ECON Macroeconomic Theory I Assignment 1. Fall Term 2013

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1 ECON Macroeconomic Theory I Assignment 1 Fall Term 2013 Due: Drop Box 2nd Floor Dunning all on Friday, September 27th before 12:00pm 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 invaluable asset in life. Question 1: National Income Accounts (30 Marks) You are asked to retrieve data from CANSIM (Statistics Canada database). Once you have retrieved the data, a spreasheet program will serve our purpose. You can access CANSIM through the library website by searching for CANSIM under Databases on the library s home page. Once you connect to CASS, 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 and from National Accounts, retrieve the following series for the period for Canada: nominal GDP at market prices (v687179) and real GDP in chained 2002 dollars. (a) calculate GDP deflators for each year over the period of 1981 and (10 marks) (b) Compute the year-to-year growth rate of GDP deflators and real GDP (either line or scattered plot is sufficient) and then plot the two series in the same graph. Please comment on interesting pattern(s) you observe from the graph (i.e., the lowest growth rate and highest growth rate and how the two series are related). (5 marks) (c) What is the 10 - year growth rate of real GDP between 2000 and 2010? Please write down the formula you use. (5 marks) (d) What is the average annual growth rate between 2000 and 2010? Please write down the formula you use. (5 marks) (e) Suppose now government sets the maximum prices (price ceiling) that sellers of goods and services are allowed to charge. Comment on the effect it has on real GDP. (5 marks) Suggested Solutions (a) See figure 1 (Either or 1981 to 2010 is fine) (b) See figure 2. From the figure, it seems that there is some counter-cyclical movement between the two series: When real GDP grows, inflation as implied by GDP deflator declines (c) The ten-year growth rate is given by: g 10 = (GDP 2010 GDP 2000 )/GDP 2000 =

2 Year Real Nominal Deflator Growth of real GDP Growth of GDP Deflator E E E E E E E E E E E E E E E E E E E E E E E+11 7E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E Figure 1: GDP Deflator 1981:2010 2

3 A Real GDP Growth GDP Deflator Growth Figure 2: Real GDP Growth vs. GDP Deflator Growth (d) Let s call the implied compounded growth rate g. To find g, we use the following equivalence: ence, (1 + g) 10 = 1 + g 10 g = (1 + g 10 ) 1/10 1 = (e) When government attempts to control prices, the prices observed no longer truly reflect the market value of the goods and services. When the prices are very low, everyone rushes to the store to get them resulting in people waiting too long to get the items they want. GDP is underestimated because shopping time (a form of home production) has not been factored in. On the other hand, when prices are too high, not many people want the goods, and hence, goods sit on the shelves unsold, resulting in overvaluation of firm s inventories and hence GDP is overestimated. You can also comment on black market (i.e., people who are able to get the good will try selling it at a much higher price, and the goods traded here is not taken into account in GDP, etc) 3

4 Question 2: Consumer Price Index (CPI) (30 Marks) Go to CANSIM and under the section labeled Provincial again, from Prices retrieve the data of Consumer Price index for Canada (v ) for the period of Jan Dec You will need to use these data to complete the following questions: (a) Calculate the monthly inflation rates for the entire period. Write down the formula you use and print out the results. (5 marks) (b) Now use the information over the period of Jan 2011 and Jan What is the annual inflation rate between Jan 2011 and Jan 2012? What is the average monthly inflation rate between the same period? (10 marks) (c) Suppose you purchased a government bond with face value 1,000 dollars in Jan In Jan 2012, you received the principal plus interest 1,080 dollars. What is the real interest rate on this government bond? Please be clear with the formula you use. (10 marks) (d) Suppose instead you are standing in Jan 2011 and are thinking whether you should invest in the government bond of face value 1000 dollars. The bond will pay back 1,080 dollars in Jan But you are not sure about the price level in Jan Modify the formula you use in part (c) to reflect your investment decision. (5 marks) Suggested Solutions (a) See Figure 3 (b) The annual inflation rate between Jan 2011 and Jan 2012 is given by π annual = CP I 2012 CP I 2011 CP I 2011 = The average monthly inflation rate is related to the annual inflation rate in the following way: ence, (c) The nominal interest rate is given by (1 + π monthly ) 12 = 1 + π annual π monthly = (1 + π annual ) 1/12 1 = i = The annual inflation rate between Jan 2011 and Jan 2012 is given by part (b). ence, the real interest rate r is r = i π annual = =.08 (d) In this case, we need to replace the annual inflation rate by Expected inflation rate, π e : r = i π e Question 3: Labor Supply (30 marks) Part (1) ome Production (10 marks) Consider the following economy where the only consumption good is tomatoes. In order to have tomatoes, one can either grow them in their own garden or purchase them in the market. Let s call the ones grown in the garden Organics and those purchased in the market Wholesales. In order to produce the Organics, one has to supply some labor, L and purchased some equipments from the market K. Formally, we write the production of Organics C O as follows: 4

5 Year-Month CPI Growth of CPI Figure 3: Inflation 5

6 C O = [0.5K ρ + 0.5L ρ ]1/ρ People must decide how much labor to supply to the production of Organics and/or Wholesales. They earn a wage income per unit labor w from engaging in the production of Wholesales, but no income from growing Organics. In addition, equipments K has to be purchased from the market at the price q dollars per unit. The price of Wholesales is normalized to 1 dollar per unit. This leads to the budget constraint: Complete the following questions: C M + qk = wl M What is the marginal product of L? With ρ = 1/2 does the marginal product of L satisfy Law of Diminishing Returns? With GDP defined by C M + qk or wl M, do you think that GDP correctly reflect the standard of living in this economy? Why? Suggested Solutions Let s define M = [0.5K ρ + 0.5L ρ ]. The marginal product of L, MP L is given by taking the first derivative of the home production function C O : C O L = 1 ρ M 1/ρ 1 (0.5ρL ρ 1 ) = 0.5M 1/ρ 1 L ρ 1 In order to see whether MP L is subject to laws of diminishing returns, we need to calculate the second derivatives of C O w.r.t. L. We call MP L subject to diminishing returns if 2 C O 0. Using the Chain L 2 Rule, we have: 2 C O L 2 = 0.5M 1/ρ 2 { 0.5(1 ρ)l 2ρ 2 { = 0.5M 1/ρ 2 L 2ρ 2 = 0.5M 1/ρ 2 L 2ρ 2 } + (ρ 1)ML ρ 2 0.5(1 ρ) + (1 + ( K } ) ρ )(ρ 1) L { 0.5(ρ 1)(1 + ( K } ) ρ ) L From the above expression, it is easy to see that 2 C O 0 iff ρ 1 0 or ρ 1. So YES, with ρ = 1/2, L 2 the marginal product of L satisfies diminishing returns. The production function of Organics belongs to the class of function with Constant Elasticity of Substitution. ρ measures the degree of Elasticity of Substitution. More specifically, the Elasticity of Substitution, ɛ is given by ɛ = 1 1 ρ. In the extreme case where ɛ approaches to, the factors of inputs, K and L become complements, i.e. K and L have to increase simultaneously in order to increase C O. On the other extreme where ɛ approaches to 0, K and L are substitutes, i.e., increasing either K or L is sufficient to increase C O. The GDP in this question is given by C W + qk or wl M. The problem with using GDP to measure welfare is that: (1) The Organics are not traded in the market and hence are not priced; (2) the labor used in the production of Organics are not paid. In both cases, GDP underestimate the actual welfare. Part (2) Wage Inequality (30 marks) 6

7 Over the period of postwar, many developed countries, such as the U.S. and Canada have witnessed rising wage inequality between skilled and unskilled workers. It has been argued that much of this rise in inequality is attributed to the emergence of capital that works better with skilled labor, such as computers. This question builds a simple economic model to explore this argument. For simplicity, we assume the production function takes the following form: Y = (k + u) θ s 1 θ Where u and s represent unskilled and skilled labor respectively and k represents the capital stock. The production function assumes that k and u are substitutes. Otherwise, it is a standard Cobb-Douglas production function you saw in class. The wage for unskilled labor is w u and that for skilled labor is w s. Complete the following question: (a) Write down the demand function for both skilled and unskilled labor. What is the ratio between the MP Ls marginal product of s and u (i.e., MP L u )? (10 marks) (b) Suppose that there is an increase in k, what will happen to the ratio in part (a)? Will you conclude that wage inequality rises? (10 marks) (c) In countries like Canada, a large fraction of the labor force growth comes from Skilled immigrants. Use the above framework to explain the effect of skilled immigration and increasing capital stock on wage inequality and illustrate the results in a diagram (ints: please look at Figure 3.14 of your textbook (6th edition)). (10 marks) Suggested Solutions Firm employs skilled labor up to the point where its marginal product equals to its wage: ence the demand function of skilled labor s is w s = MP L s = Y s = (1 θ)(k + u)θ s θ s = ( 1 θ w s ) 1/θ (k + u) Similarly, unskilled labor is employed to the point where its marginal product equals to its wage: w u = MP L u = Y u = θ(k + u)θ 1 s 1 θ ence the demand of unskilled labor is given as: The ratio between the two marginal products is: u = ( θ w u ) 1 1 θ s k MP L s MP L u = w s = ( 1 θ w u θ ) k + u s (b) Suppose there is an increase in k, from part (a), it is easy to see that the ratio increases, implying a higher ratio of marginal products and hence, higher ws w u. So yes, the introduction of new capital does increase wage inequality. (c) In this case, both s and k increase, and hence whether there will be an increase in wage inequality as reflected by the ratio of marginal products remains undetermined. We can show the effect of increase in k and s on equilibrium skilled and unskilled labor in Figure 4 in the following steps. Starting at point A, when the stock of capital k goes up, MP L s goes up. As a result, ND 0 s shift to ND 1 s The resulting equilibrium moves from A to B. Similarly, the demand for unskilled worker goes down and ND 0 u shifts to ND 1 u. Its equilibrium moves from A to B. Now starting from point B. With skilled immigration, the labor Supply for skilled workers goes up, which is represented by a rightward shift of labor supply curve from NS 0 s to NS 1 s. The equilibrium move from B 7

8 to C. Similarly, the demand for unskilled workers goes up (because now you need more unskilled workers to work with more skilled workers). This shifts ND 1 u to ND 2 u. The new equilibrium moves from B to C. With the shifts shown in Figure 4, wage inequality seems to reduce but in general, it depends on the magnitude of shifts in both demand and supply curves of skilled and unskilled workers. 8

9 9 Figure 4: Effect of Capital and Immigration on Labor Supply of Skilled and Unskilled Workers