Practice Problems EC 102.03 Questions 1. Suppose you are comparing income per capita in the United States and Ghana. You first convert the values into U.S. dollars using the current exchange rate between the U.S. dollar and the Ghanaian cedi. You also convert both values to U.S. dollars using the purchasing power parity-adjusted exchange rate. Which measure is likely to give you a more accurate picture of the living standards in both countries? Explain your answer. Answer: The nominal exchange rate converts Ghanaian cedi into U.S. dollars but does not take into account differences in prices and consumption patterns. Also, the nominal exchange rate can fluctuate for reasons that are not related to the relative price levels in either country. The purchasing power parity-adjusted exchange rate, however, is estimated by calculating how much a representative bundle of commodities costs in various countries. So, the purchasing power parity-adjusted exchange rate will show how much it will cost residents of the United States and Ghana to purchase the same bundle of goods. This means that the purchasing power parity-adjusted exchange rate is likely to be a more accurate measure of living standards in the United States and Ghana. 2. What are the disadvantages of using Big Mac Index to measure purchasing power parity? Answer: The price of a Big Mac is used as an alternative measure of the exchange rate between two countries. One of the problems with using Big Macs to measure purchasing power parity is that, instead of a bundle of diverse goods, this index simply compares a bundle consisting of just one good. Also, Big Macs are only a very small fraction of people s consumption, so their prices will not reflect true cost-of-living differences across countries. 3. Suppose that country A has higher income per capita than country B. Explain why this does not imply that most citizens of country A have higher income than most citizens of country B. Try to construct an example in which both countries have 10 citizens to demonstrate this point. Answer: Although income per capita does correlate strongly with various measures of the quality of life, it does not give a complete picture of the standard of living of all of a country s citizens. Income inequality can make income per capita a deceptive measure of economic well-being. Individual incomes can vary widely within a country and may not be reflected in a simple measure of income per capita. Imagine that countries A and B each have ten people (or ten equally large groups of people) with incomes distributed as follows:
Person Country A Income Country B Income 1 $1,000 $5,000 2 $1,500 $6,000 3 $2,000 $7,000 4 $2,500 $9,000 5 $3,000 $9,500 6 $3,500 $10,000 7 $4,000 $11,000 8 $15,000 $12,000 9 $30,000 $14,000 10 $45,000 $15,000 4. A country with a higher GDP must have a GDP per capita that is higher than that of a country with a lower GDP. Is this statement true or false? Answer: False, as GDP per capita is the gross domestic product of a country divided by its total population. If a country has a high GDP but also a large population, its GDP per capita may be lower than a country with a lower GDP but smaller population. 5. What is the correlation between income per capita and welfare measures like absolute poverty and life expectancy? What does this suggest about income per capita as a measure of welfare? Answer: Income per capita shows a strong correlation with measures like absolute poverty and life expectancy. However, income per capita might hide inequalities between countries and within countries. Also, it doesn t take into account factors like the quality of health care, the environment, and public safety. Although per capita income is by itself not a perfect measure of welfare, it does give us a lot of information about the living standards in a country. Therefore, it makes sense to first focus on income per capita and then look more deeply into data on health, education, poverty, and inequality within and across countries. 6. Suppose that there are two factors of production physical capital and labor. Given the amount of physical capital stock, explain how additional output produced depends on the existing level of employment. Answer: Holding the amount of capital fixed, adding one more worker generates a lot of additional output when there are fewer workers. When the number of workers increases, hiring one more worker does not generate as much additional output. This phenomenon is known as the Law of Diminishing Marginal Product.
7. What is productivity? Why does it vary across countries? Answer: Productivity refers to the value of goods and services that a worker generates for each hour of labor. There are three main reasons why productivity differs across countries: i. Human capital: Workers differ in terms of human capital, which is their stock of skills to produce output or economic value. Differences in human capital across countries result in differences in productivity. ii. Physical capital: Physical capital is any good, including machines (equipment)and buildings (structures) used for production. Workers will be more productive when theeconomy has a bigger physical capital stock, enabling each worker to work with more (or better) equipment and structures. iii. Technology: An economy with better technology uses its labor and capital more efficiently and thus achieves higher productivity 8. What are the two components of technology? Answer: Technology has two very distinct components: the first is knowledge that society has acquired and applied to its production process. This knowledge is embedded partly in the capital stock of firms. The second component has to do with the efficiency of production. The efficiency of production refers to the ability of society to produce the maximal amount of output at a given cost or for given levels of factors of production. 9. What are factors of production? What does the aggregate production function describe? Answer: A factor of production is an input used in producing output in an economy. An aggregate production function describes the relationship between a nation s GDP (Y) and its factors of production, such as physical capital (K) and total efficiency units of labor (H). It is written as follows: Y A F( K, H). A is an index of technology. A higher level of A implies that the economy produces more GDP with the same level of physical capital stock and total efficiency units of labor. 10. Use an expression to explain how education improves the efficiency units of labor in an economy. Answer: H = L h, where H denotes the total efficiency units of labor, L the total number of workers in the economy, and h the average efficiency or human capital of workers. Given L, as the years of schooling (h) increase, H increases. 11. Use the following diagram to explain the relationship between a country s physical capital stock and GDP.
Answer: The diagram shows the aggregate production function, holding total efficiency units of labor constant. This graph shows both the positive relationship between capital and output as well as the law of diminishing marginal product. Holding labor constant, if capital stock increases, the level of output produced also increases. However, the marginal contribution of an additional unit of capital to output how much output increases as a result of a unit increase in the capital stock eventually decreases. This can be seen by comparing a unit increase in output at two different points on the aggregate production function. At a point closer to the origin, when there is less capital in the economy, an increase in capital stock will lead to a relatively large increase in output. When we have the same unit increase starting with a larger capital stock farther to the right on the horizontal axis the corresponding increase in output is smaller. 12. How do increases in technology affect the aggregate production function? Answer: An increase in technology means that the economy can generate more output from the same set of inputs. Holding the efficiency units of labor, H, constant, the relationship between GDP and the physical capital stock shifts upward. Therefore, for every level of K, the physical capital stock, a better technology implies that the economy will be able to produce more GDP. Problems 1. You read a newspaper report that compares wages paid to employees at Starbucks in India and in the United Kingdom. At the time, 1 pound was equal to 87 rupees. The report says that Starbucks baristas in India are paid a mere 56 pence an hour, which is lower than the cheapest coffee that Starbucks sells in the United Kingdom. A friend of yours who read the report is appalled by this information and thinks that Starbucks ought to raise its salaries substantially in India. Is your friend necessarily correct? Explain your answer. Based on: http://www.firstpost.com/business/is-starbucks-milking-its-employees-not-really- 522717.html&http://www.mirror.co.uk/news/world-news/starbucks-paying-staff-25p-an-hour- 1429212
Answer: No, your friend is not necessarily correct. The flaw in the report is that it converts the wages paid in India to pounds using the current exchange rate but does not account for the cost of living (or the prices of goods) in India. So, while the wages paid to Starbucks employees in India may seem extremely low or exploitative, it is entirely possible that the cost of living in India is lower than the cost of living in the United Kingdom. If the cost of living in India is substantially lower than that in the United Kingdom, then the Starbucks employee in India is not necessarily worse off than a Starbucks employee in the United Kingdom. 2. The following table lists 2012 GDP per capita for four countries. The data are given in the national currencies of the countries. It also lists the price of a Big Mac burger in local currency in each country in 2012. The price of a Big Mac in the United States in 2012 was $4.20. Using the Big Mac burger as a representative commodity common to the countries, calculate the purchasing power parity (PPP)- adjustment factor for each country, and then the PPP level of per capita GDP in each country. Answer: Following the procedure given in the text, we first calculate the ratio of the U.S. Big Mac price and the Big Mac price in the country in question.for example, for Norway, the calculation would be $4.20/41 krone = 0.102.This is the PPP adjustment factor, which we then multiply by per capita GDP stated in the local currency.for Norway, the calculation is 0.102 579,162 = $59,328.79. Here is the table showing the results for all the countries: Country (currency) 2012 GDP per Capita 2012 Big Mac Price PPP Adjustment Factor (rounded) PPP GDP/Capita Norway (krone) 579,162 41 0.102 59,328.79 Poland (zloty) 41,398 9.1 0.462 19,106.77 Turkey (Turkish lira) 19,580 6.6 0.636 12,460.00 United Kingdom (British pound) 24,740 2.49 1.687 41,730.12
3. Let us use what we have learned in the first part of the chapter to compare living standards in the United States and a hypothetical country, Argonia, in 2008. a. The U.S. GDP in 2008 was approximately 14 trillion dollars and the U.S. population was approximately 300 million. What was the per capita GDP in the United States in 2008? b. Suppose that in the local currency, Argonian dollars, Argonia s GDP in 2008 was 1 trillion, and its population was 10 million. What was Argonia s GDP per capita in Argonian dollars? What problems do you foresee in comparing this number to the United States GDP per capita in U.S. dollars computed in part (a)? c. The Argonian dollar/u.s. dollar exchange rate was equal to 6 on January 1, 2008 (meaning that 1U.S. dollar is worth 6 Argonian dollars) and reached 9 on August 1, 2008. Compute an exchange-rate-based measure of the GDP per capita in Argonia in U.S. dollars on these two dates. Do you think the change in Argonia s exchange-rate-based measure of GDP per capita between these two dates reflects a true change in living standards? d. McDonald s has a thriving business in Argonia and sold a Big Mac for 7 Argonian dollars in 2008, while at the same time, a Big Mac sold for $3.50 in the United States. Using this information, provide an alternative estimate of GDP per capita in Argonia. Would you trust this estimate better than the one based on exchange rates? Why or why not? Answer: a. Aggregate income or GDP Per capita GDP = Total population $14 trillion 300 million = $46,667 b. Aggregate income or GDP Per capita GDP = Total population = 100,000 Argonian dollars 1 trillion Argonian dollars 10 million U.S. per capita GDP, which is in dollars, cannot be compared to the per capita GDP in Argonia, which is in Argonian dollars. To facilitate comparison, we would have to convert both values into a common unit of measurement. c. January 1, 2008:Argonia s per capita GDP in U.S. dollars = 100,000 1/6 = $16,666.67 August 1, 2008:Argonia s per capita GDP in U.S. dollars = 100,000 1/9 = $11,111.11 No, the change in Argonia s exchange-rate-based measure of per capita GDP is unlikely to reflect a change in living standards. This fluctuation is likely to have little to do with changes in prices in Argonia or the United States; instead, the significant fluctuation in the income per capita in Argonia relative to the United States is just a consequence of
converting Argonian incomes into dollars using the current exchange rate, which fluctuates for a variety of reasons unrelated to differences in costs of living. d. This information can be used to arrive at a PPP-adjusted exchange rate between the United States and Argonia. If a Big Mac costs $7 in Argonia and $3.50 in the United States, then 1 U.S. dollar = 2 Argonian dollars. It follows that the per capita GDP in Argonia in U.S. dollars = 100,000 1/2 = $50,000. Yes.The Big Mac index is commonly used as an alternative measure of exchange rates. It is a very simple example of purchasing power parity adjustment. PPP-adjustments account for the relative differences in the cost of living in various countries.because it involves the prices of an actual good in the two countries, it is more reliable than the estimate based on exchange rates. 4. In this question, we will use what you learned in the second part of the chapter to compare the performance of an economy in two different time periods, as its physical capital stock and efficiency units of labor change. a. Suppose that from period 1 to period 2, the unemployment rate in the economy increases. Everything else remains unchanged. What happens to the total efficiency units of labor? Express your results formally as an inequality, using the formula for total efficiency units of labor presented in the chapter (in particular, recall that total efficiency units of labor in two periods can be written as H 1 = L 1 h1 and H 2 = L 2 h 2 ; where L is the total number of employed workers). b. What are the consequences of this increase in unemployment for GDP? Express your results formally as an inequality, using the aggregate production function presented in the chapter. c. What are the consequences for GDP per capita and GDP per worker? d. Suppose that there is a technological advance from period 1 to period 2 but, at the same time, a decrease in physical capital stock? Can you say whether GDP will increase or decrease? Why or why not? Answer: a. The total efficiency units of labor is the product of average efficiency units of workers and the total number of workers in the economy. An increase in unemployment implies a decrease in the number of workers. Everything else remaining unchanged, a decrease in the number of workers reduces the total efficiency units of workers.this can be expressed formally as follows:l 1 > L 2 implies H 1 = L 1 h 1 >H 2 = L 2 h 2 b. The aggregate production function is expressed as Y =A F(K,H), where Y stands for GDP, K is capital stock, H is efficiency units of labor, and A is a technology index. With an increase in unemployment in period 2, the efficiency units of labor will fall. This means that GDP will also fall as there is a direct relationship between capital, labor, and aggregate output.formally, this can be expressed as follows:h 2 < H 1 implies F(K,H 2 ) < F(K,H 1 ), which implies A F(K,H 2 )<A F(K,H 1 ), which implies Y 2 < Y 1.
c. Other things remaining the same, the fall in GDP will reduce GDP per capita.the effect on GDP per worker is harder to determine. That is because both GDP and the number of workers are decreasing. d. Technological progress means that the economy can generate more output from the same set of inputs. It is difficult to conclude whether GDP will increase when physical capital stock falls but technology progresses. This is because with technological progress, more output can be produced with a smaller level of capital. It is also possible that, with technological progress, the same (or even a higher) level of GDP can be achieved, even if the capital stock declines. 5. Go to the Web site of the Penn World Table (https://pwt.sas.upenn.edu/), which provides data for sources of economic growth over time. The data shows that the real GDP (at constant 2005 national prices) in China is higher than that in India in 2010 and 2011. How do the variables given below explain the real GDP differences between China and India? Real GDP at constant 2005 national prices (in billion. 2005US$) Capital stock at constant 2005 national prices (in billion. 2005US$) Index of human capital per person, based on years of schooling TFP at constant national prices (2005=1) China India China India China India China India 2010 11,504 4,180 39,662 9,408 2.6 1.9 1.2 1.1 2011 12,563 4,467 1.9 1.2 44,643 10,299 2.6 1.1 Source: Data from Penn World Table; Alan Heston, Robert Summers and Bettina Aten, Penn World Table Version 7.1, Center for International Comparisons of Production, Income and Prices at the University of Pennsylvania (Nov 2012). Answer: Referring to the aggregate production function, Y = A x F(K,H), the real GDP depends on the value of capital stock, the efficiency units of labor (indicated by the index of human capital) and the level of technology (measured by TFP). From the table above, all these three variables have higher values in China than in India in 2010 and 2011, contributing to higher real GDP in China than in India. 6. The production function is given as: Y = A x F(K,H) = A K1/3 H2/3, where H = L h. Country Bigg s technology and human capital are twice the size of country Smala s. However, Smala has a greater physical capital stock, say, three times more than that of Bigg. Which country has a higher GDP, Bigg or Smala? Given the labor force, how can Smala increase H?
Answer: Y Bigg /Y Smala = (A K 1/3 H 2/3 ) Bigg /(A K 1/3 H 2/3 ) Smala Y Bigg /Y Smala = (2 1 1/3 2 2/3 ) Bigg / (1 3 1/3 1 2/3 ) Smala Y Bigg /Y Smala = 2.2 Bigg s GDP is two times higher than Smala s GDP. Smala can invest more in education and firms can provide more on-the-job training, thereby raising the efficiency of the workers, i.e. higher h. Given L, as h increases, H increases. Chapter 7 1. According to the aggregate production function, how does GDP increase? How is the saving rate in an economy defined? What factors help households decide whether to consume or save their income? How do household saving decisions impact investment in the economy? What is the role of human capital in the determination of a country s GDP? Answer: The aggregate production function Y = A F(K,H) links aggregate output to physical capital (K), total efficiency units of labor (H), and technology (A). To increase GDP or aggregate income, a nation can increase its stock of physical capital, K; increase the human capital of its workers, H (so that it has greater efficiency units of labor for the same workforce); or improve its technology, A. The saving rate is the fraction of total income that households save. Saving is a way of allocating some of today s resources for consumption tomorrow. So, in deciding how much to save, households are trading off consumption today for consumption tomorrow. These choices are affected by several factors: The first one is the interest rate. The interest rate determines how much households will earn on their savings. Higher interest rates typically encourage more saving. Second, expectations about future income will affect savings: Households that expect rapid income growth in the future will have less reason to save to finance future consumption (because future income growth will enable them to do this). Third, expectations about taxes will also impact saving decisions: If households expect high taxes in the future, they may save more in order to be able to pay these taxes without reducing future consumption. An increase in the saving in an economy facilitates an increase in investment.this, in turn, can lead to an increase in the economy s stock of physical capital, which we have seen is a key to economic growth. 2. What is sustained growth? Can physical capital accumulation generate sustained growth? Explain your answer. What did Malthus predict about economic growth?did his predictions come true? Why or why not? Answer: Sustained growth refers to a growth process where GDP per capita grows at a positive and relatively steady rate for a prolonged period of time. While the technological advancement which leads to productivity growth is a source of sustained growth, capital accumulation alone cannot generate sustained growth. Due to the diminishing marginal product of physical capital, more and
more physical capital translates into smaller and smaller increases in GDP and after a point, capital accumulation cannot generate growth in GDP. 3. China s economic growth depends on net exports to a large extent; some economists suggest that China needs to increase its domestic consumption rather than export to maintain its economic growth. However in the long run, increase in consumption may lower the income. Explain how an increase in consumption creates these two contradictory effects on economic growth. Answer: Using national income accounting, GDP is expressed as Y = C + I + G + (X M). Holding all else constant, an increase in consumption (C) leads to an increase in Y. However, in the long run, as people consume a larger part of their income, savings fall. A nation with lower saving rate will accumulate less capital stock. Using the aggregate production function, Y = A x F(H, K), as physical capital stock (K) falls, GDP decreases. 4. Refer to Exhibit 7.4 in the book. If the United States, Mexico, China, Rwanda, and Haiti continue to grow at the rates given in the exhibit, how many years (starting from 2010) would it take each to catch up to the United States in terms of per capita GDP? (Hint: If a country s GDP per capita is growing at a constant rate, g, then the natural log of GDP per capita t years into the future is:ln y(t) = ln y(0) + gt, where y(0) is GDP per capita in the initial year.) Answer: First of all, look carefully at the table.u.s. per capita GDP is growing at 2 percentper year.hence, any country that starts from a lower GDP per capita, and has a growth rate of 2 percent or less, will never catch up it is simply a mathematical impossibility. This means that, if the growth rates listed continue to prevail, Mexico, Rwanda, and Haiti will never catch up to the United States in terms of per capita GDP. So that leaves China, whose per capita GDP is growing at 4.72 percent. To see how long it will take China to catch up to the United States, we can use the formula provided in the hint:ln y(t) = ln y(0) + gt, where y(0) is GDP per capita in 2010. Substituting in the 2010 value for y(0) and the value for g in the United States gives the following: ln y US (t) = ln 41,365 + 0.02t The comparable equation for China is as follows: ln y China (t) = ln 7,746 + 0.0472t We want to find how many years (t) it will take for China to catch up to the United States in terms of per capita GDP.We must keep in mind that U.S. per capita GDP is continuing to grow, just not as fast as China s. To find how long it will take for China to catch up, we simply set the above equation for the United States equal to the equation for China: Solving this equation for t: ln 41,365 + 0.02t = ln 7,746 + 0.0472t
t China ln 41,365 ln 7,746 0.0272 61.6 years So if the rates of growth of GDP per capita listed in the table persist from 2010 on, China would catch up with the United States in around 62 years. 5. Draw the Solow growth model to answer the following questions. a. What is the impact of a higher saving rate on GDP? Explain the process. b. What is the impact of an increase in labor force on GDP? Explain the process. Answer: a. As an economy raises its saving rate from s to s, the investment curve shifts upward to s x A x F(K,H). Now at K*, investment exceeds depreciated physical capital, and thus the physical capital stock increases. The capital accumulation process continues until K** where the physical capital stock remains constant over time. As K** is higher than K*, the new steady-state equilibrium GDP (Y) is higher. s x A x F(K,H) s x A x F(K,H) b. As the country increases its labor force (L), H (which is equal to L x h) increases from H 1 to H 2. This shifts the investment curve shifts upward. Now at K*, investment exceeds depreciated physical capital, and thus the physical capital stock increases. The capital accumulation process continues until K** where the physical capital stock remains constant over time. As K** is higher than K*, the new steady-state equilibrium GDP (Y) is higher.
6. In the 1980s, the saving rate in Japan was extremely high. Gross saving as a percentage of GDP ranged between 30 percent and 32 percent. Can such a high saving rate lead to sustained economic growth? Use the Solow model to explain your answer. Answer: No, a high saving rate cannot sustain economic growth. With given levels of total efficiency units of labor and technology, there is a maximum amount of aggregate income that an economy can achieve by increasing saving because we can never go above a saving rate of 100 percent. This can be explained using the following figure. In the figure, the Solow model shows that economies with higher saving rates have higher aggregate incomes, but increases in the saving rate cannot be the source of sustained growth. This is because there is a maximum to how much an economy can save and thus a limit to what aggregate income it can achieve by just saving more.