospital built in 1949 and the courthouse renovation in 1987 in terms of 2000 dollars, we can use the given price indices to restate the original amounts in 2000 dollars. This process is known as inflation adjustment or converting to real dollars. Here is the step-by-step calculation:

To adjust the 1949 cost of the hospital to 2000 dollars, we use the price index increase from 14 (in 1949) to 114.5 (in 2000). The formula for adjustment is: (Cost in past year dollars) × (Price index in current year / Price index in past year).

For the hospital: $500,000 × (114.5 / 14) ≈ $4.1 million

Similarly, to adjust the 1987 cost of the courthouse restoration to 2000 dollars: $2.4 million × (114.5 / 92) ≈ $2.98 million.

Using these calculations, the correct answer is that the cost of building the hospital in 2000 dollars is approximately $4.1 million, which is more than the courthouse restoration cost of approximately $2.98 million in 2000 dollars. Therefore, the answer is (a) $4.1 million in 2000 dollars, which is more than the cost of the courthouse restoration in 2000 dollars.

Answer 2

a. $4.1 million in 2000 dollars, which is more than the cost of the courthouse restoration in 2000 dollars.

Step-by-step explanation:

The computation is shown below;

Cost in 2000 dollars is

= $500,000 × (Price index in 2000 ÷ Price index in 1949)

= $500,000 × (114.5 ÷ 14)

= 40,89,285.71

= $4.1 million

So overall we can see that the $4.1 million in the year 2000 more than the cost of the courthouse

Therefore the option a is correct