StudySpace: Economics in Development, 6th Edition

Worked Examples

1. Chapter 2 points out that international comparisons of income per capita require converting each country’s statistics to a common currency, typically U.S. dollars. The standard approach has been to convert using exchange rates. In recent years, international data have been compiled using purchasing power parity (PPP) as the basis for converting to a common currency unit. This exercise presents a simple example to show how exchange-rate conversions can produce misleading results and how the PPP methodology works.

Exercises

a. In 1990, Zambia’s GDP was K113 billion (where K stands for kwacha, the national currency). The population was 8.1 million people. To get GDP per capita in local currency units, divide GDP by the number of people. Be sure to take into account that GDP is in billions and population is in millions.

GDP per capita = K in 1990.

To convert this figure from kwacha units to U.S. dollar units using the exchange-rate method, divide by the exchange rate (kwacha per dollar). In 1991, the exchange rate averaged K29 per U.S.$, so in dollar units

GDP per capita = U.S.$ in 1990.

b. A year later, Zambia had a population of 8.4 million people and GDP of K218 billion. The large rise in GDP was due entirely to inflation; real GDP was virtually unchanged. The exchange rate averaged K65 per U.S.$ in 1991. From these numbers, you can calculate that:

In kwacha units, GDP per capita = K in 1991.

In dollar units, GDP per capita = $ in 1991.

c. Compare the results of converting Zambia’s per capita GDP into U.S. dollars using the exchange-rate method. In 1990, Zambia’s GDP per capita in dollars was $ ; the following year, GDP per capita was $ . The 1991 figure is lower than the 1990 figure by percent. Yet real GDP did not change: Even taking population growth into account, GDP per capita fell less than 4 percent, measured in kwacha units at constant prices. The conversion to dollars gives a very different result because the change in the exchange rate did not accurately reflect the change in purchasing power of the kwacha. Using the exchange rate to convert from kwacha to dollars introduced a large distortion into the dollar value of GDP per capita.

d. The PPP method avoids this by valuing each country’s output in dollar terms product by product. Take a simple example using the following data for a hypothetical economy. Calculate nominal GDP for each year by multiplying output times price for each product and then totaling the output values:

Click here for Table 2-1

Note that output remains constant but prices double between 1990 and 1991. To convert to dollar values, the PPP methodology bypasses the exchange rate altogether. Instead, each product is valued at a consistent set of dollar prices, such as

Copper: $1,000 per ton
Maize: $100 per bag
Furniture: $50 per unit

Multiply the outputs for 1990, item by item, by the respective dollar prices to obtain GDP in dollar units. Do the same for 1991 outputs. The result, in dollar units, is

GDP = $ million in 1990.

GDP = $ million in 1991.

Suppose that the population of this economy is 2.0 million in 1990 and 2.1 million in 1991. What is GDP per capita in dollar units, on the basis of the PPP conversion methodology?

GDP per capita = $ million in 1990.

GDP per capita = $ million in 1991.

Compared to the exchange rate method, this calculation gives a more accurate picture of the situation and a more consistent set of output valuations for use in making international comparisons.

2. Measuring gross national product (GNP). Begin this exercise by looking back over Table 2–1 in the textbook. A similar table with new data is reproduced here as Table 2–2.

Click here for Table 2-2

Exercises

a. Calculate the following:

(i) The market value of steel output for the United States is $ million.

(ii) The market value of retail services for the United States is $ million.  

(iii) The total value of goods and services produced in the United States is $ million. This is GNP for the United States.  

(iv) Place this information in the column of blank spaces for the United States in Table 2–2.

(v) In the same manner, calculate the value of India’s steel output, retail services, and total GNP (in millions of rupees). Then fill in the column of blank spaces for India.

• The market value of steel output for India is $ million.
• The market value of retail services for India is $ million.  
• The total value of goods and services produced in India is $ million.

b. You now have GNP figures for both countries in local currency units: millions of dollars and rupees, respectively. To compare GNP for the two countries, the GNP figures must be expressed in common currency units. Let’s convert India’s GNP to U.S. dollars using the exchange rate. Suppose that the Indian government maintains the exchange rate at Rs30 = $1.

(i) You have calculated that India’s GNP is Rs million (in rupee units). At the prevailing exchange rate this is equivalent to

$ million (in dollar units).

(ii) With both values expressed in dollars, the ratio of GNP for the
United States to GNP for India is

(GNP U.S.)/(GNP India) = .

c. Rather than using the exchange rate to convert from rupee values into dollars, one can apply pertinent dollar values directly to each of India’s goods and services. This is the purchasing power parity (PPP) method.

(i) Using the U.S. price of $210 per ton, India’s steel output has a total dollar value of $ million.

(ii) Using the U.S. price of $5,100 per person-year, India’s retail services have a total dollar value of $ billion.

(iii) Adding these together gives India’s total GNP, converted to dollars using the purchasing power parity method, as $ billion.

(iv) Based on the PPP method for converting from rupee to dollars, the ratio of GNP for the United States to GNP for India is

(GNP U.S.)/(GNP India) = .

(The economic differential is larger in per-capita terms since India’s GNP serves 31/2 times as many people.)

(v) Briefly explain why switching from the exchange-rate method to the PPP method causes such a large change in India’s GNP as measured in dollars.  

d. To look at GNP measurements over time, suppose that the table used here represents data for 2000, while Table 2–1 in the textbook represents the corresponding data for 1990.

(i) You have calculated that India’s GNP is Rs million in 2000 (in part b). In Table 2 –1 in the textbook, the corresponding figure was Rs312,000 million in 1990. (Note: The textbook table gives GNP in billions; we are using millions here, to conform with the units given for quantity measurements.

These are nominal GNP figures. To get real GNP figures for comparing the change in output levels, one must value the outputs each year using a constant set of prices. Let’s choose 1990 as the base year. The outputs for each year will now be valued at constant 1990 prices. For 1990, real and nominal GNP are identical; this must be true since the prices used to compute nominal GNP for 1990 happen to be the base-year prices. Thus real GDP for 1990 is Rs312,000 million. For 1996 things are different.

(ii) Using the base-year price of steel (Rs9,000 per ton) India’s steel output for 1996 has a value of Rs million.

(iii) Using the constant base-year price of retail services (Rs60,000 per person-year), India’s retail services in 1996 have a value of Rs billion.

(iv) India’s GNP for 1996 (at constant 1990 prices) is Rs million. This is real GNP for 2000.

(v) Compare India’s real GNP for 2000 with real GNP for 1990. Between 1990 and 2000 total output grew by percent. If you rework this calculation using 2000 as the base year, rather than 1990, the answer is altered slightly. This occurs because the baseperiod prices serve as valuation weights for averaging the change in output levels for various goods and services.

The exercise provides a very simple illustration of the real-world problem of comparing national-account statistics across countries and over time. Inevitably, the results depend on the methodology. This is the index-number problem.

 

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