Class 11 Economics (Statistics for Economics) Chapter 7 Index Numbers

Key Concept: Basic Definition

b) Changing value of a fixed aggregate of goods

[Solution Description] The weighted aggregative index measures the changing value of a fixed aggregate of goods using a pre-determined basket of commodities. It reflects price changes over time.

Key Concept: Index Types

d) Retail price index

[Solution Description]

From the syllabus, the types of index numbers listed include wholesale price index, consumer price index, index of industrial production, agricultural production index, and sensex. “Retail price index” is not included in this list.

Key Concept: Formula Identification

b) $\frac{\Sigma P_1}{\Sigma P_0} \times 100$

[Solution Description] The simple aggregative method for constructing index numbers uses the formula: $P_{01} = \frac{\Sigma P_1}{\Sigma P_0} \times 100$, where $P_1$ is the sum of prices in the current year and $P_0$ is the sum of prices in the base year.

Key Concept: Basic Definition

c) To calculate the relative change in variables

[Solution Description] The primary purpose of index numbers is to measure relative changes in a variable or group of variables over time.

Key Concept: Basic Definition

d) Average change in retail prices

[Solution Description] The Consumer Price Index (CPI) measures the average change in retail prices over time, which reflects changes in the cost of living for consumers.

Key Concept: Basic Definition

c) Average achievements in health, education, and income

[Solution Description] The Human Development Index (HDI) measures a country’s average achievements in three basic aspects of human development: life expectancy, education, and per capita income.

Key Concept: Formula Application

b) 111.11

[Solution Description]

To find the simple price index, we use the formula:

$\text{Price Index} = \left( \frac{\text{Cost in Current Year}}{\text{Cost in Base Year}} \right) \times 100$

Substituting the given values:

$\text{Price Index} = \left( \frac{500}{450} \right) \times 100 = \frac{500 \times 100}{450} = 111.11$

Therefore, the simple price index is 111.11.

Key Concept: Basic Definition

c) Bombay Stock Exchange Sensitive Index

[Solution Description] Sensex is the abbreviation of “Bombay Stock Exchange Sensitive Index.” It is a benchmark index for the Indian stock market and reflects investor confidence in the economy.

Key Concept: Weightage Identification

c) 14.4%

[Solution Description] The weightage of the Mining sector in the Index of Industrial Production (IIP) is given as 14.4%.

Key Concept: Definition Recall

c) To measure relative change in a large number of items

[Solution Description] The primary purpose of an index number is to measure relative changes in a large number of items or variables over time, allowing for comparisons.

Key Concept: Base Year Concept

b) The year used for comparison

[Solution Description]

The base year in index numbers is a reference year used for comparison purposes. It is the benchmark year against which other years are compared to determine changes in prices, production levels, etc.

Key Concept: Definition Recall

b) To measure relative changes over time or between places

[Solution Description] The primary purpose of index numbers in economics is to measure changes over time or between places for a given set of data, typically related to prices, quantities, or other economic variables.

Key Concept: Definition Check

b) A stock market index

[Solution Description] Sensex is a stock market index that tracks the performance of 30 well-established and financially sound companies listed on the Bombay Stock Exchange in India.

Key Concept: Policy Impact Evaluation, Advanced Interpretation

c) Raise interest rates

[Solution Description]

When there is a consistent rise in CPI, it reflects inflationary pressure. Central banks typically counteract inflation by implementing monetary policies that can slow down the rate of price increases.

One common approach is increasing interest rates. Higher interest rates tend to reduce consumer spending and borrowing, slowing down inflation while stabilizing the currency.

Detailed steps:

– Recognize that inflation is indicated by rising CPI values.

– Understand that one method to control inflation is increasing interest rates as it curbs excess demand.

– Consider that high-interest rates may slow down economic growth but help control inflation more effectively than lowering them.

Thus, raising interest rates is a plausible action.

Key Concept: Definition Recall

c) Paasche’s Price Index

[Solution Description]

An index number that uses current period quantities as weights is referred to as Paasche’s Price Index. This method utilizes the quantities consumed in the current year instead of the base year.

Key Concept: Basic Definition

b) Increasing investor confidence

[Solution Description]

A rising Sensex typically indicates that investor confidence in the economy is increasing. When investors are optimistic about economic growth, they invest more in stocks, leading to a rise in the Sensex.

Key Concept: Base Year Definition

b) 2011-12

[Solution Description] The base year for the Wholesale Price Index (WPI) is given in the syllabus as 2011-12, which serves as a reference point for comparison.

Key Concept: Basic Definition

d) Index of Industrial Production

[Solution Description] IIP stands for Index of Industrial Production, which measures the growth rate of different sectors of industry.

Key Concept: Conceptual Distinction

c) A price index measures changes in prices, while a quantity index measures changes in quantities.

[Solution Description]

A price index measures the average change in prices over time for a fixed basket of goods, while a quantity index measures the change in quantities produced or consumed over time. Price indices focus on monetary value changes due to inflation or deflation, whereas quantity indices track production output or consumption levels without considering prices.

Key Concept: Base Year Concept

b) The year chosen for comparison

[Solution Description] The base year in index numbers is a period with which comparisons are made and is given the index number 100.

Key Concept: Basic Definition

b) A stock market index

[Solution Description] The Sensex is the short form of Bombay Stock Exchange Sensitive Index, which is a stock market index.

Key Concept: Method Identification

b) Laspeyre’s price index

[Solution Description] Laspeyre’s Price Index is the method that uses base period quantities as weights when calculating a weighted aggregative price index. This method assumes the same quantity of goods in both periods and focuses on changes in price.

Key Concept: Core Industries

c) Textiles

[Solution Description] The Eight Core Industries are Coal, Crude Oil, Natural Gas, Refinery Products, Fertilizers, Steel, Cement, and Electricity. Textiles is not included in this list.

Key Concept: Basic Formula Identification

c) $P_{01} = \frac{\Sigma P_1}{\Sigma P_0} \times 100$

[Solution Description] The formula for calculating a simple aggregative price index is $P_{01} = \frac{\Sigma P_1}{\Sigma P_0} \times 100$. This formula compares the total prices in the current period with those in the base period.

Key Concept: Major Groups Identification

d) Primary Articles

[Solution Description] Primary Articles is one of the major groups included in the WPI, with a weightage of 22.62%.

Key Concept: Purpose Clarity

c) Value Index

[Solution Description] A value index is used to measure changes in the total monetary value, which involves both price and quantity changes. This is different from a volume index, which only measures quantity changes. Hence, to reflect changes in the total monetary value, a value index is appropriate.

Key Concept: Purpose Recognition

b) To measure retail prices

[Solution Description]

The Consumer Price Index (CPI) is primarily used to measure changes in the cost of living by tracking changes in the price level of a basket of consumer goods and services purchased by households. It serves as an indicator of inflation and assists in making economic decisions related to monetary policy.

Key Concept: Comparative Analysis

c) Both a) and b)

[Solution Description] The Consumer Price Index Numbers for Agricultural Labourers and Rural Labourers both have a base year of 1986-87, while other indices like CPI for Industrial Workers, All-India Rural, Urban, and Combined Consumer Price Indices have different base years.

Key Concept: Basic Definition

d) Average change in retail prices

[Solution Description] The CPI measures the average change in retail prices of goods and services over time.

Key Concept: Base Year Concept

b) It provides a reference point for comparative analysis

[Solution Description] Selecting a base year is crucial because it serves as a comparison point against which changes in other years are measured. This ensures uniformity and accuracy in observing relative changes across different periods.

Key Concept: Basic Definition

c) To measure the average change in retail prices

[Solution Description] The primary purpose of the CPI is to measure the average change in retail prices, often referred to as the cost of living index.

Key Concept: Formula Application

d) 100

[Solution Description] To calculate the IIP using Laspeyre’s formula, we use:

$$IIP_{01} = \frac{\sum_{i=1}^{n} q_{i1} W_i}{\sum_{i=1}^{n} W_i} \times 100 = \frac{100 \times 0.3}{0.3} \times 100 = 100$$

Therefore, the IIP is 100.

Key Concept: Laspeyre’s Formula Application

d) Laspeyre’s formula

[Solution Description] The Index of Industrial Production (IIP) uses Laspeyre’s formula for calculating the weighted arithmetic mean of quantity relatives. This involves using fixed base year weights to compute the index.

Key Concept: Economic Impact Analysis, Data Reliability Concerns

c) It could mislead policy decisions due to distorted inflation measures.

[Solution Description] Primary articles have a substantial weight in the WPI (22.62%). Inaccuracies in their pricing can result in misleading inflation rates, affecting monetary policies and resource allocation decisions, which rely heavily on accurate inflation measurement to plan subsidies, taxation levels, and investments.

Key Concept: Basic Formula Application

b) 0.0025

[Solution Description]

The purchasing power of money is calculated as $1/\text{Cost of living index}$. Here, the cost of living index is 400. Therefore, the purchasing power is: $\text{Purchasing Power} = \frac{1}{400} = 0.0025$

Thus, the purchasing power of money is 0.0025.

Key Concept: Limitations of Unweighted Index

b) It does not account for the relative importance of items.

[Solution Description] The limitation of a simple aggregative price index is that it does not take into account the relative importance or quantity of different items, as it treats all items equally regardless of their significance.

Key Concept: Basic Definition

d) Wholesale prices

[Solution Description] The Wholesale Price Index (WPI) measures the change in prices of goods at the wholesale level before they reach the retail market. It is a key indicator of inflation at the wholesale price level.

Key Concept: Base Year Understanding

c) It provides a constant reference point for measuring price changes over time

[Solution Description] The base year in CPI calculations serves as a reference point against which future price levels are compared. It allows for the calculation of percentage changes in price levels over time, making it possible to assess inflation accurately.

Key Concept: Simple Formula Application

c) 125

[Solution Description] The price index using the simple aggregative method is calculated as:

$$\text{Price Index} = \left( \frac{\text{Current Period Total Price}}{\text{Base Period Total Price}} \right) \times 100 = \left( \frac{250}{200} \right) \times 100 = 125$$

So, the price index is 125.

Key Concept: Use-based Group Weightage

b) 15.3

[Solution Description] From the syllabus, it is stated that the weightage for Consumer Non-durables in the IIP use-based groups is 15.3.

Key Concept: Weighted Index Understanding

b) 120.5

[Solution Description]

The formula for calculating the weighted index of price relatives is given by:

$P_{01} = \frac{\Sigma W_i \frac{P_1}{P_0}}{\Sigma W_i} \times 100$

For each commodity, calculate $W_i \times \frac{P_1}{P_0}$:

– For X: $25 \times 120 = 3000$

– For Y: $35 \times 110 = 3850$

– For Z: $40 \times 130 = 5200$

Sum these values: $\Sigma W_i \frac{P_1}{P_0} = 3000 + 3850 + 5200 = 12050$

Sum the weights: $\Sigma W_i = 25 + 35 + 40 = 100$

Now calculate the index: $P_{01} = \frac{12050}{100} = 120.5$

Key Concept: Basic Definition

c) Delay from occurrence of an event to its data collection

[Solution Description] Time lag refers to the delay between when an event occurs and when the data related to that event is collected or recorded.

Key Concept: Purpose of Weighting

b) To reflect the relative importance of different items

[Solution Description] Weights are used in the calculation of a price index to reflect the relative importance of different items in total expenditure. By applying weights, we ensure that more important items have a greater impact on the overall index value than less important ones.

Key Concept: Definition Check

c) A statistical device for measuring changes in a group of related variables

[Solution Description] An index number is a statistical device for measuring changes in a group of related variables over time.

Key Concept: Formula Application

c) 120

[Solution Description] To calculate the price index using the simple average of relatives method, we use the formula:

$P_{01} = \frac{\Sigma \text{{price relatives}}}{n}$

Here, the sum of the price relatives is $110 + 125 + 115 + 130 = 480$. The number of commodities $n$ is 4.

Thus, $P_{01} = \frac{480}{4} = 120$

Hence, the price index is 120.

Key Concept: Basic Definition

b) To measure relative changes over time

[Solution Description] The primary use of index numbers in economic analysis is to measure relative changes over time for various items, such as prices or quantities.

Key Concept: Purpose Clarity

d) To clearly distinguish between volume and value measurements

[Solution Description] Defining the purpose of an index number ensures that the correct type of index is constructed, such as a volume index or a value index. This helps in accurately measuring what needs to be assessed, whether it is price changes, quantity changes, or value changes.

Key Concept: Basic Definition

a) The average change in retail prices

[Solution Description] The Consumer Price Index (CPI) measures the average change in retail prices over time. It reflects how much consumers are paying for a basket of goods and services compared to a base year.

Key Concept: Concept Identification

b) It uses base period quantities as weights

[Solution Description] A simple aggregative price index does not use weights based on quantities. It treats all items equally without considering their importance or quantity consumed during any period.

Key Concept: Definition of WPI

c) Wholesale price changes

[Solution Description] The WPI measures the average change in prices at the wholesale level for baskets of goods over time. It specifically tracks price changes before retail sale.

Key Concept: Simple Calculation

c) 200

[Solution Description] To calculate the simple aggregative price index, use the formula:

$\text{Index} = \left( \frac{\text{Current Year Price}}{\text{Base Year Price}} \right) \times 100$

Substituting the given values:

$\text{Index} = \left( \frac{10}{5} \right) \times 100 = 200$

Hence, the simple aggregative price index is 200.