Assignment 1. Due: Drop Box 2nd Floor Dunning Hall by October 1, 2012 2012 ...
Prices in 2012 are 18% higher than they were in the base year, 2009. We see ...
ECON 222 Macroeconomic Theory I Fall Term 2012/13 Assignment 1 Due: Drop Box 2nd Floor Dunning Hall by October 1, 2012 2012 No late submissions will be accepted No group submissions will be accepted No ”Photocopy” answers will be accepted Remarks: Write clearly and concisely. Devote some time to give the graphs, plots and tables a format easy to understand. Also the way you present your answers matter for the final grade. Even if a question is mainly analytical, briefly explain what you are doing, stressing the economic meaning of the various steps. Being able to convey your thoughts effectively is an asset also in real life. Question 1: National Accounting (25 Marks) There are only 2 goods sold in the country of Paradisio - pineapples and coconuts. The following table shows the amount sold and price of each good: Pineapple Coconut
Amount sold Price per unit Amount sold Price per unit
2009 200 $5 50 $ 10
2010 300 $5.25 57 $ 11
2011 330 $5.50 60 $11.25
2012 255 $6 60 $11.50
a) Calculate Paradisio’s nominal GDP for each year. Answer : Nominal GDP = Pineapple sold * Price + Coconut Sold * Price
2009 2010 2011 2012
Nominal GDP $1,500 $2,202 $2,490 $2,220
b) Assume 2009 is the base year. Calculate Real GDP for each year. By what percentage does real GDP increase in each year compared to the base year? Answer : Real GDP = Pineapple sold * 2009 Price + Coconut Sold * 2009 Price % Growth Rate of Real GDP = ((Year XX Real GDP - 2009 Real GDP)/2009 Real GDP)x100 Real GDP 2009 2010 2011 2012
$1,500 $2,070 $2,250 $1,875
Growth Rate of Real GDP from 2009 NA 38% 50% 25%
c) Calculate the GDP deflator for each year. How much higher, in percentage terms is the overall level of prices in 2012 compared to the base year? Answer: GDP Deflator = Nominal GDP/Real GDP
2009 2010 2011 2012
GDP Deflator 1 1.06 1.11 1.18
Prices in 2012 are 18% higher than they were in the base year, 2009. We see this because the GDP deflator in 2012, 1.18, is 18% higher than the GDP deflator in 2009, 1. d) Suppose now that the company who farms and sells the pineapples and coconuts, Tropical Fruit Inc., expands and starts farming and selling apples in Canada in 2011. Sales and prices are in the following table:
Apples
Amount sold Price per unit
2011 150 $1.50
2012 180 $1.55
Given this new information, what is nominal GNP for the country of Paradisio each year? Assume there are no foreign businesses in Paradisio, and all sales of apples in Canada go directly to Tropical Fruit Inc. (i.e. they pay no taxes or other fees in Canada). Answer: (Nominal) GNP = (Nominal) GDP + NFP 2009 2010 2011 2012
Nominal GNP $1,500 $2,202 $2,715 $2,499
Question 2: Some Canadian Macroeconomic Data (30 Marks) This question asks you to retrieve data from CANSIM (Statistics Canada database). Once you have the data, a spreadsheet program such as Microsoft Excel or Open Office will work well for our purposes. You can access CANSIM through the library website by searching for “Cansim” under “Databases” on the library’s home page. Once you connect to CANSIM @ CHASS, you should be able to click on “CANSIM Multidimensional View”, and then on “Vital economic and social statistics” to access the data. (Note: If you try this from off-campus, you may need to use the Queen’s library webpage and read ‘help with off-campus access’ if you haven’t already set up a ‘web-proxy’.) Within the section labelled ”Provincial”, retrieve the following series for the period 1980-01-01 to 201012-31for the provinces of Alberta, Ontario and Nova Scotia: GDP in chained 2002 dollars (v15855886) (v15855724) (v15855562), Unemployment (both sexes 15 years and over seasonally adjusted) (v2064516) (v2063949) (v2063382), Population (v12) (v15) (v9). Retrieve also GDP in chained 2002 dollars for Canada 2
(v15855410) and Canadian population (v1). a) GDP per capita: Calculate GDP per capita using the GDP in chained 2002 dollars series and the Population series. Plot GDP per capita series for all three provinces and briefly comment on any trends you see. (Note: You can use either end of year Population or year average population, but you must be consistent and explicitly state what you’ve used). b) Unemployment: Plot the unemployment rates for all three provinces and briefly comment on any trends you see. c) Using the graphs created in parts a) and b), can you say if there is a relationship between the unemployment rate and GDP per capita in each province? If there is, what is this relationship? d) Compute the growth rate of GDP for each ten year period in the data series (i.e. growth rate of GDP between 1981 and 1991, 1991 and 2001, etc.), for Canada and all three provinces. Create a table with this information, and comment on the results.
Question 3: Aggregate Production Function (25 Marks) This question focuses on labour productivity, labour demand, and generally on the production function. Assume that the aggregate production function is represented by the following equation: Y = AK α N β where A is total factor productivity (TFP), K represents capital, N represents labour, and α, β (0, 1) (meaning they are between zero and one) a) Derive an analytical expression for the marginal product of capital (MPK) and marginal product of labour (MPN), then show (analytically) that for this production function the MPN and MPK both exhibit diminishing returns. Hint: This involves finding the first and second derivatives of the production function. Answer: M P N = βAK α N (β−1) M P K = αAK (α−1) N β To show that MPN is decreasing and that MPK is increasing, remember that α and β are numbers between zero and one: ∂M P N = β(β − 1)AK α N (β−2) < 0 ∂N α
AK where (β − 1) < 0 and N 2−β > 0 , thus making the expression negative. This means that as new labour is added (N increases) the MPN is falling, also called diminishing returns to labour. Similarly, MPK exhibits decreasing returns to capital:
∂M P K = α(α − 1)AK (α−2) N β < 0 ∂K β
since (α − 1) < 0 and KAN (2−α) > 0. Assume now that α = 0.75, β = 0.25, A=10 and K = 60. Additionally, labour supply is given by the following function: N S = 120[(1 − t)w] 3
where t is the tax rate on labour income, and w is the real wage rate. Hence the after-tax real wage rate is: (1 − t)w
b) Assume for now that t = 0. Find the labour demand equation. Additionally, find the equilibrium levels of wage rate and employment, and the level of total output (Y). Answer: Labour demand: w = M P N = βAK α N (β−1) = (0.25)(10)(60.75 )(N −.75 ) Re-arrange to find labour demand, N : N=
βAK α w
1/(1−β)
= (60)
2.5 w
1/.75
The equilibrium wage rate is determined by setting N = N S (labour demanded=labour supplied): 1/(1−β) βAK α = 120[(1 − t)w] w and we set t = 0, so 120(w) = (60)
2.5 w
1/.75
2.51/.75 60 = w1.75/.75 120 =⇒ w = (2.5)1/1.75 (0.5).75/1.75 =⇒
=⇒ w ≈ 1.25 Employment level: N ∗ = 120 ∗ w ≈ 150.51 Total output: Y = (10) ∗ (60).75 ∗ (150.51).25 ≈ 755.10
c) Suppose now that the tax rate on labour income, t, equals 0.5. What is the total after-tax wage income of workers? Does total output change? If so, what is the new total output level? Answer: The labour demand function is unchanged: N = (60) Set N = N S: (60)
2.5 w
2.5 w
1/.75
1/.75 = 120[(1 − t)w] = 120(0.5w)
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Solving for w gives: w = 2.51/1.75 ≈ 1.69 Then the after-tax income a worker would take home is: (1 − t) ∗ w = 0.5 ∗ 1.69 = 0.85 Employment level: N ∗ = 120(1 − .5)0.85 = 51 The level of total output will change. It is now: Y = (10)(60.75 )(51.25 ) ≈ 576.11
d) Suppose again that t = 0, and that the government has imposed a minimum wage of $2. What is the new equilibrium level of unemployment? The unemployment rate? Answer: The labour demanded is: 1/(1−β) 1/.75 2.5 βAK α = (60) = 80.79 N∗ = w 2 The labour supplied is: N S = 120 ∗ w = 240 This gives us an equilibrium unemployment level of: N S − N ∗ = 240 − 80.79 = 159.21 About 159 people are unemployed. The unemployment rate is: 240 − 80.79 ∗ 100 ≈ 66.33% 240 Thus we can see that imposing a minimum wage results (in this case) in a large fraction of the economy being unemployed. Question 4: Employment (20 Marks) Consider an economy in which only two goods are produced: bicycles and running shoes. There is an initial labour force of 2000 people, of whom 1800 are employed. The follow table shows macroeconomic data for the industries: Year: 2012 Bicycles 1000 1.5 $300
# Workers employed Total output per worker Price per unit
Running Shoes 800 3 $100
a) What is Nominal GDP? What is the unemployment rate? Answer: Nominal GDP = 1000 ∗ 1.5 ∗ 300 + 800 ∗ 3 ∗ 100 = $690, 000 5
Unemployment rate = (
(2000 − 1000 − 800) ) ∗ 100 = 10% 2000
b) The economy enters a recession the following year, in 2013. Employment falls by 2% in each industry. Additionally, 30% of the previously unemployed labour force becomes discouraged at the prospects of finding a job and leaves the labour force (this would be 30% of people who were unemployed prior to the recession). After the recession begins, how many workers are left in the labour force in 2013? How many workers are unemployed and what is the unemployment rate? Answer: Before the recession employment rate was 90%, now it will be 88%. Alternative calculation using persons employed shows that there will now be 1000 ∗ (1 − 0.02) = 980 persons employed in the bicycle industry and 800 ∗ (1 − 0.02) = 784 employed in the running shoe industry, for total employment of 1764 persons. This is an employment rate of 1764/2000 = 88%. 30% of previously unemployed persons have left the labour force: 200 ∗ 0.3 = 60 Thus, the size of the labour force is now: Labour Force = 2000 − 60 = 1940 persons. The number of persons unemployed: Unemployed persons = 1940 − 1764 = 176 The unemployment rate is then: Unemployment rate = [(1940 − 1764)/1940] ∗ 100 = 9.07% We see here that the official unemployment rate has actually fallen during the recession. The unemployment rate is often criticized for not being representative of the actual number of persons without work in an economy, as this question shows - those who’ve left the labour force are no longer accounted for. c) Assume that output per worker is unchanged during the recession, but prices have risen slightly bicycles now cost $310 and running shoes $105. The number of workers employed in each sector is as described in part b). What is the Nominal GDP for the year 2013? Using 2012 as the base year, calculate Real GDP for 2012 and 2013. Calculate the GDP deflator. Answer: Nominal GDP 2013 = 980 ∗ 1.5 ∗ 310 + 784 ∗ 3 ∗ 105 = $702, 660 Real GDP 2013 w/base 2012 = 980 ∗ 1.5 ∗ 300 + 784 ∗ 3 ∗ 100 = $676200 Nominal GDP ∗ 100 = 100 GDP Deflator 2012= RealGDP 702, 660 GDP Deflator 2013= ∗ 100 = 104 676, 200
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