# Statistics Indian Statistical Service Part 3 Question-5 Solved Solution

**5.(a) Explain the technique of 'concentration curves' assuming Pareto's form of **the **income**
**distribution. **
Concentration curves are a graphical tool used to illustrate the distribution of a variable across a population, typically with a focus on inequality. The technique assumes a Pareto distribution, which is a common assumption for income distributions.
In a concentration curve, the cumulative percentage of the variable (such as income or wealth) is plotted against the cumulative percentage of the population. This produces a curve that shows the degree of inequality in the distribution of the variable. If the curve is a straight line, then the distribution is perfectly equal. However, if the curve is concave (bending downwards), then the distribution is more unequal, and if the curve is convex (bending upwards), then the distribution is less unequal.
Assuming a Pareto distribution, the concentration curve can be used to estimate the Gini coefficient, which is a commonly used measure of inequality. The Gini coefficient is calculated by dividing the area between the concentration curve and the line of equality (which represents perfect equality) by the total area below the line of equality. The resulting value ranges from 0 (perfect equality) to 1 (perfect inequality).
For example, suppose we want to estimate the degree of income inequality in a country. We first sort the population by income, from the lowest to the highest, and calculate the cumulative percentage of income and population. We then plot the cumulative percentage of income on the x-axis and the cumulative percentage of the population on the y-axis. The resulting curve will show us the degree of inequality in the income distribution. We can then calculate the Gini coefficient by dividing the area between the concentration curve and the line of equality by the total area below the line of equality.
In summary, concentration curves are a useful graphical tool for illustrating the distribution of a variable across a population, assuming a Pareto distribution. They can be used to estimate the Gini coefficient, which is a commonly used measure of inequality.

**5.(b) Define price elasticity of demand. Given that **the **demand function is ***p =7 - ***8x2, then **
**for what value of x, the elasticity of demand will be unity? [Here x is the quantity demanded and ***p ***is the price]. **
Price elasticity of demand (PED) measures the responsiveness of the quantity demanded of a good or service to a change in its price. Mathematically, it is expressed as the percentage change in quantity demanded divided by the percentage change in price, i.e.,
PED = (% change in quantity demanded) / (% change in price)
When the elasticity of demand is equal to 1, it is said to be unit elastic. This means that the percentage change in quantity demanded is exactly equal to the percentage change in price.
To find the value of x at which the elasticity of demand is unity, we need to calculate the derivative of the demand function with respect to x and use it in the formula for PED:
p = 7 - 8x^2
Taking the derivative of p with respect to x, we get:
dp/dx = -16x
Now we can plug this into the formula for PED:
PED = (% change in quantity demanded) / (% change in price)
= [(dq/dp) * (p/x)] / [(dp/dx) * (x/p)]
= [(dp/dx) * (x/p)] / [(dq/dp) * (p/x)]
= -16x * (x/p) / [(-16x) * (p/x)]
= 1
Simplifying this equation, we get:
x^2 = 7/8
Taking the square root of both sides, we get:
x = Â±âˆš(7/8)
Since x represents the quantity demanded, it cannot be negative. Therefore, the value of x at which the elasticity of demand is unity is:
x = âˆš(7/8)

CSO (Central Statistics Office) is the apex statistical organization in India, responsible for the collection, compilation, analysis and dissemination of statistical data on various socio-economic sectors of the country. CSO is responsible for coordinating the statistical activities of different government departments and agencies, as well as for conducting national-level surveys and censuses.

The role of CSO in the Indian statistical system is multi-dimensional and crucial. Some of the key responsibilities of CSO include:

1. Developing statistical standards and methodologies: CSO is responsible for developing statistical standards and methodologies for data collection, analysis and dissemination, in order to ensure consistency and accuracy of statistical data.

2. Conducting national-level surveys and censuses: CSO conducts various national-level surveys and censuses, such as the National Sample Survey (NSS), Census of India, Annual Survey of Industries (ASI), etc., to collect data on various socio-economic parameters of the country.

3. Compiling and disseminating statistical data: CSO collects data from various government departments and agencies, and compiles and disseminates statistical data on various sectors of the economy, such as agriculture, industry, trade, services, health, education, etc.

4. Coordinating statistical activities of different government departments and agencies: CSO coordinates statistical activities of different government departments and agencies, such as the Ministry of Agriculture, Ministry of Health, Ministry of Education, etc., in order to ensure consistency and comparability of statistical data.

5. Providing technical assistance and training: CSO provides technical assistance and training to other government departments and agencies, as well as to academic institutions and research organizations, in order to build capacity for statistical activities.

Overall, CSO plays a critical role in providing accurate and reliable statistical data to support evidence-based policy-making and planning in India.

**5. (c) (i) Describe the role of CSO in **the **Indian Statistical System.**
**(ii) Distinguish between **the **'Income Method' and 'Expenditure Method' of estimating the national income in India. **

The Income Method and Expenditure Method are two commonly used methods for estimating national income in India. Here's how they differ:

1. Income Method: The Income Method estimates national income by adding up all the income earned by individuals and businesses in the country. This includes wages and salaries, profits, rents, interest, and other forms of income. The Income Method is based on the idea that all income generated in an economy eventually ends up as either consumption or savings. Therefore, by adding up all the income earned in a year, we can estimate the total output of the economy.

2. Expenditure Method: The Expenditure Method estimates national income by adding up all the spending on final goods and services in the economy. This includes spending on consumer goods, investment goods, government purchases, and net exports (exports minus imports). The Expenditure Method is based on the idea that all production in an economy is eventually sold and consumed, either by households, businesses, or the government. Therefore, by adding up all the spending on final goods and services in a year, we can estimate the total output of the economy.

In India, both methods are used to estimate national income. The Income Method is more commonly used for estimating the income generated by different sectors of the economy, such as agriculture, industry, and services. The Expenditure Method is more commonly used for estimating the overall size of the economy and the level of aggregate demand. However, both methods are interrelated and provide a comprehensive picture of the economy, and the estimates obtained from both methods are usually reconciled to arrive at a more accurate estimate of national income.

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