Queen s University Department of Economics ECON 222 Macroeconomic Theory I Fall Term Section 001 Midterm Examination 31 October 2012

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1 Queen s University Department of Economics ECON 222 Macroeconomic Theory I Fall Term 2012 Section 001 Midterm Examination 31 October 2012 Please read all questions carefully. Record your answers in the answer booklet provided. You are encouraged to draw diagrams to support your answers. Please label the axis and lines or curves on your diagrams. The exam has two parts. Marks will be awarded also on the basis of the logical arguments given to support your answers. Part A consists of short questions. Do FOUR of the six questions. Each question is worth 10 marks for a total of 40 marks. Part B consists of long questions. Do BOTH of these questions. Each question is worth 30 marks for a total of 60 marks. The exam is 80 minutes long. Budget your time carefully. Hand calculators (non programmable) are permitted for this exam. Upon completion of your exam, only hand in the answer booklet clearly labeled with your student number and class section. Any cheating attempt will be sanctioned with the toughest possible punishment.

2 PART A: Short Questions. Answer FOUR of the following six questions. Each question is worth 10 marks for a total of 40 marks. Answers without any explanations will receive zero marks. Question A.1: Inter-temporal Budget Constraint (10 Marks) Assume a representative agent lives for two periods. He receives an income of y 1 in period one and y 2 in period two, he also faces an interest rate of r 1. His consumption in period one is denoted by c 1 and in period two by c 2. Draw the agent s inter-temporal budget constraint on a graph with current consumption on the horizontal axis and future consumption on the vertical axis. Then suppose the interest rate he faces falls to r 2, so r 1 > r 2. Draw the new inter-temporal budget constraint which corresponds to r 2 on the same graph. Write formulas for all intercepts, as well as any points where the the two curves intersect (if there is any such points). Answer: 2

3 c2 Budget Constraint with lower r c2 = y1(1+r1) + y2 Inital Budget Line c2 = y1(1+r2) + y2 No borrowing point c1 = y1 and c2 = y2 y2 New Budget Line y1 c1 = y1+ y2/(1+r1) c1 = y1+ y2/(1+r2) c1 3

4 bigskip Question A.2: Employment (10 Marks) The Table 1 presents employment data for Canada during the year Table 1: Canadian Labour Force Statistics (measured in millions of persons) Employed Unemployed Working Age Population Total Population Using this data, calculate the following statistics for each year. Round all answers to two decimal places. A) The labour force; B) The participation rate; C) The unemployment rate; D) The employment rate; E) The growth rate of the labour force between 2010 and ANSWER: A) LF2010 = employed + unemployed = 16900, ,500,000 = 18,400,000 LF2011 = employed + unemployed = 17,200, ,400,000 = 18,600,000 B) Participation2010 = Labour Force / working age population = 18,400,000/27,500, % Participation2011 = Labour Force / working age population = 18,600,000/27,800, % C) UnemploymentRate2010 = Unemployed/LabourForce = 1,500,000/18,400, % UnemploymentRate2011 = Unemployed/LabourForce = 1,400,000/18,600, % D) EmploymentRate2010: Employed/WorkingAgePopulation = 16,900,000/27,500, % EmploymentRate2011: Employed/WorkingAgePopulation =17,200,000/27,800, % 4

5 E) Labour Force Growth Rate = (LF LF2010 )/LF2010 = (18,600,000-18,400,000)/18,400, % Question A.3: Neoclassical Growth Model (10 Marks) In the context of the neoclassical growth model explain (also known as the Solow-Swan model) what is the steady state and what is the golden rule of capital-labour ratio. Show using graphs if you think they will be helpful. Explain what happens in this model when there is an increase in the population growth rate. ANSWER In the neoclassical growth model, in the absence of productivity growth the economy will eventually reach what we call a steady state in the long run. A steady state is a situation in which the economy s output per worker, consumption per worker, and capital stock per workers are constant - that is in the steady state, y t, c t, and k t do not change over time. That means that Y t, C t and K t are all growing at the same rate as the population growth rate, n. In the steady state, because capital per worker is constant, the level of investment must ensure this is the case. Investment must be sufficient each year to replace capital lost to depreciation d and to accumulate new capital sufficiently quickly to keep up with population growth n. I t = (n + d)k t (in the steady state) Steady state consumption is output less steady state investment: in per capita terms this is C t Y t (n + d)k t (in the steady state) c = Af(k) (n + d)k (in the steady state) So long as an economy isn t in a poverty trap, it will eventually reach the steady state, regardless of whether it starts off with a higher or lower capital-labour ratio. If k > k, then investment required to keep capitallabour ratio constant is above the actual savings rate, so capital-labour ratio will fall until the economy hits the steady state. If k < k the the savings rate is greater than the level of investment required to keep the capital-labour ratio constant, and the capital-labour ratio will rise until it reaches the steady state. The Golden Rule capital-labour ratio is the level of capital-labour ratio that maximizes consumption per worker in the steady state. This level of capital-labour ratio is not necessarily the same as the steady state level of capital-labour ratio. If k < k G then an increase in capital-labour ratio will raise consumption, if k > k G then and increase in capital-labour ratio will lower consumption. Figure 6.4 in our textbook shows the steady-state and Golden Rule together. 5

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7 Question A.4: Permanent Income Hypothesis (10 Marks) Consider a consumer who follows the Permanent Income Hypothesis (PIH) discussed in class (also know as the consumption-smoothing motive). This consumer lives for two periods. In the first period of his life he is a borrower (he s consumes more than he s earning in this period). Which of the following statements is TRUE? Give a detailed explanation of your choice (i.e. why you know the statement is true, why you know the other statements are false, and including graphs if appropriate). (a) An increase in the real interest rate will effectively mean a loss of wealth for the borrower. The borrower will respond to this decline in wealth by reducing both current and future consumption. A reduction in current consumption means that current savings increases (that is, borrowing decreases). Both the income and substitution effects increase the saving of a borrower. (b) An increase in the interest rate raises the price of consumption in the first period compared to the second period. The substitution effect says that the borrower will reduce current consumption and increase future consumption, but the income effect says that with a higher interest rate the borrower will increase current consumption while maintaining the same level of future consumption. The overall affect is ambiguous. ANSWER: (A) is True. When an individual is a borrower, and increase in the interest rate increases the amount of interest payments that a borrower must make, thereby making the borrower unable to afford the same levels of current and future consumption as before the increase in the real interest rate. The borrower has effectively suffered a loss of wealth, and he responds to this loss of wealth by reducing both current and future consumption. By reducing current consumption, his current savings increases (that is, borrowing decreases). (B) is False, it described the reaction of a saver from an increase in the real interest rate, not a borrower. Question A.5: National Accounts (10 Marks) Table 2 presents data from Canada s national accounts in Table 2: 2011 Canadian National Accounts (in billions of dollars) Nominal Value in 2002 Value Chained Dollars Personal expenditure Investment expenditure Government purchases Exports Imports Statistical discrepancy Using Table 2 calculate the following statistics. Round all numbers to 2 decimal places. A) Nominal GDP & Real GDP for 2011 B) GDP deflator for 2011 C) Inflation rate from 2011 to 2012, assuming the GDP deflator in 2012 is (Note: The inflation rate should be expressed in percentage terms) 7

8 ANSWER A) Nominal GDP = C + I + G +NX = $ Real GDP = Sum of 2011 value in 2002 chained dollars = $ B) GDP Deflator = nominal GDP/real GDP = / = textbfc) Inflation rate = (deflator deflator2011)/deflator2011 = ( )/1.29 = % Question A.6: Labour Market Equilibrium (10 Marks) Draw a graph depicting the labour market equilibrium. Be sure to label all axis carefully, as well as any points where curves may interesct. Show graphically what will happen to the original equilibrium under the following circumstances, and comment briefly on how wages and employment change (or state that the equilibrium will not change). (i) All cities and countryside in Canada are hit by extreme flooding. This drastically reduces the amount of goods and services which firms are able to supply for a single period of time. (Hint: This is a temporary adverse supply shock) (ii) The federal government passes a law allowing more immigration of young workers into Canada. ANSWER: 8

9 Labour market equilibrium (See also figure 3.11 in text): Real Wages, w Labour Supply, NS w E N Labour Demand, ND Labour, N Extreme flooding is a \emph{temporary adverse supply shock}. This means that the labour demand curve will shift to the left, which reduces both wages and employment. Figure 3.12 in our textbook also shows what this looks like. w 1 A w 2 B ND 1 ND 2 N 2 N 1 9

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11 Real Wage NS 1 NS 2 w 1 w 2 A B N 1 N 2 ND Labour If the federal government passes a law allowing more immigrants into Canada to work, this will shift the labour supply curve to the right. Wages will fall and employment will rise. 11

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13 PART B: Long Questions. Answer BOTH of the following two questions. Each question is worth 30 marks for a total of 60 marks. Answers without any explanations will receive zero marks. Question B.1: Consumption (30 Marks) Suppose the productions side of a closed economy is characterized by the following equations: MP K f = K f I = K f K + dk Y = 3600 K = 660 d = 0.4 p K = 1 where MP K f is future marginal product of capital. MP K f describes the relationship between future marginal product of capital and the future capital stock, K f. I is the standard equation for investment, Y is full employment output, K is initial capital stock, d the rate of depreciation of capital, and p K the price of capital. The interest rate in this economy is defined as r. There are no taxes on capital in this economy. (a)[5 MARKS] Using the information provided above, find the user cost of capital. Then, using your equation for the user cost of capital find desired future capital stock K f as a function of the interest rate r. ANSWER: Capital: uc = p K (d + r) MP K = p K (d + r) K f = 1(0.4 + r) 0.2K f = r K f = 498 5r (b) [5 MARKS] We want to determine the aggregate investment decision. Using your expression for K f, find the desired investment stock, I d, as a function of r. Investment: I d = K f (1 d)k = 498 5r (1 0.4)660 = 102 5r (c)[5 MARKS] Aggregate consumption in the economy is defined by the equation C d = (Y T ) 100r Government expenditure are equal to G = 460, and taxes paid by consumers are equal to zero, T = 0. Using this additional information find an equation for desired national savings in terms of the interest rate, r. 13

14 ANSWER: S d = S P V T + S GOV = Y C d G = r 460 = r (d) [5 MARKS] Given the desired investment and savings equations derived in parts (b) and (c), define the goods market equilibrium. That is, find the market clearing interest rate r and use this to find the equilibrium levels of savings and investment. Show graphically what this equilibrium looks like. ANSWER: In equilibrium in a closed economy it must be that S d = I d : Then S d = r I d = 102 5r r = 102 5r 105r = 2 r = r 1.9% S d = (0.019) I d = 102 5(0.019) Which we know is correct since in a closed economy it must be that S d = I d! 14

15 r S d r = 1.9% I d S d = I d = Desired national savings, S d Desired national investment, I d 15

16 (e) [10 MARKS] Now assume this country is able to trade with the rest of the world. The country has no influence on the world real interest rate, r w, and so takes it as given (i.e. this country is a small open economy). The prevailing world real interest rate is r w = 0.10 (or r w = 10%). Calculate the new levels of desired national savings and investment now that this country can invest and borrow from abroad, as well as the value of the current account balance. Is the economy a net lender or a net borrower? Represent this situation graphically. ANSWER: For a small open economy it must be that S d = I d + CA at the given real world interest rate. S d = (0.10) = 110 I d = (0.1) = CA d = S d I d = = 8.5 This country is a net lender (saver), which is see from the positive current account. 16

17 r w S d, r w = 3% I d I d = S d = 103 Desired National Savings, S d, and desired investment, I d CA = 3.15 Note: This graph is not to scale. 17

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19 Question B2: Long Run Growth (30 Marks) Suppose that aggregate production in an economy can be described by the following function: Y t = K α t (A t N t ) 1 α where Y t is output (GDP) produced at time t, K t is capital used at time t, N t is the number of workers employed at time t, and A t is labour productivity measured at time t. We call A t labour-augmenting technology in this production function. In this economy capital depreciates at rate d, and the population and labour force grow proportionately at rate n = N/N. Moreover, the savings rate is s is proportional to output, S t = sy t and 0 < s < 1. The steady state level of investment is i = (n + d + g A )k. Where g A A/A is the labour productivity growth rate. The economy is closed. We want to characterize this economy in terms of the neoclassical growth model (also called the Solow-Swan model). Note: This model differs slightly from the one described in class, the productivity term A t is specifically labour-augmenting instead of being a general productivity measure. (a) [5 MARKS] Rewrite the production function so that you have output per effective worker (i.e. y t Y t /(A t N t )) on the left-hand side. Use this equation to an write and expression for savings per effective worker (s). ANSWER: Y t = Kα t (A t N t ) 1 α A t N t A t N t y t = Kt α (A t N t ) 1 α 1 ( Kt y t = A t N t y t = k α ) α We know that savings is proportional to output, the savings rate is s. Thus the aggregate savings is: S t = sy t = sk α t (A t N t ) 1 α (don t need to show aggregate savings) and savings per effective worker is: s t = sy t = sk α (b) [10 MARKS] Using your result from (a) and the other information provided, find an expression for the steady state level of capital per effective worker (k ), and the steady state level of output per effective worker (y ). Assume capital per worker is below the steady state ratio (k < k ). Is it still possible for the economy to reach this steady state in the future? Explain. ANSWER: 19

20 The steady state level of capital is found by setting s t = i t and solving for k: sk α = (n + d + g A )k k α = (n + d + g A) k s k α 1 = (n + d + g A) s k 1 α s = (n + d + g A ) ( k s = (n + d + g A ) ( y = k α = ) 1 1 α s (n + d + g A ) ) α 1 α Yes, if the economy starts off with capital below the steady state level then S > I. The extra savings will go towards building extra capital. Extra capital will keep being produced until the economy reaches the steady state level of capital. This is a stable steady state. (c) [5 MARKS] What is the key determinant of long-term growth in this model and why? ANSWER: Productivity growth is key for sustained growth in the general neoclassical growth model. The effect of a productivity improvement (e.g. a new technology) causes the value of total factor productivity (TFP), A, to increase. This causes the per-worker production function to increase (y t = Af(k t )) as well as an increase in the savings curve (s t = saf(k t )). Over time the capital-labour ratio will also rise. As a result of the productivity improvement, steady-state consumption per worker rises at every capital-labour ratio (c = y i, y has risen by more than i has risen). Overall, a productivity improvement raises steady-state output and consumption per worker in two ways. First, it directly increases the amount that can be produced at any capital-labour ratio. Second, by raising the supply of saving, a productivity improvement has doubly beneficial impact on the standard of living. Productivity improvements are even more beneficial to society because they don t involve the short-term pain associated with the long-term gain in living standards, as is the case with an increase in savings. See figure 6.7 in textbook for a graphical representation of an increase in productivity. Since the industrial revolution (if not before) people have shown remarkable ingenuity in becoming more and more productive. In the very long run, according to this model, only these continuing increases in productivity hold the promise of perpetually better living standards. Increases and savings and decreases in the population growth rate do not see to have the same effect. (d) [10 MARKS] Canadian citizens are deeper in debt than they ve ever been in the past. This has led the Bank of Canada to encourage Canadians to increase their savings (reduce debt levels). Suppose Canadians listen to the Bank of Canada and the savings rate rises (s gets larger). What affect (if any) will this rise in the savings rate have on the steady state levels of consumption, output and capital? Explain both in words and graphically. ANSWER: In the neoclassical growth model, and increase in the savings rate will shift the savings curve upwards, s t = s y t > s t = sy t, when s > s. This causes an increase in the steady state level of capital, an increase 20

21 in output, and an increase in investment. The rise in savings also leads to an increase in consumption, but only in the long run. In the short run, when output is still close to it s initial levels, the rise in savings will mean a decrease in consumption. This is what is referred to as short term pain for long term gain. Figure 6.5 demonstrates this graphically: 21