Summer 2014 Week 3 Tutorial Questions (Ch2) Solutions

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1 Chapter 2: Q1: Macroeconomics P.52 Numerical Problems #3 Q2: Macroeconomics P.52 Numerical Problems #6 Q3: Macroeconomics P.53 Numerical Problems #7 Q4: Macroeconomics P.53 Numerical Problems #9 Q5: Macroeconomics P.53 Analytical Problems #3 Q1: ABC Computer Company has a $20, 000,000 factory in Kanata. During the current year, ABC builds $2,000,000 worth of computer components. ABC s costs are labour $1,000,000; interest on debt, $100,000; and taxes, $200,000. ABC sells all its output to XYZ Supercomputer. Using ABC s components, XYZ builds four supercomputers at a cost of $800,000 each ($500,000 worth of components, $200,000 in labour costs, and $100,000 in taxes per computer). XYZ has a $30,000,000 factory. XYZ sells three of the supercomputers for $1,000,000 each; at year s end, it has not sold the fourth. The unsold computer is carried on XYZ s books as an $800,000 increase in inventory. a. Calculate the contributions to GDP of these transactions, showing that all three approaches give the same answer. ABC produces output valued at $2 million and has total expenses of $1.3 million ($1 million for labour, $0.1 million interest, $0.2 million taxes). So its profits are $0.7 million. XYZ produces output valued at $3.8 million ($3 million for the three computers that were sold, plus $0.8 million for the unsold computer in inventory) and has expenses of $3.2 million ($2 million for components, $0.8 million for labour, and $0.4 million for taxes). So its profits are $0.6 million. According to the product approach, the GDP contributions of these companies are $3.8 million, the value of the final product of XYZ. ABC s production is of an intermediate good, used completely by XYZ, and so is not counted in GDP. According to the expenditure approach, the GDP contribution is also $ 3.8 million, with $3 million (of sold computers) adding to the capital stock (as investment spending), and $0.8 million (the unsold computer) as inventory investment. The income approach yields the same GDP total contribution. The amounts are: Week 3 Page 1

2 ABC XYZ Total Labour $1.0 million $0.8 million $1.8 million Profit $0.7 million $0.6 million $1.3 million Taxes $0.2 million $0.4 million $0.6 million Interest $0.1 million $0.0 million $0.1 million Total of all incomes = $3.8 million b. Repeat part (a), but now assume that in addition to its other costs, ABC also paid $500,000 for imported computer chips. If ABC pays an additional $.5 million for computer chips from abroad, the results change slightly. The correct answer is easiest to see using the expenditure approach. As in part a, there is $3.8 million expenditure on final goods, but not there are also net exports of $5 million. So the total expenditure on domestically produced goods is only $3.3 million. The product approach gets the same answer if it is realized that the $.5 million is a contribution to GDP of the country in which the chips were made, and so must be deducted from the GDP of Canada. The value added in Canada is only $3.3 million. Finally, the income approach gives the same answer as in part a, except that the cost of importing the chips reduces ABC s profits by $.5 million, so the sum of the incomes is only $3.3 million. Q2: Consider an economy that produces only three types of fruit: apples, oranges, and bananas. In the base year (a few years ago), the production and price data were as follows: Fruit Quantity Price Apples 3000 bags $2 per bag Bananas 6000 bunches $3 per bunch Oranges 8000 bags $4 per bag In the current year, the production and price data are as follows: Fruit Quantity Price Apples 4000 bags $3 per bag Bananas bunches $2 per bunch Oranges bags $5 per bag Week 3 Page 2

3 Base-year quantities at current-year prices: at base-year prices: Apples x $3 = $ x $2 = $ Bananas x $2 = $ x $3 = $ Oranges x $5 = $ x $4 = $ Total $ $ Current-year quantities at current-year prices: at base-year prices: Apples x $3 = $ x $2 = $ Bananas x $2 = $ x $3 = $ Oranges x $5 = $ x $4 =$ Total $ $ a. Find nominal GDP in the current year and in the base year. What is the percentage increase since the base year? Nominal GDP is just the dollar value of production in a year at prices in that year. Nominal GDP is $ in the base year and $ in the current year. Nominal GDP grew 257% between the base year and the current year: [($ /$56 000) 1] x 100% = 257%. b. Find real GDP in the base year and in the current year. By what percentage does real GDP increase from the base year to the current year? Real GDP is calculated by finding the value of production in each year at base-year prices. Thus, from the table above, real GDP is $ in the base year and $178,000 in the current year. In percentage terms, real GDP increases from the base year to the current year by [($ / $56 000) 1] x 100% = 218%. c. Find the GDP deflator for the current year and the base year. By what percentage does the price level change from the base year to the current year? The GDP deflator is the ratio of nominal GDP to real GDP. In the base year, nominal GDP equals real GDP, so the GDP deflator is 1. In the current year, the GDP deflator is $ / $ = Thus the GDP deflator changes by [(1.124 / 1) 1] x 100% = 12.4% from the base year to the current year. Week 3 Page 3

4 d. Would you say that the percentage increase in nominal GDP in this economy since the base year is due more to increases in prices or increases in the physical volume of output? Nominal GDP rose 257%, prices rose 12.4%, and real GDP rose 218%, so most of the increase in nominal GDP is because of the increase in real output, not prices. Q3: For the consumer price index values shown, calculate the rate of inflation in each year from 1930 to What is unusual about this period, relative to recent experience? Year CPI Calculating inflation rates: : [(14.0 / 14.2) 1] x 100% = 1.4% : [(12.7 / 14.0) 1] x 100% = 9.3% : [(11.5 / 12.7) 1] x 100% = 9.4% : [(10.9 / 11.5) 1] x 100% = 5.2% These all show deflation (prices are declining over time), whereas recently we have had nothing but inflation (prices rising over time). Q4: The GDP deflator in Econoland is 200 on January 1, The deflator rises to 242 by January 1, 2012, and to by January 1, a. What is the annual rate of inflation over the two-year period between January 1, 2010, and January 1, 2012? In other words, what constant yearly rate of inflation would lead to the price rise observed over those two years? The annual rate of inflation from January 1, 2010 to January 1, 2012, is 10%. This can be found by calculating the constant rate of inflation that would raise the deflator from 200 to 242 in two years. This gives the equation (1 + π) x (1 +π) = 242 / 200), which has the solution π = 10% An easy way to think about this question is this. A constant inflation rate of π raises the deflator from 200 Week 3 Page 4

5 on January 1, 2010, to 200 x (1 + π) on January 1, 2011, and to 200 (1 + π) x (1 + π) = 242 on January 1, So we need to solve the expression (1 + π)² = 242 / 200. b. What is the annual rate of inflation over the three-year period from January 1, 2010, to January 1, 2013? By similar reasoning, the inflation rate over the three-year period is (1 + π )³ = / 200, or π = 10%. c. In general, if P 0 is the price level at the beginning of an n-year period, and P n is the price level at the end of that period, show that the annual rate of inflation π over that period satisfies the equation (1 + π )^n = (P 0 / P n ) We can derive a general expression in the same way: 1 + π= P 1 / P π = P 2 / P π = P n / P n-1 Multiplying all these lines together, we get: (1 + π)ⁿ = (P 1 / P 0 ) x (P 2 / P 1 ) x x (P n / P n 1 ) = P n / P 0 Q5: Consider a closed economy with a single telephone company, Calls-R-Us. The residents of the country make two million phone calls per year and pay $3 per phone call. One day, a new phone company, CheapCall, enters the market and charges only $2 per phone call. All the residents immediately stop using Calls-R- Us and switch to CheapCall. They still make two million phone calls per year. The executives of CheapCall are proud of their market share. They post billboards stating Our country has increased its national saving by $2 million per year by switching to CheapCall. Comment on the accuracy of the statement on the billboards. Week 3 Page 5

6 National saving does not rise because of the switch to CheapCall because although consumption spending declines by $2 million, so have total expenditures (GDP), which equal total income. Since income and spending both declined by the same amount, national saving is unchanged. Week 3 Page 6

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