Chapter 2 -- Quiz -- General

Thomas Piketty, Capital in the 21st Century (Harvard University Press 2014)

Patrick Toche

Question 1

The period of higher world population growth is

  1. 0-1500
  2. 1500-1600
  3. 1600-1700
  4. 1700-1800
  5. 1800-1900
  6. 1900-2000

World population in the year 0 was about 300 million. In 1500, it was about 500 million. Current world population is about 7 billion.

See Table 2.1.

Based on United Nations estimates (Department of Economic and Social Affairs): World population in 1500 was about 500 million; in 1600 about 550 million; in 1700 about 600 million; in 1800 about 1 billion; in 1900 about 1.5 billion; in 1925 about 2 billion; in 1950 about 2.5 billion; in 1960 about 3 billion; in 1975 about 4 billion; in 1990 about 5 billion; in 2000 about 6 billion; in 2010 about 7 billion; by 2025 probably about 8 billion; by 2040 probably about 9 billion; by 2060 about 10 billion; some time after 2100 about 11 billion.

Question 2

The period of higher world output growth is

  1. 0-1500
  2. 1500-1600
  3. 1600-1700
  4. 1700-1800
  5. 1800-1900
  6. 1900-2000

The third industrial revolutions spurred larger growth rates than the first and second industrial revolutions.

See Table 2.1.

Question 3

An annual growth rate of 1% compounded over 100 years results in a total increase by a factor of

  1. 0.7
  2. 1.7
  3. 2.7
  4. 3.7
  5. 4.7
  6. 5.7

An annual growth rate of \(g\) compounded \(T\) times results in a total ('non-annual') growth rate of \(G = (1 + g)^{T} - 1\).

An annual growth rate of \(0.01\) compounded \(100\) times results in a total increase: \[ 1 + G = (1 + 0.01)^{100} \simeq 2.7 \]

Question 4

An annual growth rate of 10% compounded over 10 years results in a total growth rate of

  1. 0.6
  2. 1.6
  3. 2.6
  4. 3.6
  5. 4.6
  6. 5.6

An annual growth rate of \(g\) compounded \(T\) times results in a total ('non-annual') growth rate of \(G = (1 + g)^{T} - 1\).

An annual growth rate of \(0.10\) compounded \(10\) times results in total growth: \[ G = (1 + 0.1)^{10} - 1 \simeq 1.6\% \]

Question 5

Which gives the greater growth? (a) annual growth rate of 1% compounded over 100 years; (b) annual growth rate of 10% compounded over 10 years.

  1. (a) and (b) give exactly the same growth.
  2. (a) and (b) give almost the same growth, but (a) is a little greater.
  3. (a) and (b) give almost the same growth, but (b) is a little greater.
  4. (a) and (b) give very different growth, with (a) much greater.
  5. (a) and (b) give very different growth, with (b) much greater.
  6. There is not enough information to answer the question.

Precision: 'much' means a more than 20% difference — 'little' means less than a 10% difference.

Case (a). An annual growth rate of \(0.01\) compounded \(100\) times gives: \[ 1 + G = (1 + 0.01)^{100} \simeq 2.7 \] or \(G \simeq 1.7\%\)

Case (b). An annual growth rate of \(0.10\) compounded \(10\) times gives: \[ 1 + G = (1 + 0.1)^{10} \simeq 2.6 \] or \(G \simeq 1.6\%\)

The compounding effect is a little larger in case (a).

Question 6

Which gives the greater average growth rate? (a) annual growth of 1% followed by 2%; (b) annual growth of 2% followed by 1%.

  1. (a) and (b) always give exactly the same average growth rate.
  2. (a) always gives greater average growth rate than (b).
  3. (b) always gives greater average growth rate than (a).
  4. (a) gives a greater rate than (b) if the starting value is greater.
  5. (b) gives a greater rate than (a) if the starting value is greater.
  6. There is not enough information to answer the question.

Experiment with a starting value of \$100.

The starting value is irrelevant. The order of the growth episodes is irrelevant. Let \(A_{t}\) denote the value at date \(t\). Let \(g_{t}\) denote the growth rate between date \(t\) and date \(t+1\). After 1 year, the value has grown to \[ A_{t+1} = A_{t} (1+g_{t}) \] After another year, \[ A_{t+2} = A_{t+1} (1+g_{t+1}) \] Taken together, \[ A_{t+2} = A_{t} (1+g_{t}) (1+g_{t+1}) \] It is clear from the above that the order of the growth rates is irrelevant.

The overall growth rate is \[ \frac{A_{t+2} - A_{t}}{A_{t}} = \frac{A_{t+2}}{A_{t}} - 1 = (1+g_{t}) (1+g_{t+1}) - 1 \] It is now clear that the starting value is also irrelevant.

Question 7

An asset initially worth \$100 (a) rises by 10%, then falls by 10%; (b) falls by 10%, then rises by 10%. What is the final value of the asset?

  1. \$101 in both cases.
  2. \$100 in both cases.
  3. \$99 in both cases.
  4. \$101 in case (a), \$99 in case (b).
  5. \$101 in case (b), \$99 in case (a).
  6. There is not enough information to answer the question.

The question assumes the starting value is used as a base — do not use the mid-point method!

The order of the growth rates is irrelevant. In both cases, the final value of the asset is \[ \$100 \times (1 + 0.1) \times (1 - 0.1) = \$100 \times 1.1 \times 0.9 = \$100 \times 0.99 = \$99 \]

Question 8

United Nations estimates suggest that world population growth

  1. averaged 1.8% during 1970-1990, and 1.8% again during 1990-2010.
  2. averaged 1.3% during 1970-1990, and 1.3% again during 1990-2010.
  3. rose to 1.3% during 1970-1990, and again to 1.8% during 1990-2010.
  4. fell to 1.3% during 1970-1990, and rose to 1.8% during 1990-2010.
  5. rose to 1.8% during 1970-1990, and fell to 1.3% during 1990-2010.
  6. fell to 1.8% during 1970-1990, and again to 1.3% during 1990-2010.

See Chapter 2.

See Chapter 2 and Table 2.3.

Question 9

The current structure of employment in the rich countries (U.S., Germany, Japan):

  1. Manufacturing accounts for more than 50% of total employment. Services account for less than 30%. Agriculture accounts for less than 5%.
  2. Manufacturing accounts for more than 50% of total employment. Services account for more than 30%. Agriculture accounts for less than 5%.
  3. Manufacturing accounts for more than 50% of total employment. Services account for more than 30%. Agriculture accounts for more than 5%.
  4. Services account for more than 50% of total employment. Manufacturing accounts for less than 30%. Agriculture accounts for less than 5%.
  5. Services account for more than 50% of total employment. Manufacturing accounts for more than 30%. Agriculture accounts for less than 5%.
  6. Services account for more than 50% of total employment. Manufacturing accounts for more than 30%. Agriculture accounts for more than 5%.

See Table 2.4.

See Chapter 2 and Table 2.4.

Question 10

In the United States, the United Kingdom, Germany, France, the following periods were characterized by:

  1. 1700-1900: high inflation — 1914-1929: high inflation — 1970-1980: high inflation.
  2. 1700-1900: high inflation — 1914-1929: high inflation — 1970-1980: low inflation.
  3. 1700-1900: high inflation — 1914-1929: low inflation — 1970-1980: high inflation.
  4. 1700-1900: low inflation — 1914-1929: low inflation — 1970-1980: low inflation.
  5. 1700-1900: low inflation — 1914-1929: high inflation — 1970-1980: low inflation.
  6. 1700-1900: low inflation — 1914-1929: high inflation — 1970-1980: high inflation.

'Low inflation' refers to annual inflation rates ranging from -1% to +2%. High inflation refers to annual inflation rates in excess of 4%. 'A period' refers to most years within the given dates (at least half of the time) and for most countries (at least 3 of 5 countries).

The period 1700-1914 was a period in which most currencies were pegged to gold or other precious metals at a fixed rate, resulting in moderate price fluctuations (caused mostly by gold discoveries and shortages). The period 1914-1929 was a period of post-war reconstruction, with government finances damaged by the first world war (especially Germany who was being forced to pay for the cost of the war), and goods and stock prices soaring. France and Germany experienced hyperinflation in the early 1920s. The period 1970-1980 was a period of two oil price shocks and lax monetary policy (in an attempt my governments to reduce unemployment).