Terms of Trade: Concepts, Calculation, and Determinants Practice Questions — JAMB UTME

Question 1Question →

In a given trade period, Country X recorded an export price index of $150$ and an import price index of $120$ . What is the Net Barter Terms of Trade for Country X?

125.0

80.0

130.0

180.0

Show answer & explanation

Answer: $125.0$

Answer

The Net Barter Terms of Trade for Country X is

125.0

.

The Net Barter Terms of Trade is defined as the ratio of the index of export prices to the index of import prices, multiplied by

100

. Substituting

150

for export prices and

120

for import prices gives

\frac{150}{120} \times 100 = 125.0

. A value above

100

indicates a favorable terms of trade.

Step-by-Step Solution

1

Identify the formula for Net Barter Terms of Trade

\text{Net Barter Terms of Trade} = \left( \frac{\text{Index of Export Prices}}{\text{Index of Import Prices}} \right) \times 100

The Net Barter Terms of Trade measures the relative price of exports in terms of imports.

2

Substitute the given values into the formula

\text{Net Barter Terms of Trade} = \left( \frac{150}{120} \right) \times 100

The export price index is

150

and the import price index is

120

.

3

Compute the final ratio

1.25 \times 100 = 125.0

Dividing

150

by

120

yields

1.25

, which multiplied by

100

gives an index of

125.0

.

Key Concept

Net Barter Terms of Trade

Question 2Question →

Match each Terms of Trade concept on the left with its correct mathematical formula and interpretation on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Net Barter Terms of Trade matches with

\left(\frac{P_x}{P_m}\right) \times 100

; Income Terms of Trade matches with

\left(\frac{P_x}{P_m}\right) \times Q_x

; Single Factoral Terms of Trade matches with

\left(\frac{P_x}{P_m}\right) \times Z_x

; Gross Barter Terms of Trade matches with

\left(\frac{Q_m}{Q_x}\right) \times 100

.

Each concept correctly maps to its definition and formula: Net Barter Terms of Trade measures price indices (

\% P_x / P_m

), Income Terms of Trade measures capacity to import based on export revenue (

\% P_x / P_m \times Q_x

), Single Factoral Terms of Trade incorporates domestic export productivity (

\% P_x / P_m \times Z_x

), and Gross Barter Terms of Trade measures physical trade quantities (

Q_m / Q_x

).

Step-by-Step Solution

1

Identify the formula for Net Barter Terms of Trade

Net Barter Terms of Trade measures price movement of exports relative to imports:

\left(\frac{P_x}{P_m}\right) \times 100

.

It forms the baseline commodity terms of trade index.

2

Identify the formula for Income Terms of Trade

Income Terms of Trade reflects export purchasing power:

\left(\frac{P_x}{P_m}\right) \times Q_x

.

Multiplying commodity terms of trade by export quantity index (

Q_x

) yields total import capacity derived from exports.

3

Identify the formula for Single Factoral Terms of Trade

Single Factoral Terms of Trade incorporates domestic productivity:

\left(\frac{P_x}{P_m}\right) \times Z_x

.

Z_x

represents the productivity index in the domestic export sector.

4

Identify the formula for Gross Barter Terms of Trade

Gross Barter Terms of Trade evaluates physical quantities of trade:

\left(\frac{Q_m}{Q_x}\right) \times 100

.

Unlike Net Barter TOT which uses prices, Gross Barter TOT compares the total quantity of imports received to exports given up.

Key Concept

Terms of Trade Concepts and Formulas

Question 3Question →

In a given trading period, a nation recorded an export price index of $140$ and an import price index of $175$ , with the base year index set at $100$ . What is the Net Barter Terms of Trade for this nation?

80.00

125.00

157.50

35.00

Show answer & explanation

Answer: $80.00$

Answer

The Net Barter Terms of Trade is

80.00

, indicating an unfavorable terms of trade since the index is below

100

.

The Net Barter Terms of Trade is defined as the ratio of the index of export prices to the index of import prices, expressed as a percentage:

TOT = (P_x / P_m) \times 100

. Substituting

P_x = 140

and

P_m = 175

gives

(140 / 175) \times 100 = 80.00

.

Step-by-Step Solution

1

Identify the formula for Net Barter Terms of Trade (TOT).

TOT = \left(\frac{\text{Index of Export Prices}}{\text{Index of Import Prices}}\right) \times 100

Net Barter Terms of Trade measures the ratio between export price changes and import price changes relative to a base period.

2

Substitute the given values into the formula.

TOT = \left(\frac{140}{175}\right) \times 100

The export price index is

140

and the import price index is

175

.

3

Perform the division and simplify.

TOT = 0.80 \times 100 = 80.00

Dividing

140

by

175

yields

0.80

, which scales to

80.00

when multiplied by

100

.

Key Concept

Net Barter Terms of Trade Calculation

Estimated Time:1m 30s

Question 4Question →

In international economics, terms of trade can be expressed through various metrics depending on whether price levels, physical quantities, or factor productivities are being evaluated. Match each Terms of Trade concept on the left with its correct mathematical representation on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Gross Barter Terms of Trade matches

\left(\frac{Q_m}{Q_x}\right) \times 100

; Income Terms of Trade matches

\left(\frac{P_x}{P_m}\right) \times Q_x

; Single Factoral Terms of Trade matches

\left(\frac{P_x}{P_m}\right) \times Z_x

; Double Factoral Terms of Trade matches

\left(\frac{P_x}{P_m}\right) \times \left(\frac{Z_x}{Z_m}\right)

.

Each Terms of Trade concept correctly aligns with its economic formula: Gross Barter measures physical volume ratios, Income Terms of Trade calculates total import purchasing capacity based on export revenue, Single Factoral accounts for domestic export productivity improvements, and Double Factoral accounts for relative productivity between domestic and foreign trading sectors.

Step-by-Step Solution

1

Analyze the scope and variables of each Terms of Trade metric.

Gross Barter uses physical volume indices (

Q_m, Q_x

); Income Terms of Trade measures total import capacity using export volume (

Q_x

); Single Factoral adjusts for export productivity (

Z_x

); Double Factoral adjusts for both export (

Z_x

) and import (

Z_m

) productivities.

Different concepts refine commodity terms of trade to account for volume changes and factor productivity changes.

2

Match each economic concept with its precise algebraic formula.

Gross Barter

\rightarrow \left(\frac{Q_m}{Q_x}\right) \times 100

, Income Terms of Trade

\rightarrow \left(\frac{P_x}{P_m}\right) \times Q_x

, Single Factoral

\rightarrow \left(\frac{P_x}{P_m}\right) \times Z_x

, Double Factoral

\rightarrow \left(\frac{P_x}{P_m}\right) \times \left(\frac{Z_x}{Z_m}\right)

.

These formulas directly correspond to the classical definitions of international trade metrics.

Key Concept

Classification and Formulation of Terms of Trade Metrics

Question 5Question →

In a given trade cycle, a nation establishes its base year export price index, import price index, and export volume index all at $100$ . In the current year, export prices rise by $25\%$ , import prices rise by $50\%$ , and the volume of exports increases by $20\%$ . What is the nation's Income Terms of Trade ( $ITT$ ) for the current year, and what does this imply about its total capacity to import?

100.0

, implying that the nation's overall capacity to import remains unchanged relative to the base year.

144.0

, implying that the nation's overall capacity to import has increased by

44\%

relative to the base year.

83.3

, implying that the nation's overall capacity to import has declined by

16.7\%

relative to the base year.

103.3

, implying that the nation's overall capacity to import has increased by

3.3\%

relative to the base year.

Show answer & explanation

Answer: $100.0$ , implying that the nation's overall capacity to import remains unchanged relative to the base year.

Answer

The Income Terms of Trade for the current year is

100.0

, indicating that the nation's total capacity to import remains unchanged compared to the base year.

The Income Terms of Trade measures a country's total capacity to import by adjusting its price ratio (

NB\,TOT

) by the quantity of exports (

Q_x

). Given

P_x = 125

,

P_m = 150

, and

Q_x = 120

, the calculation

\left(\frac{125}{150}\right) \times 120 = 100.0

confirms that the physical volume expansion of exports fully counteracts the worsening unit price ratio, leaving the country's overall purchasing power for imports unchanged.

Step-by-Step Solution

1

Calculate the current period export price index (

P_x

) and import price index (

P_m

).

P_x = 100 + (0.25 \times 100) = 125

;

P_m = 100 + (0.50 \times 100) = 150

.

Percentage increases are added to the base year index of 100.

2

Determine the current period export volume index (

Q_x

).

Q_x = 100 + (0.20 \times 100) = 120

.

The volume of exports expanded by 20% over the base index.

3

Apply the Income Terms of Trade formula:

ITT = \left(\frac{P_x}{P_m}\right) \times Q_x

.

ITT = \left(\frac{125}{150}\right) \times 120 = \frac{5}{6} \times 120 = 100.0

.

Income Terms of Trade measures a country's physical capacity to import based on export earnings.

4

Interpret the resulting index in comparison to the base year value of 100.

Since

ITT = 100.0

, the nation's total capacity to import is equal to that of the base year.

An index of 100 signifies no net change in real import purchasing power.

Key Concept

Income Terms of Trade (

ITT

) and Capacity to Import

Question 6Question →

Match each Terms of Trade concept or structural analytical framework on the left with its precise economic formulation and conceptual interpretation on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Single Factoral Terms of Trade matches with

T_c \times Z_x

; Income Terms of Trade matches with

T_c \times Q_x

; Gross Barter Terms of Trade matches with

\left(\frac{Q_m}{Q_x}\right) \times 100

; and Prebisch-Singer Hypothesis matches with the long-run structural decline in primary commodity terms of trade due to low income elasticity of demand.

Each concept correctly aligns with its unique formula and analytical purpose: Single Factoral includes productivity (

Z_x

), Income incorporates export volume (

Q_x

) to determine capacity to import, Gross Barter compares physical import-to-export quantities (

Q_m / Q_x

), and Prebisch-Singer explains long-term terms of trade determinants for developing economies.

Step-by-Step Solution

1

Analyze Single Factoral Terms of Trade (

T_s

)

T_s = \left(\frac{P_x}{P_m}\right) \times Z_x = T_c \times Z_x

Single factoral TOT incorporates productivity gains in the domestic export sector (

Z_x

), showing import efficiency per productive factor employed.

2

Analyze Income Terms of Trade (

T_y

)

T_y = \left(\frac{P_x}{P_m}\right) \times Q_x = T_c \times Q_x

Income terms of trade measures total purchasing power of exports by taking net barter TOT and multiplying by export quantity index (

Q_x

).

3

Analyze Gross Barter Terms of Trade (

T_g

)

T_g = \left(\frac{Q_m}{Q_x}\right) \times 100

Unlike net barter TOT which uses price indices (

P_x / P_m

), gross barter TOT uses physical volume indices in reversed order (

Q_m / Q_x

).

4

Analyze the Prebisch-Singer Hypothesis on Determinants

Identified as structural deterioration of primary producers' TOT

This macroeconomic theory establishes that primary commodities suffer deteriorating terms of trade over time due to low income elasticity of demand and technical progress in industrial countries.

Key Concept

Classification, mathematical formulations, and structural determinants of Terms of Trade (Net Barter, Gross Barter, Income, Single Factoral, and Prebisch-Singer thesis).

Question 7Question →

During a specific trading period, a nation's import price index rose to $160$ relative to a base year index of $100$ . If the nation's Net Barter Terms of Trade for the period was recorded as $87.5$ , by what percentage did the export price index change from the base year?

An increase of

40\%

An increase of

82.9\%

A decrease of

12.5\%

A decrease of

27.5\%

Show answer & explanation

Answer: An increase of $40\%$

Answer

An increase of

40\%

The correct answer is derived using the standard formula

N = \frac{P_x}{P_m} \times 100

. Substituting the given terms of trade (

87.5

) and import price index (

160

) gives

87.5 = \frac{P_x}{160} \times 100

. Rearranging yields

P_x = 140

. Comparing

140

to the base year index of

100

confirms an increase of

40\%

.

Step-by-Step Solution

1

Identify the given variables and standard formula for Net Barter Terms of Trade.

The formula is

N = \frac{P_x}{P_m} \times 100

, where

N = 87.5

(Net Barter Terms of Trade) and

P_m = 160

(Import Price Index).

Net Barter Terms of Trade measures the ratio of export prices to import prices relative to a base period.

2

Rearrange the formula to solve for the Export Price Index (

P_x

).

P_x = \frac{N \times P_m}{100} = \frac{87.5 \times 160}{100} = 140

.

Multiplying both sides by

P_m

and dividing by

100

isolates the current period export price index.

3

Calculate the percentage change from the base year export price index (

100

).

\text{Percentage Change} = \frac{140 - 100}{100} \times 100\% = +40\%.

Comparing the current export price index of

140

to the baseline of

100

shows a

40\%

increase.

Key Concept

Calculation of Net Barter Terms of Trade and unknown index components

Estimated Time:2m 0s

Question 8Question →

Match each specific terms of trade concept on the left with its corresponding analytical definition or mathematical formulation on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Gross Barter Terms of Trade corresponds to the physical import-to-export volume ratio ($\frac{Q_m}{Q_x} \times 100$); Income Terms of Trade corresponds to the capacity to import ($\frac{P_x}{P_m} \times Q_x$); Single Factoral Terms of Trade corresponds to domestic export sector productivity adjustment ($\frac{P_x}{P_m} \times Z_x$); Double Factoral Terms of Trade corresponds to productivity adjustment in both domestic export and foreign import sectors ($\frac{P_x}{P_m} \times \frac{Z_x}{Z_m}$).

Gross Barter Terms of Trade measures the physical volume relationship between imports and exports. Income Terms of Trade measures the purchasing power of exports (capacity to import). Single Factoral Terms of Trade adjusts commodity terms of trade for productivity improvements in the domestic export sector, whereas Double Factoral Terms of Trade incorporates productivity changes in both the home export sector and foreign import-producing sector.

Step-by-Step Solution

1

Define Gross Barter Terms of Trade

Identified as the physical volume ratio of imports to exports:

\frac{Q_m}{Q_x} \times 100

.

Gross barter terms focus on physical quantities traded rather than monetary price indices.

2

Define Income Terms of Trade

Identified as total capacity to import:

\frac{P_x}{P_m} \times Q_x

.

Income terms of trade weigh price ratios against actual export quantity to measure import capacity.

3

Differentiate Single Factoral from Double Factoral Terms of Trade

Single Factoral adjusts for domestic export sector productivity (

Z_x

), while Double Factoral adjusts for both domestic export (

Z_x

) and foreign import (

Z_m

) sector productivities.

Factoral terms of trade incorporate input productivity indices into commodity price terms of trade.

Key Concept

Analytical concepts and mathematical formulations of Terms of Trade

Question 9Question →

A country recorded an Income Terms of Trade index of $144$ and an export volume index of $120$ relative to the base year index of $100$ . If the country's import price index stood at $125$ during the same period, what was its export price index?

Show answer & explanation

Answer: 150

Answer

The export price index is 150.

The Income Terms of Trade (

ITT

) formula is

ITT = \left(\frac{P_x}{P_m}\right) \times Q_x

. Substituting the given values (

ITT = 144

,

Q_x = 120

,

P_m = 125

) gives

144 = \left(\frac{P_x}{125}\right) \times 120

. Rearranging the equation to solve for the export price index yields

P_x = \frac{144 \times 125}{120} = 150

.

Step-by-Step Solution

1

Identify the relationship between Income Terms of Trade, price indices, and volume index

ITT = \left(\frac{P_x}{P_m}\right) \times Q_x

Income Terms of Trade measures a nation's capacity to import based on export earnings, combining the net barter terms of trade with export quantity.

2

Substitute given values into the formula

144 = \left(\frac{P_x}{125}\right) \times 120

The given values are

ITT = 144

,

Q_x = 120

, and

P_m = 125

.

3

Isolate the unknown variable

P_x

P_x = \frac{144 \times 125}{120} = 150

Multiplying both sides by

125

and dividing by

120

isolates

P_x

to determine the export price index.

Key Concept

Income Terms of Trade Calculation

Terms of Trade: Concepts, Calculation, and Determinants

Answer

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