Foundations of Economics for International Business Selected Solutions to Assignment 1 INSTRUCTOR: XIN TANG Department of World Economics Economics and Management School Wuhan University Fall 2015 1 MULTIPLE CHOICES: 45% Instructions: Choose the one alternative that best completes the statement or answers the question. If you think any of the problems is not clear, explain where you think is not clear, and justify your answer. The first two questions intend to help you understand the general methodology of macroeconomics. 1. In a simple model of the supply and demand for pizza, when aggregate income increases, the price of pizza and the quantity purchased. (A) increases; decreases (B) increases; increases (C) decreases; increases (D) decreases; decreases 2. In the relationship expressed in functional form, Y = G(K, L), Y stands for real GDP, K stands for the amount of capital in the economy, and L stands for the amount of labor in the economy. In this case G( ): (A) is the growth rate of real GDP when the amount of capital and labor in the economy is fixed. (B) indicates that the variables inside the parenthesis are endogenous variables in the model. (C) is the symbol that stands for government input into the production process. (D) is the function telling how the variables in the parenthesis determine real GDP Questions 3 through 8 aim to help refresh some of the concepts related to gross domestic products. 1
3. All of the following transactions that took place in 2009 would be included in GDP for 2009 except the purchase of a: (A) book printed in 2009, entitled The Year 3000. (B) 2001 Jeep Cherokee. (C) year 2010 calendar printed in 2009. (D) ticket to see the movie 2001. 4. Assume that a firm buys all the parts that it puts into an automobile for $10,000, pays its workers $10,000 to fabricate the automobile, and sells the automobile for $22,000. In this case, the value added by the automobile company is: (a) $10,000 (b) $12,000 (c) $20,000 (d) $22,000 5. Assume that apples cost $0.50 in 2002 and $1 in 2009, whereas oranges cost $1 in 2002 and $1.50 in 2009. If four apples were produced in 2002 and five in 2009, whereas three oranges were produced in 2002 and four in 2009, then real GDP (in 2002 prices) in 2009 was: (A) $5 (B) $6.5 (C) $9.5 (D) $11 6. Assume that apples cost $0.50 in 2002 and $1 in 2009, whereas oranges cost $1 in 2002 and $1.50 in 2009. If four apples were produced in 2002 and five in 2009, whereas three oranges were produced in 2002 and five in 2009, then the GDP deflator in 2009, using a base year of 2002, was approximately: (A) 1.5 (B) 1.7 (C) 1.9 (D) 2.0 7. If nominal GDP grew by 5 percent and real GDP grew by 3 percent, then the GDP deflator grew by approximately percent. (A) 2 (B) 3 (C) 5 2
(D) 8 8. GNP equals GDP income earned domestically by foreigners income that nationals earn abroad. (A) plus; plus (B) minus; minus (C) minus; plus (D) plus; minus Questions 9 to 12 require the knowledge on concepts related to consumer price index. 9. The CPI is determined by computing: (A) an average of prices of all goods and services. (B) the price of a basket of goods and services that changes every year, relative to the same basket in a base year. (C) the price of a fixed basket of goods and services, relative to the price of the same basket in a base year. (D) nominal GDP relative to real GDP. 10. Assume that apples cost $0.50 in 2002 and $1 in 2009, whereas oranges cost $1 in 2002 and $0.50 in 2009. If ten apples and five oranges were purchased in 2002, and five apples and ten oranges were purchased in 2009, the CPI for 2009, using 2002 as the base year, is: (A) 0.75 (B) 0.8 (C) 1 (D) 1.25 11. An increase in the price of imported goods will show up in: (A) the CPI but not in the GDP deflator. (B) the GDP deflator but not in the CPI. (C) both the CPI and the GDP deflator. (D) neither the CPI nor the GDP deflator. 12. Assume that the market basket of goods and services purchased in 2004 by the average family in the United States costs $14,000 in 2004 prices, whereas the same basket costs $21,000 in 2009 prices. However, the basket of goods and services actually purchased by the average family in 2009 costs $20,000 in 2009 prices, whereas this same basket would have cost $15,000 in 2004 prices. Given these data, a Paasche index for 2009 using 2004 prices would be: 3
(A) 1.05. (B) approximately 1.07. (C) approximately 1.33. (D) 1.50 The last three questions are about unemployment. 13. According to the definition used by the U.S. Bureau of Labor Statistics, a person is not in the labor force if that person: (A) is going to school full time. (B) is temporarily absent from a job because of illness. (C) has been temporarily laid off. (D) is out of a job and looking for work during the previous four weeks. 14. If 7 million workers are unemployed, 143 million workers are employed, and the adult population equals 200 million, then the unemployment rate equals approximately percent. (A) 3.5 (B) 4.7 (C) 4.9 (D) 7 15. The household survey conducted by the Bureau of Labor Statistics provides estimates of the number of workers, while the establishment survey provides estimates of the number of workers. (A) self-employed; unemployed (B) unemployed; self-employed (C) with jobs; on firms payrolls (D) on firms payrolls; with jobs 2 NUMERICAL PROBLEMS: 55% Remember you have to show the detailed process of your solution. 1. (5%) The production function for an economy can be expressed as Y = F (K, L), where Y is real GDP, K is the quantity of capital in the economy, and L is the quantity of labor in the economy. 4
(a) If F ( ) = 100 + 3K + 9L, what is real GDP if the quantity of capital is 200 and the quantity of labor is 500? (3%) (b) What is/are the endogenous variable(s) in this model? (1%) (c) What is/are the exogenous variable(s) in this model? (1%) 2. (10%) Assume that the equation for demand for bread at a small bakery is Q d = 60 10P b + 3Y, where Q d is the quantity of bread demanded in loaves, P b is the price of bread in dollars per loaf, and Y is the average income in the town in thousands of dollars. Assume also that the equation for supply of bread is Q s = 30 + 20P b 30P f, where Q s is the quantity supplied and P f is the price of flour in dollars per pound. Assume finally that markets clear, so that Q d = Q s. (a) If Y is 10 and P f is $1, solve mathematically for equilibrium Q and P b. (6%) (b) If the average income in the town increases to 15, solve for the new equilibrium Q and P b. (4%) 3. (20%) Consider an economy that produces and consumes bread and automobiles. Refer to Table 1 Table 1: GDP Data Year 2000 Year 2010 Good Quantity Price Quantity Price Automobiles 100 $50,000 120 $60,000 Bread 500,000 $10 400,000 $20 (a) Using the year 2000 as the base year, compute the following statistics for each year: nominal GDP, real GDP, the GDP Deflator, and a CPI. (10%) (b) How much have prices risen between 2000 and 2010? Compare the answers given by the Laspeyres and Paasche price indices. Explain the difference. (10%) 4. (20%) Abby consumes only apples. In year 1, red apples cost $1 each, green apples cost $2 each, and Abby buys 10 red apples. In year 2, red apples cost $2, green apples cost $1, and Abby buys 10 green apples. (a) Compute a consumer price index for apples each year. Assume that year 1 is the base year in which the consumer basket is fixed. How does your index change from year 1 to year 2? (2%) (b) Compute Abby s nominal spending on apples in each year. How does it change from year 1 to year 2? (2%) 5
(c) Using year 1 as the base year, compute Abby s real spending on apples in each year. How does it change from year 1 to year 2? (6%) (d) Defining the implicit price deflator as nominal spending divided by the real spending, compute the deflator for each year. How does the deflator change from year 1 to year 2? (4%) (e) Suppose that Abby is equally happy eating red or green apples. How much has the true cost of living increased for Abby? Compare this answer to your answers to parts (a) and (d). What does this example tell you about Laspeyres and Paasche price indices? (6%) 3 SOLUTIONS Multiple Choices: 1 5 B D B B B; 6 10 B A C C D; 11 15 A D A B C Numerical: 1. (a) Y = 100 + 3(200) + 9(500) = 5,200 (b) Y (c) K, L 2. (a) Q = 60 loaves, P b = $3 (b) Q = 70 loaves, P b = $3.50 3. (a) (i) Nominal GDP is the total value of goods and services measured at current prices. Therefore, Nominal GDP 2000 = P 2000 Q 2000 + P 2000 bread Q2000 bread = ($50,000 100) + ($10 500,000) = $5,000,000 + $5,000,000 = $10,000,000. Nominal GDP 2010 = P 2010 Q 2010 + P 2010 bread Q2010 bread = ($60,000 120) + ($20 400,000) = $7,200,000 + $8,000,000 = $15,200,000. 6
(ii) Real GDP is the total value of goods and services measured at constant prices. Therefore, to calculate real GDP in 2010 (with base year 2000), multiply the quantities purchased in the year 2010 by the 2000 prices: Real GDP 2010 = P 2000 Q 2010 + P 2000 bread Q2010 bread = ($50,000 120) + ($10 400,000) = $6,000,000 + $4,000,000 = $10,000,000. Real GDP for 2000 is calculated by multiplying the quantities in 2000 by the prices in 2000. Since the base year is 2000, real GDP2000 equals nominal GDP 2000, which is $10,000,000. Hence, real GDP stayed the same between 2000 and 2010. (iii) The implicit price deflator for GDP compares the current prices of all goods and services produced to the prices of the same goods and services in a base year. It is calculated as follows: Implicit Price Deflator 2010 = Nominal GDP 2010 Real GDP 2010. Using the values for Nominal GDP 2010 and Real GDP 2010 calculated above: Implicit Price Deflator 2010 = $15,200,000 $10, 000, 000 = 1.52. This calculation reveals that prices of the goods produced in the year 2010 increased by 52 percent compared to the prices that the goods in the economy sold for in 2000. (Because 2000 is the base year, the value for the implicit price deflator for the year 2000 is 1.0 because nominal and real GDP are the same for the base year.) (iv) The consumer price index (CPI) measures the level of prices in the economy. The CPI is called a fixed-weight index because it uses a fixed basket of goods over time to weight prices. If the base year is 2000, the CPI in 2010 is an average of prices in 2010, but weighted by the composition of goods produced in 2000. The CPI 2010 is calculated as follows: P 2010 + P 2010 CPI 2010 = Q 2000 + P 2000 bread Q2000 bread P 2000 Q 2000 ($60,000 100) + ($20 500,000) bread Q2000 bread = ($50,000 100) + ($10 500,000) = $16,000,000 $10, 000, 000 = 1.6. 7
This calculation shows that the price of goods purchased in 2010 increased by 60 percent compared to the prices these goods would have sold for in 2000. The CPI for 2000, the base year, equals 1.0. (b) The implicit price deflator is a Paasche index because it is computed with a changing basket of goods; the CPI is a Laspeyres index because it is computed with a fixed basket of goods. From (6.a.iii), the implicit price deflator for the year 2010 is 1.52, which indicates that prices rose by 52 percent from what they were in the year 2000. From (6.a.iv.), the CPI for the year 2010 is 1.6, which indicates that prices rose by 60 percent from what they were in the year 2000. If prices of all goods rose by, say, 50 percent, then one could say unambiguously that the price level rose by 50 percent. Yet, in our example, relative prices have changed. The price of rose by 20 percent; the price of bread rose by 100 percent, making bread relatively more expensive. As the discrepancy between the CPI and the implicit price deflator illustrates, the change in the price level depends on how the goodsąŕ prices are weighted. The CPI weights the price of goods by the quantities purchased in the year 2000. The implicit price deflator weights the price of goods by the quantities purchased in the year 2010. The quantity of bread consumed was higher in 2000 than in 2010, so the CPI places a higher weight on bread. Since the price of bread increased relatively more than the price of, the CPI shows a larger increase in the price level. (c) There is no clear-cut answer to this question. Ideally, one wants a measure of the price level that accurately captures the cost of living. As a good becomes relatively more expensive, people buy less of it and more of other goods. In this example, consumers bought less bread and more. An index with fixed weights, such as the CPI, overestimates the change in the cost of living because it does not take into account that people can substitute less expensive goods for the ones that become more expensive. On the other hand, an index with changing weights, such as the GDP deflator, underestimates the change in the cost of living because it does not take into account that these induced substitutions make people less well off. 4. (a) The consumer price index uses the consumption bundle in year 1 to figure out how much weight to put on the price of a given good: P 2 + CPI 2 = red Q1 red P 1 red Q1 red ($2 10) + ($1 0) = ($1 10) + ($2 0) = 2. According to the CPI, prices have doubled. P 2 green Q1 green + P 1 green Q1 green (b) Nominal spending is the total value of output produced in each year. In year 1 and year 2, Abby 8
buys 10 apples for $1 each, so her nominal spending remains constant at $10. For example, Nominal Spending 2 = P 2 red Q2 red + P 2 green Q2 green = ($2 0) + ($1 10) = $10. (c) Real spending is the total value of output produced in each year valued at the prices prevailing in year 1. In year 1, the base year, her real spending equals her nominal spending of $10. In year 2, she consumes 10 green apples that are each valued at their year 1 price of $2, so her real spending is $20. That is, Real Spending 2 = P 1 red Q2 red + P 1 green Q2 green = ($1 0) + ($2 10) = $20. Hence, Abbyąŕs real spending rises from $10 to $20. (d) The implicit price deflator is calculated by dividing Abby s nominal spending in year 2 by her real spending that year: Implicit Price Deflator 2 = Nominal Spending 2 Real Spending 2 = $10 $20 = 0.5. Thus, the implicit price deflator suggests that prices have fallen by half. The reason for this is that the deflator estimates how much Abby values her apples using prices prevailing in year 1. From this perspective green apples appear very valuable. In year 2, when Abby consumes 10 green apples, it appears that her consumption has increased because the deflator values green apples more highly than red apples. The only way she could still be spending $10 on a higher consumption bundle is if the price of the good she was consuming fell. (e) If Abby thinks of red apples and green apples as perfect substitutes, then the cost of living in this economy has not changedąłin either year it costs $10 to consume 10 apples. According to the CPI, however, the cost of living has doubled. This is because the CPI only takes into account the fact that the red apple price has doubled; the CPI ignores the fall in the price of green apples because they were not in the consumption bundle in year 1. In contrast to the CPI, the implicit price deflator estimates the cost of living has been cut in half. Thus, the CPI, a Laspeyres index, overstates the increase in the cost of living and the deflator, a Paasche index, understates it. 9