ECON 222 Macroeconomic Theory I Winter 2014

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1 ECON 222 Macroeconomic Theory I Winter 2014 Assignment 1 Due: Drop Box 2nd Floor Dunning Hall by January 24, 2014 at noon 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. The assignment is on 60 points and each question is worth 20 points Question 1: National Accounting (20 Points) Brewlandia produces beer and nachos. While its inhabitants consume all the beer and nachos, they still need to import chicken wings from abroad to satisfy their appetite. Assume that the wings are produced by foreigners. Table 1: Brewlandia s economy Year 1 Produces 10 Beers $4/each 5 Nachos $10/each Imports 8 wings $2/each Year 2 Produces 12 Beers $5/each 4 Nachos $8/each Imports 8 wings $1/each a) Calculate Brewlandia s nominal GDP for each year using: i) The product approach ii) The expenditure approach Product Approach (Final goods produced within Brewlandia at market prices) Nominal GDP for year 1: (10 beers * 4) + (5 Nachos * 10) = $90 Nominal GDP for year 2: (12 beers * 5) + (4 Nachos * 8) = $92 Expenditure Approach (Y = C - IM)

2 Nominal GDP for year 1: (10 beers * 4) + (5 Nachos * 10) + (8 wings * 2) - (8 wings * 2) = $90 Nominal GDP for year 2: (12 beers * 5) + (4 Nachos * 8) + (8 wings * 1) - (8 wings * 1) = $92 b) Calculate the real gdp and the GDP deflator using Year 1 as base year. Real GDP for year 1 = Nominal GDP for year 1 = $90 Real GDP for year 2 = (Quantities of year 2 * prices of year 1) = 12 Beers x Nachos x 10 = $88 Deflator of year 1 = 1 or 100 (base year) Deflator of Year 2 = nominal gdp year 2 / real gdp year 2 = 92/88 = c) Calculate real consumption for each year (base year 1). Real consumption for year 1 = Nominal consumption in year 1 = 10 Beers x Nachos x Wings x2 = 106 Real consumption for year 2 = Quantities of year 2 at prices of year 1: 12beers x nachos x wings x 2 = 104 d) Calculate real GDP growth and inflation rate using the GDP deflator (base year 1). 100*((Real GDP Year 2 - Real GDP Year 1)/ Real GDP Year 1) = real GDP growth = 100*((88-90)/90) = 2.22% inflation rate = 100*( )/1 = 4.55% e) The fixed basket of goods to calculate the CPI includes 2 beers, 1 nachos and 2 wings. Calculate the inflation rate between year 1 and 2 using the CPI (base year 1). CPI of year 1 = 1 or 100 CPI of year 2 = (Qty of the basket*price of year 2)/(Qty of the basket*price of year 1) = (2 beers x Nachos x wings x 1)/(2 beers x Nachos x wings x 2 ) = 20/22 = Therefore inflation is equal to 100 ( )/1 = 9.09% Question 2: Production Function (20 Points) Assume that the production function of the Canadian economy follows a Cobb-Douglas: Y = AK α N (1 α) a) Derive analytically the marginal product of labour (MPL) and the marginal product of capital (MPK). MP L = Y N = (1 α)a ( K N ) α MP K = Y K = αa ( N K ) 1 α (1) 2

3 b) Show graphically or analytically that the MPL and MPK exhibit diminishing marginal productivity. Explain why. Second derivative of the MPK and MPL are negative. MP L N MP K K = α(1 α)ak α N α 1 = (1 α)αan 1 α K α 2 (2) For the graphical answer, see Macroeconomics p MPK exhibits diminishing marginal productivity of capital: as we increases capital and keep labour fixed, there s more capital per worker. However, when capital is plentiful there s less and less benefits to add more capital. (ex. from 2 secretaries with 1 computer vs 2 secretaries with 3 computers). Similarly for MPL, it exhibits diminishing marginal productivity of labour: as we increases labour and keep capital fixed, there s less capital per worker. Less benefit to add a worker. (ex. from 1 secretary with 1 computer to 3 secretaries with 1 computer). Does this type of Cobb-Douglas has constant, increasing or decreasing return to scale? What does it mean? Constant. α + 1 α = 1. If we double K and N, Y also double. d) Go on Cansim (see Data sources on the course website) and retrieve the following series V , V , V , V from 1981 to Use the deflator to express the capital stock and GDP in real terms. Finally, assume that α = 0.3. i) Plot Total Productivity (A) growth; ii) Plot MPL and MPK on the same graph (ideally with their own y-axis) iii) Does the behaviour (trend) of MPK and MPL look similar over time? Yes. They are quite similar. MPK decreases more starting in but in general they look alike. 3

4 Question 3: Unemployment (20 Points) There are 100 people (N) living in Brewlandia. 57 are employed (E) and 5 are unemployed (U). In 2001, the economy entered a small boom period. An unemployed person found a job while 2 inactive people decided to join the labour force (LF). The total number of people stayed the same. a) Complete Table 2 4

5 Table 2: Brewlandia s population E U LF N Answer: Only 1 person found a new job (Employment went from 57 to 58 and unemployment changed from 5 to 4). However, the labour force population increased by 2 (from 62 to 64) which increases the unemployment pool (from 4 to 6). E U LF N b) Find the employment rates and the unemployment rates for 2000 and Explain how these rates changed from 2000 to Answer: Employment rate = E/N. In 2000 it s 57% and in 2001 it s 58%. Unemployment rate = U/LF. In 2000 it s 5/62 = 8.1% and in 2001 it s 6/64 = 9.4% The employment rate increases but since 2 people join the active, the unemployment rate also increases. c) For 2000, assume that the total output per employed worker is 2 and the price of each output is $2. Also, the unemployed and the inactive population produce service for themselves at home (e.g. childcare) that would cost $1 on a formal market. Find the nominal GDP. Answer: Homeproduction is not counted in the GDP. Therefore the nominal GDP is only 57*2*2 = $228 Part 2 Forget everything from part 1. Brewlandia s National account is described in Table 3. a) Find the Gross National Product, GNP, the private savings, S pvt, and the current account balance, CA. S pvt = (Y+NFP-T+TR+INT)-C = = 35 GNP = GDP + NFP = = 95 CA = NX + NFP = 0-5 = -5 b) Does the government has a budget surplus or deficit? Deficit. G: Y=C+I+G+XN so 100 = G+0 G = 20 S govt = T-(G+TR+INT) = 20-( ) = -20 5

6 Table 3: Brewlandia s National Account Y 100 NFP -5 TR 10 INT 10 T 20 C 60 I 20 XN 0 6