If EP -3500, EPg. = 3850, then the Cost of living Index (CL1) for 1950 wr. to base 1960 is?

Question

Answer

Calculating the Cost of Living Index (CL1) for 1950 with Base Year 1960

The Cost of Living Index (CL1) measures the change in the cost of goods and services over a period of time. To calculate the CL1 for 1950 with a base year of 1960, we need to follow these steps:

Step 1: Calculate the Price Ratio

The price ratio compares the cost of a basket of goods and services in the current year to the cost of the same basket in the base year. We can calculate the price ratio using the formula:

Price Ratio = (EPg. / EP) x 100

where:

EP = Expenditure in the base year (1960)

EPg. = Expenditure in the current year (1950)

Substituting the given values, we get:

Price Ratio = (3850 / 3500) x 100 = 110.00

Step 2: Calculate the Geometric Mean of Price Ratios

The geometric mean of price ratios measures the average change in the cost of goods and services over a period of time. We can calculate the geometric mean of price ratios using the formula:

Geometric Mean = [(Price Ratio1 x Price Ratio2 x ... x Price RatioN)^(1/N)] x 100

where:

Price Ratio1, Price Ratio2, ..., Price RatioN = Price ratios for each year in the period

N = Number of years in the period

Since we are calculating the CL1 for only one year (1950), the geometric mean formula simplifies to:

Geometric Mean = (Price Ratio)^(1/N) x 100

where N = 1

Substituting the calculated price ratio and N, we get:

Geometric Mean = (110.00)^(1/1) x 100 = 110.00

Step 3: Calculate the Cost of Living Index (CL1)

The CL1 is the ratio of the geometric mean of price ratios for the current year to the geometric mean of price ratios for the base year (which is always 100). We can calculate the CL1 using the formula:

CL1 = (Geometric Mean of Price Ratios for Current Year / Geometric Mean of Price Ratios for Base Year) x 100

Since the base year is 1960, the geometric mean of price ratios for the base year is always 100. Therefore, the formula simplifies to:

CL1 = Geometric Mean of Price Ratios for Current Year

Substituting the calculated geometric mean, we get:

CL1 = 110.00

Result

Therefore, the Cost of Living Index (CL1) for 1950 with a base

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