Assignment 2

Answers for these questions come from both the course content and the readings. Each question is worth one point, for a total of 20 points. Passing this module requires at least 65% (13 out of 20 correct). Email your answers to one of the course instructors (either Steve Martin or Shaoxiong Wang or Anastasiia Nosach) when you are finished.

Question 1 True or false: The Laspeyres index is a cost-of-living index if consumers do not substitute away from more expensive goods when prices change.

Question 2 True or false: The time-reversal test says that a price index between period 0 and period 1 is the same as the reciprocal of the price index between period 1 and period 0.

Question 3 What is the difference between the economic and axiomatic approaches to index numbers?

  1. Prices and quantities are independent in the axiomatic approach and dependent in the economic approach.

  2. The economic approach treats prices as fixed, whereas the axiomatic approach treats prices as random.

  3. The economic approach consists of a series of test based on economic theory to gauge the appropriateness of an index number, while the axiomatic approach uses the fundamental axioms from set theory to gauge how well an index number compares lists of prices.

  4. The axiomatic approach and the economic approach are equivalent.

  5. None of the above.

Question 4 What weights does the Palgrave index use to aggregate price relatives between period 0 and period 1?

  1. Period-0 expenditure/revenue shares.

  2. Period-1 expenditure/revenue shares.

  3. The geometric average of period-0 and period-1 expenditure/revenue shares.

  4. The harmonic average of period-0 and period-1 expenditure/revenue shares.

  5. None of the above.

Question 5 True or false: The Fisher index is highly regarded as an index number because it satisfies the most important axioms and always corresponds to a cost-of-living index.

Question 6 True or false: The time-reversal test says that a price index and a quantity index have the same functional form.

Question 7 Which axiom does the Dutot index not satisfy?

  1. Monotonicity.

  2. Continuity.

  3. Dimensional invariance.

  4. Circularity.

  5. None of the above.

Question 8 True or false: It is impossible for a geometric Laspeyres index to be a cost-of-living index.

Question 9 What type of index should be used to calculate a Laspeyres quantity index by deflating the change in aggregate value between two periods?

  1. Palgrave index.

  2. Laspeyres index.

  3. Paasche index.

  4. Fisher index.

  5. Geometric Laspeyres index.

Question 10 True or false: The Jevons index is a biased estimator of the geometric index in the population under random sampling.

The next 4 questions use data in the following table that contains a population of three price relatives, each with equal probability, and all possible samples from this population.

Population of price relatives Sample 1 Sample 2 Sample 3
1.2 1.2 1.2 1.1
1.1 1.1 1.35 1.35
1.35 … … …

Question 11 What is the value of the geometric index in the population?

  1. 121.2

  2. 100

  3. 120.5

  4. 129.8

  5. 98.7

Question 12 What is the (arithmetic) average value of the Jevons indices in each sample?

  1. 121.2

  2. 119.4

  3. 121.3

  4. 100

  5. 123.1

Question 13 What is the value of the bias in the Jevons index?

  1. 0

  2. -0.2

  3. 0.1

  4. 0.8

  5. -1.3

Question 14 What is the value of the bias in the Carli index?

  1. 1.1

  2. -0.4

  3. -0.2

  4. 0.7

  5. 0

Question 15 True or false: If a representative consumer has a constant elasticity of substitution utility function, the magnitude of the substitution bias increases as the elasticity of substitution increases.

The next four questions use data in the following table that contains information on prices and quantities for two inputs over two periods, along with a true input-price index.

Period Price 1 Price 2 Quantity 1 Quantity 2 Input-price index
0 100 60 141 391 100.0
1 120 80 160 360 128.0

Question 16 What is the value of the Laspeyres index?

  1. 101.0

  2. 133.3

  3. 128.0

  4. 128.3

  5. 99.3

Question 17 What is the value of the Paasche index?

  1. 127.7

  2. 131.2

  3. 101.0

  4. 99.1

  5. 130.0

Question 18 What is the value of the Jevons index?

  1. 120.1

  2. 128.2

  3. 99.0

  4. 126.5

  5. 98.4

Question 19 True or false: The Jevons index calculated in question 18 is closer in value to the input-price index than the Fisher index.

Question 20 True or false: It is possible to construct an input-price index for a firm that has market power for the goods it sells.