Chapter 17, Problem 1.1SR

To determine

To find: The index for each of the countries by using country U as the base period and to find what percent of metal China produces more than that produced by country U.

Answer to Problem 1.1SR

The table that shows the simple index of all countries is given below:

Country	Amount (millions of tons)	Index
China	831.7	$1026.790123$
Japan	104.7	129.2592593
US	81	100
India	101.5	125.308642
Russia	71.5	88.27160494

China produces approximately $26.79\%$ more metal than country U.

Explanation of Solution

Given information:

Country	Amount (millions of tons)
China	831.7
Japan	104.7
US	81
India	101.5
Russia	71.5

Formula used:

The simple index for the period $t$

with the base period 0 is calculated as:

  $P_{}=\frac{p_t}{p_0}\times 100$

Where $p_t$ is the price of period $t$ and $P_0$ is the price of period 0. The index for the base period is 100.

Calculation:

The base is country U and the amount for country U is 81 million tons, that is, $p_0=81$. For country C, the simple index is calculated as:

  $\begin{array}{c}{\text{Index}}_{\text{China}}=\frac{831.7}{81}\times 100\\ =1026.790123\end{array}$

The table that shows the simple index of all periods is given below:

Country	Amount (millions of tons)	Index
China	831.7	$\frac{831.7}{81}\times 100=1026.790123$
Japan	104.7	129.2592593
US	81	100
India	101.5	125.308642
Russia	71.5	88.27160494

The index for country C is 1026.790123. Hence, country C produces approximately $26.79\%$ more metal than country U.