Circular Test and Price Indices

Circular test is a test to verify the consistency of the price index numbers. When a circular test is conducted, it is expected that the index numbers obtained from different methods should be consistent with each other. In this context, the following points are pertinent:

- Laspeyres Index number: The Laspeyres index number is a fixed-weighted price index that measures the average change in prices of a fixed basket of goods and services over time. The formula for calculating the Laspeyres index is the sum of the product of the base-year quantities and the current-year prices, divided by the sum of the base-year quantities and prices. The Laspeyres index tends to overestimate the cost of living, as it assumes that consumers continue to purchase the same goods in the same quantities regardless of price changes. In the context of the circular test, the Laspeyres index may or may not satisfy the circular test, depending on the data used and the method of calculation.

- Paasches Index number: The Paasches index number is a variable-weighted price index that measures the average change in prices of a variable basket of goods and services over time. The formula for calculating the Paasches index is the sum of the product of the current-year quantities and prices, divided by the sum of the current-year quantities and prices. The Paasches index tends to underestimate the cost of living, as it assumes that consumers can always switch to cheaper goods and services. In the context of the circular test, the Paasches index may or may not satisfy the circular test, depending on the data used and the method of calculation.

- Simple geometric mean of price relatives: The simple geometric mean of price relatives is a method of calculating a price index that involves taking the geometric mean of the ratios of current-year prices to base-year prices. The formula for calculating the simple geometric mean of price relatives is the nth root of the product of the price relatives, where n is the number of goods and services in the basket. The simple geometric mean of price relatives tends to be unbiased, as it assumes that consumers adjust their consumption patterns in response to price changes. In the context of the circular test, the simple geometric mean of price relatives is expected to satisfy the circular test.

- Weighted aggregative with fixed weights: The weighted aggregative with fixed weights is a method of calculating a price index that involves taking the sum of the product of the base-year quantities and the current-year prices, divided by the sum of the base-year quantities and prices, weighted by the share of each good or service in the total expenditure. The weighted aggregative with fixed weights tends to be biased, as it assumes that consumers do not adjust their consumption patterns in response to price changes. In the context of the circular test, the weighted aggregative with fixed weights may or may not satisfy the circular test, depending on the data used and the method of calculation.

Conclusion

In conclusion, the correct answer to the question is option C, the simple geometric mean of price relatives and the weighted aggregative with fixed weights may or may not satisfy the circular test, depending on the data used and the method of calculation. However, in general, the simple geometric mean of price relatives tends to be more unbiased than the Laspeyres and Paasches indices, while the weighted aggregative with fixed weights tends to be more biased.