ECON 222 Macroeconomic Theory I Fall Term 2012/13

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 ill be accepted No group submissions ill be accepted No Photocopy ansers ill be accepted Remarks: Write clearly and concisely. Devote some time to give the graphs, plots and tables a format easy to understand. Also the ay you present your ansers matter for the final grade. Even if a question is mainly analytical, briefly explain hat 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 folloing table shos the amount sold and price of each good: 2009 2010 2011 2012 Pineapple Amount sold 200 300 330 255 Price per unit $5 $5.25 $5.50 $ 6 Coconut Amount sold 50 57 60 60 Price per unit $ 10 $ 11 $11.25 $11.50 a) Calculate Paradisio s nominal GDP for each year. Anser : Nominal GDP = Pineapple sold * Price + Coconut Sold * Price Nominal GDP 2009 $1,500 2010 $2,202 2011 $2,490 2012 $2,220 b) Assume 2009 is the base year. Calculate Real GDP for each year. By hat percentage does real GDP increase in each year compared to the base year? Anser : Real GDP = Pineapple sold * 2009 Price + Coconut Sold * 2009 Price % Groth Rate of Real GDP = ((Year XX Real GDP - 2009 Real GDP)/2009 Real GDP)x100 Real GDP Groth Rate of Real GDP from 2009 2009 $1,500 NA 2010 $2,070 38% 2011 $2,250 50% 2012 $1,875 25%

c) Calculate the GDP deflator for each year. Ho much higher, in percentage terms is the overall level of prices in 2012 compared to the base year? GDP Deflator = Nominal GDP/Real GDP GDP Deflator 2009 1 2010 1.06 2011 1.11 2012 1.18 Prices in 2012 are 18% higher than they ere 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 no that the company ho 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 folloing table: 2011 2012 Apples Amount sold 150 180 Price per unit $1.50 $1.55 Given this ne information, hat 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). (Nominal) GNP = (Nominal) GDP + NFP Nominal GNP 2009 $1,500 2010 $2,202 2011 $2,715 2012 $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 ill ork ell for our purposes. You can access CANSIM through the library ebsite 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 Vie, 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 ebpage and read help ith off-campus access if you haven t already set up a eb-proxy.) Within the section labelled Provincial, retrieve the folloing series for the period 1980-01-01 to 2010-12-31for 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 hat 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 beteen the unemployment rate and GDP per capita in each province? If there is, hat is this relationship? d) Compute the groth rate of GDP for each ten year period in the data series (i.e. groth rate of GDP beteen 1981 and 1991, 1991 and 2001, etc.), for Canada and all three provinces. Create a table ith 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 folloing equation: Y = AK α N β here A is total factor productivity (TFP), K represents capital, N represents labour, and α, β ɛ (0, 1) (meaning they are beteen zero and one) a) Derive an analytical expression for the marginal product of capital (MPK) and marginal product of labour (MPN), then sho (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. MP N = βak α N (β 1) MP K = αak (α 1) N β To sho that MPN is decreasing and that MPK is increasing, remember that α and β are numbers beteen zero and one: MP N N = β(β 1)AKα N (β 2) < 0 here (β 1) < 0 and AKα > 0, thus making the expression negative. This means that as ne N 2 β labour is added (N increases) the MPN is falling, also called diminishing returns to labour. Similarly, MPK exhibits decreasing returns to capital: MP K K = α(α 1)AK(α 2) N β < 0 since (α 1) < 0 and AN β > 0. K (2 α) Assume no that α = 0.75, β = 0.25, A=10 and K = 60. Additionally, labour supply is given by the folloing function: NS = 120[(1 t)] 3

here t is the tax rate on labour income, and is the real age rate. Hence the after-tax real age rate is: (1 t) b) Assume for no that t = 0. Find the labour demand equation. Additionally, find the equilibrium levels of age rate and employment, and the level of total output (Y). Labour demand: Re-arrange to find labour demand, N: = MP N = βak α N (β 1) = (0.25)(10)(60.75 )(N.75 ) ( ) βak α 1/(1 β) ( ) 1/.75 2.5 N = = (60) The equilibrium age rate is determined by setting N = N S (labour demanded=labour supplied): ( ) βak α 1/(1 β) = 120[(1 t)] and e set t = 0, so 120() = (60) ( ) 1/.75 2.5 = 2.51/.75 60 = 1.75/.75 120 = = (2.5) 1/1.75 (0.5).75/1.75 = 1.25 Employment level: Total output: N = 120 150.51 Y = (10) (60).75 (150.51).25 755.10 c) Suppose no that the tax rate on labour income, t, equals 0.5. What is the total after-tax age income of orkers? Does total output change? If so, hat is the ne total output level? The labour demand function is unchanged: N = (60) ( ) 1/.75 2.5 Set N = NS: (60) ( ) 1/.75 2.5 = 120[(1 t)] = 120(0.5) 4

Solving for gives: = 2.5 1/1.75 1.69 Then the after-tax income a orker ould take home is: (1 t) = 0.5 1.69 = 0.85 Employment level: N = 120(1.5)0.85 = 51 The level of total output ill change. It is no: Y = (10)(60.75 )(51.25 ) 576.11 d) Suppose again that t = 0, and that the government has imposed a minimum age of $2. What is the ne equilibrium level of unemployment? The unemployment rate? The labour demanded is: ( ) βak N α 1/(1 β) ( ) 1/.75 2.5 = = (60) = 80.79 2 The labour supplied is: NS = 120 = 240 This gives us an equilibrium unemployment level of: NS N = 240 80.79 = 159.21 About 159 people are unemployed. The unemployment rate is: 240 80.79 100 66.33% 240 Thus e can see that imposing a minimum age results (in this case) in a large fraction of the economy being unemployed. Question 4: Employment (20 Marks) Consider an economy in hich only to goods are produced: bicycles and running shoes. There is an initial labour force of 2000 people, of hom 1800 are employed. The follo table shos macroeconomic data for the industries: Year: 2012 Bicycles Running Shoes # Workers employed 1000 800 Total output per orker 1.5 3 Price per unit $300 $100 a) What is Nominal GDP? What is the unemployment rate? Nominal GDP = 1000 1.5 300 + 800 3 100 = $690, 000 5

(2000 1000 800) Unemployment rate = ( ) 100 = 10% 2000 b) The economy enters a recession the folloing 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 ould be 30% of people ho ere unemployed prior to the recession). After the recession begins, ho many orkers are left in the labour force in 2013? Ho many orkers are unemployed and hat is the unemployment rate? Before the recession employment rate as 90%, no it ill be 88%. Alternative calculation using persons employed shos that there ill no 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: Thus, the size of the labour force is no: The number of persons unemployed: The unemployment rate is then: 200 0.3 = 60 Labour Force = 2000 60 = 1940 persons. Unemployed persons = 1940 1764 = 176 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 ithout ork in an economy, as this question shos - those ho ve left the labour force are no longer accounted for. c) Assume that output per orker is unchanged during the recession, but prices have risen slightly - bicycles no cost $310 and running shoes $105. The number of orkers 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. Nominal GDP 2013 = 980 1.5 310 + 784 3 105 = $702, 660 Real GDP 2013 /base 2012 = 980 1.5 300 + 784 3 100 = $676200 ( ) Nominal GDP GDP Deflator 2012= 100 = 100 RealGDP ( ) 702, 660 GDP Deflator 2013= 100 = 104 676, 200 6