PRC-2 · Chapter 9
Indices MCQs with Answers
60 multiple-choice questions on Indices for PRC-2 Quantitative Analysis for Business. Try each one before revealing the answer and explanation.
Practise this chapter interactivelyQuestion 1
Which of the following best describes the fundamental purpose of constructing economic index numbers?
- A) To calculate precise future values of single investments.
- B) To measure relative changes in the magnitude of variables, like prices or quantities, over time.
- C) To determine the absolute statistical variance of a population.
- D) To establish the correlation coefficient between two specific industries.
Show answer & explanation
Answer: B) To measure relative changes in the magnitude of variables, like prices or quantities, over time.
Index numbers are specialized statistical tools designed strictly to measure relative changes in the level of a phenomenon (like prices, wages, or production volumes) with respect to time or geographical location.
Question 2
In the construction of an index number, the period against which all other periods are being compared is technically referred to as the:
- A) Current period
- B) Base period
- C) Linked period
- D) Weighted period
Show answer & explanation
Answer: B) Base period
The base period (or base year) is the reference point in time. It is typically assigned an index value of 100, and subsequent current periods are calculated as a percentage relative to this base.
Question 3
Which standard mathematical formula is used to calculate a 'Simple Price Relative' for a single commodity?
- A) (Current Price / Base Price) * 100
- B) (Base Price / Current Price) * 100
- C) Current Price - Base Price
- D) (Current Quantity / Base Quantity) * 100
Show answer & explanation
Answer: A) (Current Price / Base Price) * 100
A simple price relative expresses the price of a single item in the current period (p1) as a percentage of its price in the base period (p0). The formula is (p1 / p0) * 100.
Question 4
In the Laspeyres Price Index formula, what specific values are used to weight the prices of the commodities?
- A) Current year quantities
- B) Base year quantities
- C) An average of base and current year quantities
- D) Current year prices
Show answer & explanation
Answer: B) Base year quantities
The Laspeyres Index resolves the weighting problem by holding the quantities constant. Specifically, it uses the quantities consumed in the base year (q0) as the weights for all calculations.
Question 5
Which characteristic is a primary limitation of using the Paasche Price Index in practice?
- A) It tends to overstate inflation systematically.
- B) It requires the denominator to be recalculated every single year using current quantities.
- C) It completely ignores the time value of money.
- D) It only functions properly if prices are falling.
Show answer & explanation
Answer: B) It requires the denominator to be recalculated every single year using current quantities.
Because the Paasche index uses current year quantities (q1) for its weights, both the numerator and the denominator must be fully recalculated each year, requiring extensive new data collection annually.
Question 6
Fisher’s Ideal Index is technically defined as the:
- A) Arithmetic mean of the Laspeyres and Paasche indices.
- B) Geometric mean of the Laspeyres and Paasche indices.
- C) Harmonic mean of the Laspeyres and Paasche indices.
- D) Difference between the Laspeyres and Paasche indices.
Show answer & explanation
Answer: B) Geometric mean of the Laspeyres and Paasche indices.
Fisher's Ideal Index crosses the gap between the Laspeyres (base-weighted) and Paasche (current-weighted) methods by calculating the strict geometric mean (the square root of their product) of the two indices.
Question 7
How is the 'purchasing power of money' mathematically related to a general price index like the Consumer Price Index (CPI)?
- A) It is directly proportional to the price index.
- B) It is completely independent of the price index.
- C) It is inversely proportional to the price index.
- D) It moves parallel to the price index.
Show answer & explanation
Answer: C) It is inversely proportional to the price index.
As general prices go up (inflation indicated by a higher index), the actual volume of goods a unit of currency can buy decreases. Therefore, purchasing power is inversely proportional to the price index.
Question 8
If a worker's nominal monthly salary increases from Rs. 50,000 to Rs. 60,000, but the relevant price index rises from 100 to 125, what has happened to their 'Real Wage'?
- A) It has increased to Rs. 60,000.
- B) It has decreased to Rs. 48,000.
- C) It remains exactly the same.
- D) It has increased to Rs. 75,000.
Show answer & explanation
Answer: B) It has decreased to Rs. 48,000.
Real wage is calculated by dividing the nominal wage by the price index. Real Wage = (60,000 / 125) * 100 = 48,000. Despite the nominal increase, the worker's true purchasing power has fallen compared to the base year.
Question 9
When constructing an index using the 'Simple Aggregate Method', what is a major structural flaw?
- A) It requires the use of logarithms.
- B) It gives disproportionate influence to items with naturally high unit prices.
- C) It forces quantities to be fixed in the current year.
- D) It only measures qualitative data.
Show answer & explanation
Answer: B) It gives disproportionate influence to items with naturally high unit prices.
The simple aggregate method merely sums prices. Therefore, an item measured in tonnes costing Rs. 50,000 will overwhelmingly dominate the index compared to an item measured in grams costing Rs. 50, completely ignoring their relative importance.
Question 10
Which specific statistical index tracks the cost of a fixed basket of goods and services typically purchased by an average household?
- A) Producer Price Index
- B) Quantity Aggregate Index
- C) Consumer Price Index (CPI)
- D) Value Index
Show answer & explanation
Answer: C) Consumer Price Index (CPI)
The Consumer Price Index (CPI) is the standard measure used globally to track changes in the retail prices of a representative 'basket' of consumer goods and services, acting as a primary gauge for inflation.
Question 11
In standard index construction, why do economists occasionally perform a process known as 'base shifting'?
- A) To hide severe inflationary periods from the public.
- B) To switch from a Laspeyres to a Paasche index model.
- C) To move the reference point to a more recent, relevant period.
- D) To convert a price index directly into a quantity index.
Show answer & explanation
Answer: C) To move the reference point to a more recent, relevant period.
Over time, old base years become outdated due to technological changes and shifting consumption habits. Base shifting resets the index to 100 at a newer, more relevant year to make current comparisons meaningful.
Question 12
What does a Quantity Index measure?
- A) The change in retail prices of commodities over time.
- B) The absolute value of currency in a domestic market.
- C) The changes in the physical volume of goods produced, consumed, or distributed.
- D) The ratio between Laspeyres and Fisher indices.
Show answer & explanation
Answer: C) The changes in the physical volume of goods produced, consumed, or distributed.
While a price index measures changes in monetary cost, a quantity index is specifically designed to measure relative changes in the actual physical volume or number of items over time.
Question 13
If the Laspeyres index for a dataset is 120 and the Paasche index is 125, what is the approximate Fisher's Ideal Index?
- A) 122.47
- B) 125.00
- C) 150.00
- D) 145.45
Show answer & explanation
Answer: A) 122.47
Fisher's index is the geometric mean of the Laspeyres and Paasche indices. √(120 * 125) = √(15000) = approximately 122.47.
Question 14
A fundamental characteristic of the Laspeyres Index is that it tends to:
- A) Drastically understate the rate of inflation.
- B) Slightly overstate inflation by ignoring consumer substitution to cheaper goods.
- C) Yield the exact same result as the Paasche Index every time.
- D) Only work for agricultural commodities.
Show answer & explanation
Answer: B) Slightly overstate inflation by ignoring consumer substitution to cheaper goods.
Because Laspeyres uses fixed base-year quantities, it assumes consumers buy the exact same basket of goods regardless of price changes. It ignores the reality that consumers substitute away from expensive goods, thereby usually overstating living costs.
Question 15
What is the primary formula representing a Value Index?
- A) Sum(p1 * q1) / Sum(p0 * q0) * 100
- B) Sum(p1 * q0) / Sum(p0 * q0) * 100
- C) Sum(p0 * q1) / Sum(p1 * q1) * 100
- D) Sum(p1) / Sum(p0) * 100
Show answer & explanation
Answer: A) Sum(p1 * q1) / Sum(p0 * q0) * 100
A Value index measures the total combined change in both price and quantity. The formula takes the total current value (p1 * q1) divided by the total base value (p0 * q0), multiplied by 100.
Question 16
What is a defining characteristic of the Laspeyres price index regarding its denominator?
- A) It must be fully recalculated every single year using new quantities.
- B) It utilizes current year prices exclusively.
- C) The denominator does not change from year to year because it uses fixed base-year quantities.
- D) It purely calculates the geometric mean.
Show answer & explanation
Answer: C) The denominator does not change from year to year because it uses fixed base-year quantities.
In the standard Laspeyres price index, the denominator strictly uses base period quantities, meaning it fundamentally does not change from year to year.
Question 17
Why is the Laspeyres price index typically used more frequently in practical economic applications than the Paasche price index?
- A) It completely eliminates all traces of inflation.
- B) It does not require gathering new quantity data every year to recalculate the denominator.
- C) It automatically accounts for perfect consumer substitution.
- D) It only uses qualitative variables.
Show answer & explanation
Answer: B) It does not require gathering new quantity data every year to recalculate the denominator.
Laspeyres is used more heavily in practice because, unlike Paasche, its denominator is fixed and does not have to be recalculated every year to account for newly discovered quantities.
Question 18
Which of the following statements accurately describes a chain index series?
- A) Each new value in the index is strictly calculated based on the fixed base year.
- B) Each new value in the index is calculated based on the immediate previous year.
- C) It is exclusively used for tracking stock market prices.
- D) It only measures the absolute standard deviation.
Show answer & explanation
Answer: B) Each new value in the index is calculated based on the immediate previous year.
A chain index series is an index where each new sequential value is mathematically calculated based on the previous year rather than being tied to a single fixed base.
Question 19
The Consumer Price Index (CPI) is fundamentally designed to mathematically measure:
- A) The total industrial production output of a massive nation.
- B) The raw material costs directly for wholesale manufacturers.
- C) The cost of a specific consumer basket purchased by a typical urban family at a given point in time compared to a base year.
- D) The internal rate of return of corporate investments.
Show answer & explanation
Answer: C) The cost of a specific consumer basket purchased by a typical urban family at a given point in time compared to a base year.
The Consumer Price Index (CPI) explicitly measures the cost of a consumer basket purchased by a typical urban family at a specific point in time against a chosen base year.
Question 20
If an inflation price index is calculated as 116 in the current year with a base year index of 100, what is the precise interpretation?
- A) The price of the product will automatically increase by 16% every future year.
- B) Prices have increased by an average of 16% since the base year.
- C) The pure purchasing power has magically increased by 16%.
- D) Total physical quantities sold have dropped by exactly 16%.
Show answer & explanation
Answer: B) Prices have increased by an average of 16% since the base year.
An index increase directly from 100 to 116 signifies mathematically that the average price of the tracked product or basket has increased by exactly 16%.
Question 21
A commodity's price was Rs. 4,500 in the base year 20X8 and rose to Rs. 5,400 in 20Y0. What is the simple price relative index for 20Y0?
- A) 83.33
- B) 100.00
- C) 120.00
- D) 145.00
Show answer & explanation
Answer: C) 120.00
The simple price relative is calculated as (Current Price / Base Price) * 100. Here, (5400 / 4500) * 100 equals an index of exactly 120.
Question 22
Which statistical index number explicitly utilizes the current period's consumed quantities (q1) as its strict weighting factor?
- A) Laspeyres Index
- B) Paasche Price Index
- C) Simple Aggregate Index
- D) Fixed Base Index
Show answer & explanation
Answer: B) Paasche Price Index
The Paasche index requires its denominator to be recalculated every single year specifically to take account of the most recent current period quantities.
Question 23
When calculating a chained index, how is the link relative for a specific year manually determined?
- A) (Current Year Price / Base Year Price) * 100
- B) (Current Year Price / Previous Year Price) * 100
- C) (Previous Year Price / Base Year Price)
- D) By subtracting the previous year completely from the current year
Show answer & explanation
Answer: B) (Current Year Price / Previous Year Price) * 100
A chained index links data sequentially, calculating the current period's relative value strictly based on the immediate previous year's data.
Question 24
In general index construction, what is the most significant disadvantage of using the Simple Aggregate Method?
- A) It requires complex logarithmic calculations.
- B) It is heavily skewed by commodities with naturally large numerical unit prices, ignoring their actual economic importance.
- C) It forcefully commands quantities to be fixed.
- D) It cannot measure price changes over long periods of time.
Show answer & explanation
Answer: B) It is heavily skewed by commodities with naturally large numerical unit prices, ignoring their actual economic importance.
Simple aggregations only sum up raw prices, meaning a highly-priced but rarely used item will improperly dominate the index compared to cheap essentials.
Question 25
If the calculated value of Fisher's Ideal Index is 144, and the Laspeyres index is 140, which formula structure is being utilized to combine them?
- A) Arithmetic Mean of Laspeyres and Paasche
- B) Geometric Mean of Laspeyres and Paasche
- C) Harmonic Mean of Laspeyres and Paasche
- D) The squared mathematical difference
Show answer & explanation
Answer: B) Geometric Mean of Laspeyres and Paasche
Fisher's Ideal Index is universally defined in statistics as the strict geometric mean (the square root of the product) of the Laspeyres and Paasche indices.
Question 26
A chain index series demonstrates annual sales index figures of 107.0, 115.02, and 123.07 for three consecutive years. What does this progression indicate?
- A) A steady decline in overall sales.
- B) A compounding annual sales growth.
- C) A completely stagnant retail market.
- D) Extreme economic deflation.
Show answer & explanation
Answer: B) A compounding annual sales growth.
A steadily rising chained index graphically indicates that the annual sales growth is compounding year over year.
Question 27
The primary overarching mathematical purpose of constructing index numbers is to:
- A) Find the absolute net profit of a specific firm.
- B) Measure relative changes in the magnitude of variables (like prices) over time.
- C) Establish the optimal corner point of a complex feasible region.
- D) Calculate conditional statistical probabilities.
Show answer & explanation
Answer: B) Measure relative changes in the magnitude of variables (like prices) over time.
Index numbers are fundamentally used to statistically measure and track relative percentage changes over time, such as inflation or production volumes.
Question 28
If the base period price of Material A is Rs. 0.50 and the current period price is Rs. 0.75, what is the exact price relative?
- A) 50
- B) 75
- C) 150
- D) 125
Show answer & explanation
Answer: C) 150
The price relative is strictly the current price divided by the base price, multiplied by 100. (0.75 / 0.50) * 100 = exactly 150.
Question 29
When converting a nominal wage into a real wage, what mathematical role does the price index play?
- A) It is forcefully multiplied by the nominal wage.
- B) It is continuously added to the nominal wage.
- C) It is used as the divisor to mathematically strip away the effects of inflation.
- D) It is completely ignored.
Show answer & explanation
Answer: C) It is used as the divisor to mathematically strip away the effects of inflation.
To find true real purchasing power, the nominal wage is divided by the current price index and multiplied by 100, effectively stripping away the artificial effects of inflation.
Question 30
Why do statisticians periodically engage in the practice of 'base shifting' when maintaining long-term index numbers?
- A) To artificially lower the reported inflation rate.
- B) To transition the reference point to a more recent and economically relevant period.
- C) To convert a Laspeyres index directly into a Paasche index.
- D) To change the foundational weighting from prices to quantities.
Show answer & explanation
Answer: B) To transition the reference point to a more recent and economically relevant period.
Over long stretches of time, consumer habits fundamentally change, making old base years obsolete. Base shifting manually resets the index to a more recent, relevant year to ensure ongoing accuracy.
Question 31
When maintaining a long-term index series, what is the statistical process of 'base shifting'?
- A) Converting a price index into a quantity index.
- B) Changing the reference period (the base year 100) to a more recent, economically relevant year.
- C) Averaging the base year and current year prices.
- D) Eliminating outliers from the index.
Show answer & explanation
Answer: B) Changing the reference period (the base year 100) to a more recent, economically relevant year.
Base shifting occurs when the original base year becomes obsolete due to changing consumer habits over time. The index is recalibrated so a more recent year acts as the new baseline of 100.
Question 32
How is 'Real Income' or true purchasing power mathematically calculated using the Consumer Price Index (CPI)?
- A) (Nominal Income × CPI) / 100
- B) Nominal Income - CPI
- C) (Nominal Income / CPI) × 100
- D) (CPI / Nominal Income) × 100
Show answer & explanation
Answer: C) (Nominal Income / CPI) × 100
To strip away the effects of inflation and find true purchasing power, the nominal (raw) wage is divided by the current CPI and multiplied by 100. This is known as deflating the income.
Question 33
In index construction theory, what is Fisher's Ideal Index fundamentally defined as?
- A) The arithmetic mean of the Laspeyres and Paasche indices.
- B) The geometric mean (square root of the product) of the Laspeyres and Paasche indices.
- C) The simple aggregate of base year prices.
- D) The harmonic mean of current quantities.
Show answer & explanation
Answer: B) The geometric mean (square root of the product) of the Laspeyres and Paasche indices.
Fisher's Ideal Index resolves the respective biases of the Laspeyres and Paasche indices by mathematically crossing them, taking the strict geometric mean of the two.
Question 34
A known statistical flaw of the Laspeyres price index is its tendency to mathematically:
- A) Understate the true rate of inflation.
- B) Overstate the true rate of inflation because it ignores the fact that consumers substitute away from expensive goods.
- C) Force prices to remain constant.
- D) Deflate nominal wages too heavily.
Show answer & explanation
Answer: B) Overstate the true rate of inflation because it ignores the fact that consumers substitute away from expensive goods.
Because Laspeyres rigidly uses older, fixed base-year quantities, it assumes consumers buy the exact same amount of a good even after its price skyrockets, typically causing it to overstate actual inflation.
Question 35
If the sum of prices for three commodities in the base year was Rs. 50, and the sum of their prices in the current year is Rs. 75, what is the Simple Aggregate Price Index?
- A) 125
- B) 150
- C) 200
- D) 250
Show answer & explanation
Answer: B) 150
The simple aggregate method merely sums the current prices and divides by the sum of the base prices, multiplied by 100. Here, (75 / 50) * 100 = 150.
Question 36
In economic statistics, the 'purchasing power of money' is strictly defined as:
- A) The exact geometric mean of all household wages.
- B) The reciprocal of the Consumer Price Index (1 / CPI).
- C) The absolute variance of retail inflation.
- D) The standard error of the Paasche index.
Show answer & explanation
Answer: B) The reciprocal of the Consumer Price Index (1 / CPI).
As prices (CPI) rise, the actual value or purchasing power of a single unit of currency inversely falls. It is mathematically calculated as the exact reciprocal of the price index.
Question 37
When formulating a Paasche *Quantity* Index (rather than a price index), what data is utilized as the mathematical weighting factor?
- A) Base year prices (p0)
- B) Base year quantities (q0)
- C) Current year prices (pn)
- D) Current year quantities (qn)
Show answer & explanation
Answer: C) Current year prices (pn)
A quantity index tracks changes in physical volumes. Following Paasche's fundamental rule of using 'current' data for weights, a Paasche Quantity Index weights the volumes using current year prices (pn).
Question 38
Conversely, what does the Laspeyres *Quantity* Index exclusively use as its weighting factor?
- A) Base year prices (p0)
- B) Base year quantities (q0)
- C) Current year prices (pn)
- D) Current year quantities (qn)
Show answer & explanation
Answer: A) Base year prices (p0)
Laspeyres always relies on historical, base-period data for weighting. Therefore, a Laspeyres Quantity index will weight the shifting volumes using the fixed base year prices (p0).
Question 39
Which of the following index calculation methods relies heavily on the use of sequential 'link relatives'?
- A) The Fixed Base Index
- B) The Simple Aggregate Method
- C) The Chain Index
- D) The Standard Normal Distribution
Show answer & explanation
Answer: C) The Chain Index
A chain index uses link relatives, which are calculated by comparing the current period's data strictly against the immediate preceding period, chaining them together to form a long-term index.
Question 40
What is a 'Value Index' designed to mathematically measure?
- A) Only the change in raw prices over time.
- B) Only the change in physical quantities over time.
- C) The relative change in total monetary value, which incorporates both price changes and quantity changes (p × q).
- D) The absolute net profit of an individual firm.
Show answer & explanation
Answer: C) The relative change in total monetary value, which incorporates both price changes and quantity changes (p × q).
A Value Index measures changes in total expenditure or revenue, meaning it simultaneously evaluates the change in price multiplied by the change in quantity (∑pnqn / ∑p0q0).
Question 41
When selecting a 'base year' for a price index, statisticians generally aim to pick a year that is:
- A) The absolute highest inflation year on record.
- B) A year of extreme economic depression.
- C) A 'normal' economic year free from extreme crises, wars, or massive abnormalities.
- D) Always exactly 50 years in the past.
Show answer & explanation
Answer: C) A 'normal' economic year free from extreme crises, wars, or massive abnormalities.
The base year serves as the foundation for all future comparisons (index = 100). If an abnormal crisis year is chosen, all subsequent data will appear artificially distorted.
Question 42
What is considered a massive, practical advantage of utilizing a Chained Index over a Fixed Base Index?
- A) It is much simpler to calculate manually.
- B) It allows for obsolete items to be easily dropped and new commodities to be seamlessly introduced into the basket each year.
- C) It completely removes the need for weightings.
- D) It ensures the base year never changes.
Show answer & explanation
Answer: B) It allows for obsolete items to be easily dropped and new commodities to be seamlessly introduced into the basket each year.
Because a chained index only compares the current year to the immediately preceding year, the consumer basket can be updated annually, making it highly responsive to new products (like smartphones replacing landlines).
Question 43
What is the formula to manually calculate a 'Simple Price Relative' for a single commodity?
- A) (Current Price / Base Price) × 100
- B) (Base Price / Current Price) × 100
- C) (Current Price - Base Price) / 100
- D) (Current Quantity / Base Quantity) × 100
Show answer & explanation
Answer: A) (Current Price / Base Price) × 100
A simple price relative isolates a single good and calculates its percentage growth by dividing the current period price (pn) by its base period price (p0) and multiplying by 100.
Question 44
In the standard mathematical notation for index construction, what does the expression 'pn * q0' explicitly dictate?
- A) Base year prices multiplied by base year quantities.
- B) Current year prices multiplied by base year quantities.
- C) Current year prices multiplied by current year quantities.
- D) Base year prices multiplied by current year quantities.
Show answer & explanation
Answer: B) Current year prices multiplied by base year quantities.
The subscript 'n' denotes the current year, and the subscript '0' denotes the fixed base year. Therefore, pn * q0 dictates calculating the cost of the base year's physical basket at today's prevailing prices.
Question 45
If an official government price index rises from 100 in 2015 to 142 in 2024, what is the precise interpretation of this data?
- A) The exact physical volume of goods produced has increased by 42%.
- B) The standard error has expanded by 42 points.
- C) Average prices of the goods in the index basket have increased by exactly 42% since 2015.
- D) Wages have automatically risen by 42%.
Show answer & explanation
Answer: C) Average prices of the goods in the index basket have increased by exactly 42% since 2015.
Index numbers express relative changes as percentages compared to a base of 100. A shift to 142 mathematically indicates a 42% increase in the variable being tracked (in this case, prices).
Question 46
What is the standard formula utilized to calculate a 'Simple Price Relative' for a single, isolated commodity?
- A) (Base Price / Current Price) × 100
- B) (Current Price / Base Price) × 100
- C) (Current Price - Base Price) / 100
- D) (Current Quantity / Base Quantity) × 100
Show answer & explanation
Answer: B) (Current Price / Base Price) × 100
A simple price relative tracks the inflation of a single item by dividing the current period price (pn) by the historical base period price (p0) and mathematically multiplying by 100.
Question 47
In the construction of a Laspeyres Price Index, what specific data is utilized as the fixed mathematical weighting factor?
- A) Current year quantities (qn)
- B) Base year quantities (q0)
- C) Current year prices (pn)
- D) Current year values (pn * qn)
Show answer & explanation
Answer: B) Base year quantities (q0)
The Laspeyres price index relies entirely on a fixed, historical basket of goods. Therefore, it mathematically uses the base year quantities (q0) strictly as its weighting factor in both the numerator and denominator.
Question 48
Conversely, what specific data does the Paasche Price Index utilize as its weighting factor?
- A) Base year quantities (q0)
- B) Base year prices (p0)
- C) Current year quantities (qn)
- D) Arithmetic mean quantities
Show answer & explanation
Answer: C) Current year quantities (qn)
Unlike Laspeyres, the Paasche index measures the cost of today's exact consumption. It uses current year quantities (qn) as the weighting factor, requiring the denominator to be recalculated every single year.
Question 49
How is Fisher's Ideal Index mathematically defined in statistical theory?
- A) The arithmetic mean of the Laspeyres and Paasche indices.
- B) The simple aggregate of base year prices.
- C) The geometric mean (square root of the product) of the Laspeyres and Paasche indices.
- D) The harmonic mean of all current index links.
Show answer & explanation
Answer: C) The geometric mean (square root of the product) of the Laspeyres and Paasche indices.
Fisher's Ideal Index perfectly resolves the respective biases of the Laspeyres (upward bias) and Paasche (downward bias) indices by mathematically calculating the strict geometric mean of the two.
Question 50
What is a massive, practical advantage of utilizing a 'Chain Base Index' method rather than a Fixed Base Index?
- A) It is much simpler to manually calculate.
- B) It allows obsolete commodities to be seamlessly dropped and new commodities introduced into the basket each year.
- C) It mathematically eliminates all inflation.
- D) It ensures the base year never changes.
Show answer & explanation
Answer: B) It allows obsolete commodities to be seamlessly dropped and new commodities introduced into the basket each year.
Because a chain base index calculates links by strictly comparing the current year to the immediate preceding year, the consumer basket can be freely updated annually, making it highly responsive to shifting economic trends.
Question 51
To properly convert a nominal wage into a 'real' wage (reflecting true inflation-adjusted purchasing power), what mathematical operation is executed?
- A) The nominal wage is multiplied by the standard error.
- B) The nominal wage is divided by the current Consumer Price Index (CPI) and multiplied by 100.
- C) The current CPI is directly subtracted from the wage.
- D) The nominal wage is squared.
Show answer & explanation
Answer: B) The nominal wage is divided by the current Consumer Price Index (CPI) and multiplied by 100.
Dividing the raw nominal wage by the prevailing price index mathematically strips away the artificial inflation factor, revealing the true 'real' purchasing power (or deflated value) of the income.
Question 52
In economic statistics, the 'purchasing power of money' is mathematically defined strictly as:
- A) The arithmetic sum of all household wages.
- B) The absolute variance of retail inflation.
- C) The exact reciprocal of the Consumer Price Index (1 / CPI).
- D) The geometric mean of the Paasche index.
Show answer & explanation
Answer: C) The exact reciprocal of the Consumer Price Index (1 / CPI).
As general prices (CPI) rise, the actual value or purchasing power of a single unit of currency inversely falls. It is therefore mathematically defined as the exact reciprocal of the price index.
Question 53
If an official government price index rises from a base of 100 in 2018 to exactly 165 in 2025, what is the precise statistical interpretation of this data?
- A) Absolute sales volumes have dropped by 65%.
- B) The physical volume of goods produced has increased by 65%.
- C) Average prices of the goods in the index basket have increased by exactly 65% since 2018.
- D) Nominal wages have automatically risen by 165%.
Show answer & explanation
Answer: C) Average prices of the goods in the index basket have increased by exactly 65% since 2018.
Index numbers express relative changes as percentages compared to a fixed base of 100. A shift to 165 mathematically indicates an exact 65% increase in the variable being tracked.
Question 54
If the sum of prices for four raw materials in the base year was Rs. 80, and the sum of their prices in the current year is Rs. 100, what is the computed Simple Aggregate Price Index?
- A) 110
- B) 120
- C) 125
- D) 150
Show answer & explanation
Answer: C) 125
The simple aggregate method merely sums the unweighted current prices and divides by the sum of the base prices, multiplied by 100. Here, (100 / 80) * 100 = 125.
Question 55
When formulating a Laspeyres *Quantity* Index (rather than a standard price index), what historical data is utilized as the mathematical weighting factor?
- A) Base year quantities (q0)
- B) Base year prices (p0)
- C) Current year quantities (qn)
- D) Current year prices (pn)
Show answer & explanation
Answer: B) Base year prices (p0)
Because it is a Laspeyres index, it must rely on historical, base-period data for weighting. To track changing physical quantities, a Laspeyres Quantity index weights the volumes using fixed base year prices (p0).
Question 56
Conversely, when formulating a Paasche *Quantity* Index, what data is exclusively used as the weighting factor?
- A) Base year prices (p0)
- B) Base year quantities (q0)
- C) Current year prices (pn)
- D) Current year quantities (qn)
Show answer & explanation
Answer: C) Current year prices (pn)
Following Paasche's fundamental rule of using 'current' data for weights, a Paasche Quantity Index tracks changing volumes by weighting them against current year prices (pn).
Question 57
What is an inherent statistical flaw of utilizing the 'Simple Aggregate Method' to construct a price index?
- A) It ignores quantities completely and is heavily, artificially skewed by individual items with naturally large numerical unit prices.
- B) It forces the base year to change constantly.
- C) It strictly requires geometric interpolation.
- D) It cannot mathematically measure price drops.
Show answer & explanation
Answer: A) It ignores quantities completely and is heavily, artificially skewed by individual items with naturally large numerical unit prices.
The simple aggregate method merely sums raw prices without logical volume weights. Thus, a high-priced item (like a diamond) will completely dominate the index over a highly consumed essential (like bread), making it economically inaccurate.
Question 58
What is a 'Value Index' designed to mathematically measure?
- A) Only the change in raw prices over time.
- B) Only the change in physical quantities over time.
- C) The relative change in total monetary expenditure or revenue, incorporating both price changes and quantity changes (p × q).
- D) The absolute net profit margin of an individual firm.
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Answer: C) The relative change in total monetary expenditure or revenue, incorporating both price changes and quantity changes (p × q).
A Value Index comprehensively measures changes in total expenditure, meaning it simultaneously evaluates the change in price mathematically multiplied by the change in quantity (∑pnqn / ∑p0q0).
Question 59
When maintaining a long-term index series, what is the statistical process known as 'base shifting'?
- A) Converting a price index into a quantity index.
- B) Changing the reference period (the year set to 100) to a more recent, economically relevant year.
- C) Averaging the base year and current year prices.
- D) Stripping away extreme outliers from the index basket.
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Answer: B) Changing the reference period (the year set to 100) to a more recent, economically relevant year.
Base shifting occurs when the original base year becomes obsolete due to long-term changing consumer habits. The index is mathematically recalibrated so a more recent year acts as the new 100 baseline.
Question 60
What is the primary economic and statistical purpose of calculating the Consumer Price Index (CPI)?
- A) To measure the absolute net worth of a nation's gold reserves.
- B) To track wholesale manufacturing input costs.
- C) To measure the changing cost of a specific basket of consumer goods and services purchased by a typical urban household.
- D) To calculate the standard error of corporate dividends.
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Answer: C) To measure the changing cost of a specific basket of consumer goods and services purchased by a typical urban household.
The Consumer Price Index (CPI) is the most widely utilized measure of inflation, explicitly designed to track the changing cost of living by pricing a specific basket of retail goods purchased by a typical household.