ECON20001 INTERMEDIATE MACROECONOMICS SEMESTER 2 ASSESSMENT, 2018
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SEMESTER 2 ASSESSMENT, 2018
ECON20001 INTERMEDIATE MACROECONOMICS
SOLUTION
SECTION A
This section is compulsory and contains 12 multiple-choice questions. Suggested time allotment: 40 minutes for the section, slightly over 3 minutes per response. All questions are equally weighted.
A1. Consider the simple aggregate demand Z = C(Y, T)+I+G, where C(Y, T) = c0 +c1 (Y -T).
Suppose the marginal propensity to consume c1 equals 0.8. Given this information, which of the following event(s) will cause the largest increase in output?
*(a) G increases by 200
(b) T decreases by 200
(c) I increases by 150
(d) both (a) and (b)
A2. Which of the following generally occurs when a central bank pursues a contractionary
monetary policy?
(a) the central bank purchases bonds and the interest rate increases
(b) the central bank purchases bonds and the interest rate decreases
*(c) the central bank sells bonds and the interest rate increases
(d) the central bank sells bonds and the interest rate decreases
A3. In the IS-LM model, if there are an expansionary fiscal policy and a contractionary mon-
etary policy at the same time, then output and the interest rate .
(a) may rise or fall, falls
(b) falls, rises
(c) falls, falls
*(d) may rise or fall, rises
A4. In the Phillips curve equation, which of the following will cause an increase in the current
inflation?
(a) an increase in the expected inflation rate
(b) a reduction in the unemployment rate
(c) an increase in the natural rate of unemployment
*(d) all of the above
A5. Consider the dynamic AS-AD model. Which of the following is true on impact when there
is a favourable aggregate supply shock?
*(a) the DAS curve shifts out
(b) the DAD curve shifts out
(c) the DAS curve shifts in
(d) the DAD curve shifts in
A6. Which of the following is false in the dynamic AS-AD model?
(a) holding all else equal, output is more variable when θY is small
*(b) holding all else equal, inflation is more variable when θT is big
(c) there is no trade-off between inflation and output in the long run
(d) there is a trade-off between inflation variability and output variability
A7. Consider the basic Solow model with production function Y = Kα N1-α and no employ-
ment growth. Which of the following must be false if the saving rate increases?
(a) consumption per worker decreases in the long run
(b) total capital stock increases in the long run
*(c) the growth rate of capital per worker increases in the long run
(d) the growth rate of capital per worker increases in the short run
A8. Consider the basic Solow model with production function Y = Kα N1-α , saving rate of
16% and depreciation rate of 5%. Which of the following is true? An increase in capital income share α will:
(a) decrease steady-state output per worker but leave the steady-state capital/output
ratio unchanged
(b) decrease steady-state output per worker but increase the steady-state capital/output
ratio
(c) increase steady-state output per worker but increase the steady-state capital/output ratio
*(d) increase steady-state output per worker and leave the steady-state capital/output
ratio unchanged
A9. Assume that the domestic economy is an open economy. Which of the following will make
the government spending multiplier smaller?
(a) a move towards a more closed economy
*(b) an increase in the marginal propensity to import
(c) an increase in the marginal propensity to consume
(d) a decrease in foreign output
A10. The existence of the J-curve suggests that a real depreciation will cause
(a) an initial increase in net exports
(b) an initial increase in economic activity
(c) a final reduction in net exports
*(d) an initial reduction in the demand for domestic goods
A11. Assume that policy makers are pursuing a fixed exchange rate regime and that the economy
is initially operating at the natural level. Which of the following occur as a result of a devaluation?
(a) the real exchange rate will be permanently higher in the long run *(b) the real exchange rate will be the same in the long run
(c) the real exchange rate will be permanently lower in the long run
(d) the effects of this devaluation on the real exchange rate will be ambiguous in the long run
A12. Consider the model of monetary policy rules versus discretion. In equilibrium, which of
the following is true?
*(a) with a rule, inflation is lower and unemployment is the same as with discretion (b) with a rule, inflation is lower and unemployment is lower than with discretion
(c) with discretion, unemployment is higher and the central bank has a bigger loss than with a rule
(d) with discretion, inflation is higher and the central bank has the same loss as with a rule
SECTION B
This section is compulsory and is worth 20 marks. Answer two of the following three questions. Each question is worth 10 marks. Suggested time: 40 minutes.
B1. IS-LM model. Consider an IS-LM model with the central bank controlling the interest
rate. The consumption and investment functions are
C = 50 + 0.4(Y - T)
and
I = 50 + 0.3Y - 1000i
and suppose G = 15 and T = 10. Let the money demand function be
M/P = Y - 2000i
and let i = i0 = 0.03.
(a) Solve for the equilibrium values of output Y and real money supply M/P . (2 points)
(b) Now suppose that the interest rate, i0 , is increased to 0.06. Solve for the equilibrium
values of Y and M/P . What are the effects of a contractionary monetary policy on output and real money supply? Explain. (2 points)
(c) Set the interest rate back to 0.03. Now suppose that the government wants to reduce the fiscal budget deficit and achieves a fiscal budget surplus. So the government pursues a contractionary fiscal policy by reducing G to G = 9. If the central bank keeps the interest rate unchanged, what are the effects of this fiscal contraction on Y and C? Explain. (3 points)
(d) Set the interest rate back to 0.03, G = 15 and T = 10. Suppose that the interest- sensitivity of investment demand is 500 instead of 1000. Consider the contractionary monetary policy where the interest rate rises to 0.06. Would the monetary contraction be more contractionary in terms of its effect on output? Explain. (3 points)
[Total: 10 marks]
(a) Goods market equilibrium condition is
Y = C + I + G = 111 + 0.7Y - 1000i
As the central bank’s target interest rate is i = 0.03, the equilibrium value of output is Y = 270. Using the money market clearing condition, the real money supply is
M/P = Y - 2000i = 210
(b) If the interest rate increased to i = 0.06, we use the goods market equilibrium con-
dition to solve for Y = 170. The money market clearing condition gives M/P = 50. The contractionary monetary policy reduces output. Both the lower output and the higher interest rate lead to a decrease in real money supply.
(c) When G reduces to G = 9, the goods market equilibrium condition leads to Y = 105 + 0.7Y - 1000i
With i = 0.03, Y = 250. Consumption is C = 50 + 0.4(250 - 10) = 146. The contractionary fiscal policy reduces output and consumption because a reduction of G lowers aggregate demand. Through the direct and multiplier effect, output decreases. Since consumption depends positively on output and taxes do not change, consumption also falls.
(d) When the interest-sensitivity of investment demand is 500, the investment function is I = 50 + 0.3Y - 500i. The goods market equilibrium condition implies
Y = 111 + 0.7Y - 500i
Setting i = 0.03, we have Y = 320. Setting i = 0.06, we have Y = 270. When investment is more senstive to the interest rate, output reduces from 270 to 170. Now output reduces from 320 to 270. The contractionary monetary policy is less contractionary. The less sensitive investment is to the interest rate, the less the response of output to changes in the interest rate. Here the same rise of the interest rate induces less reduction in investment and output with a relative interest-insensitive investment function.
B2. Labor market flows. Suppose the change in unemployment ut is given by ut+1 - ut = s(1 - ut ) - fut
(a) Solve for the steady-state unemployment rate. How do the job finding rate f and the
job separation rate s affect the speed of adjustment if there are shocks to unemploy- ment? (2 points)
(b) Suppose now that f (θt ) = Aθ The labor market tightness θt is defined as θt = vt /ut
where vt is the job vacancy rate. Derive the Beveridge curve. Use a diagram with clear labels to illustrate the Beveridge curve. (2 points)
(c) Suppose that firms post vacancies until the vacancy filling rate q(θt ) satisfies q(θt )J = c, where q(θt ) is the vacancy filling rate, J is the value of a filled position and c is the cost of creating a vacancy. If A = 0.3, J = 3, c = 0.9, and s = 0.02 per month, solve for the equilibrium labor market tightness θ * . Use the diagram that you draw in part (b) to add the job creation curve. Solve for the steady-state unemployment rate and vacancy rate. (3 points)
(d) Suppose now the cost of creating a vacancy rises to c = 1.2. Use the diagram you draw in the previous parts to illustrate how the increase in c affects the Beveridge curve and the job creation curve. Calculate the new equilibrium values of labor market tightness and steady-state unemployment. Give intuition for your answers. (3 points)
[Total: 10 marks]
(a) The steady state unemployment is where ut = ut+1 ,
s
u =
The speed of adjustment is given by λ = 1 - s - f . Therefore, a higher s or f leads to a faster speed of adjustment.
(b) The Beveridge curve is derived from
s
u =
After a few steps of algebra, we have
[s(1 - u)]3
A3u2
(c) The job finding rate and the vacancy filling rate are related by
f (θ) = q(θ)θ
We have
q(θ) = Aθ -2/3
vacancy rate
unemployment rate
Figure 1: Beveridge curve
The job creation decision satisfies q(θ)J = c and
Aθ -2/3J = c
Plugging in the values A = 0.3, J = 3, c = 0.9, the equilibrium labor market tightness is θ = 1. Using the steady-state unemployment equation, we have
s 0.02
s + f (θ) 0.02 + 0.3
and v = θu = 0.0625.
vacancy rate
Beveridge curve
Job creation curve
v*
u* unemployment rate
Figure 2: Equilibrium in the labor market
(d) The increase in the cost of creating vacancy rotates down the job creation curve, but does not affect the Beveridge curve. The new equilibrium should have a higher unemployment rate and a lower vacancy rate. Using the numbers,
0.3θ -2/33 = 1.2
The equilibrium labor market tightness is θ = (3/4)3/2 = 0.650. The job finding rate is f (θ) = 0.260. The unemployment rate is
s 0.02
s + f (θ) 0.02 + 0.260
Intuitively, the higher cost of creating vacancy discourages firms from creating va- cancies. The labor market tightness should decrease. Since the Beveridge curve does not change, the lower vacancy rate should be associated with a higher unemployment rate.
vacancy rate
Beveridge curve
Job creation curve
Job creation curve (higher c)
v*
v*’
u* u*’ unemployment rate
Figure 3: A rise in the cost of creating vacancy
B3. Mundell Fleming model. Consider an open economy with flexible exchange rates. Suppose
the domestic central bank keeps a target interest rate.
(a) With the help of a diagram, show the effect of an increase in foreign output, Y* ,
on domestic output, Y. What happens to the nominal exchange rate E? Explain. (3 points)
(b) With the help of a diagram, show the effect of an increase in the foreign interest rate,
i* , on domestic output, Y. What happens to the nominal exchange rate E? Explain. (3 points)
(c) Given the discussion of the effects of fiscal policy in the IS-LM model, what effect is a foreign fiscal expansion likely to have on foreign output, Y* , and on foreign interest rate, i* ? Given the discussion of the effects of monetary policy in the IS-LM model, what effect is a foreign monetary expansion likely to have on Y* and i* ? Explain. (2 points)
(d) Given your answers to parts (a), (b) and (c), how does a foreign fiscal expansion affect domestic output? How does a foreign monetary expansion affect domestic output? Explain. (2 points)
[Total: 10 marks]
(a) The increase in foreign output raises demand for domestic goods and shifts the IS
curve out. Domestic output will increase. Given that the interest rate is controlled by the central bank and does not change, the nominal exchange rate does not change.
Y Y’
output
E
exchange rate
Figure 4: A rise in foreign output
(b) The increase in the foreign interest rate rotates the interest parity condition up and
depreciates the nominal exchange. The lower exchange rate increases net exports and shifts the IS curve out. Domestic output increases.
i
Y Y’
output
Interest parity (with higher i*)
E’ E
exchange rate
Figure 5: A rise in foreign interest rate
(c) In the IS-LM model, a foreign expansionary fiscal policy shifts the foreign IS curve out and leads to a higher Y* with an unchanged interest rate. A foreign expansionary monetary policy shifts down the LM curve, which lowers i* and raises Y* .
(d) A foreign fiscal expansion leads to a higher Y* without affecting the interest rate. Therefore, from part (a), domestic output should increase. A foreign monetary ex- pansion lowers i* and raises Y* . The higher Y* tends to raise domestic output, but the lower i* tends to decrease domestic output. Overall, the effect on domestic output is ambiguous.
SECTION C
This section is compulsory and is worth 20 marks. Answer two of the following three questions. Each question is worth 10 marks. Suggested time: 40 minutes.
C1. Dynamic AS-AD model. Consider a dynamic AS-AD model with the Phillips curve Tt = 匝t-1 (Tt ) + (Yt - ) + vt
where the expected inflation is formed according to 匝t-1 (Tt ) = Tt-1 . The output equation is
Yt = - (rt - ρ) + εt
Suppose that the monetary policy rule is given by
it = ρ + Tt + (Tt - T* ) + (Yt - )
Lastly, the Fisher equation is
it = rt + 匝t (Tt+1)
(a) Compute the long run equilibrium values for output, inflation, nominal interest rate
and real interest rate. (2 points)
Expected inflation plays a key role in both the Phillips curve equation and the Fisher equation. Suppose instead of assuming that 匝t-1 (Tt ) = Tt-1 , people form their expec- tations of inflation based on past inflation and the inflation target. That is, 匝t-1 (Tt ) = βTt-1 + (1 - β)T* , where 0 < β < 1. A smaller β implies that the expected inflation is more anchored to the inflation target. Use this new assumption of expected inflation to complete the following parts.
(b) Derive the DAS curve. (2 points)
(c) Derive the DAD curve. (2 points)
(d) Suppose that vt = εt = 0. Use the new DAS curve and DAD curve to derive a formula that allows you to compute this year’s inflation Tt as a function of last year’s inflation Tt-1 , the inflation target T* and the parameter β . (2 points)
(e) Following part (d), when β = 0, how does Tt depend on Tt-1 and T* ? Explain.
(2 points)
[Total: 10 marks]
(a) The long run equilibrium values are Y = , T = T* , r = ρ and i = ρ + T* .
(b) With the new expected inflation, 匝t-1 (Tt ) = βTt-1 + (1 - β)T* , the DAS curve is Tt = βTt-1 + (1 - β)T* + (Yt - ) + vt
(c) To derive the DAD curve, we start from the output equation by substituting rt by
it - 匝t (πt+1),
Yt = - [it - βπt - (1 - β)π* - ρ] + εt
Then we use monetary policy rule to substitute it ,
Yt = - [ρ + πt + (πt - π * ) + (Yt - ) - βπt - (1 - β)π* - ρ] + εt
After rearranging, the DAD curve is
Yt = - (πt - π * ) + εt
(d) We can use the DAS curve to find Yt - and substitute it into the DAD curve to
find
2β 4 - 3β
4 - β 4 - β
(e) When β = 0, πt = π * . Now the expected inflation is always anchored at the inflation
target. Past inflation does not affect current inflation. The actual inflation rate always equals the inflation target.
C2. Solow growth model. Consider the production function Y = K1/2(AN)1/2 . Assume that
the saving rate s equals 20% and the depreciation rate δ equals 2%. Further, assume the growth rate of employment gN is 1% and the growth rate of technological progress gA is 2%.
(a) Find the steady-state values of (i) capital per effective worker, (ii) output per effective
worker, (iii) the growth rate of output per effective worker, (iv) the growth rate of output per worker, and (v) the growth rate of output. (2 points)
(b) The golden rule saving rate maxmises the steady-state consumption per effective
worker. Set up the proper maximisation problem and derive the golden rule saving rate sG . (2 points)
(c) Suppose that firms are competitive and both capital and labor are paid their marginal products. Calculate the return to capital r on the balanced growth path. Calculate the growth rate of the wage rate w on the balanced growth path. (2 points)
In the standard Solow growth model, technological progress is labor-augmenting. An alternative view of technological progress is that technological progress is capital aug- menting. This is known as embodied technological progress (technological progress must be “embodied” in new capital before it can raise output). One simple way of modeling technological progress as capital-augmenting is to assume that the produc- tion function takes the form: Y = (AK)α N1-α .
(d) Show that the economy has a balanced growth path. (Hint: normalize Y and K properly to find a steady state) (3 points)
(e) Find the growth rates of Y and K on the balanced growth path. (1 point) [Total: 10 marks]
(a) Normalizing the production function to per effective worker term, y = f (k) = k1/2 .
The capital accumulation equation for capital per effective worker yields the steady state capital per effective worker
sf (k) = (δ + gA + gN )k
It follows that
k* = ( ) 1 1一α = ( )2 = 16
Then y* = 4. The growth rate of output per effective worker is 0. The growth rate of output per worker is gA = 0.02 and the growth rate of output is gA + gN = 0.03.
(b) The golden rule saving rate maximizes consumption per effective worker
s
c = (1 - s)y = (1 - s)
The first order condition gives the golden role saving rate being 1/2.
(c) The return to capital satisfies
r = K-1/2(AN)1/2 = =
Y and K by A 1 一α N ,
y = A 1Yα一α N = ╱ A 1N、α = k α
α α
sf (k) = (δ + gN + gA\ )k
Once k and y are in the steady state, K and Y will be on the balanced growth path.
(e) On the balanced growth path, the growth rates of K and Y are gN +gA\ = gN + gA .
C3. Endogenous growth model. Consider the endogenous growth model with production func-
tion Y = AK, productivity level A = 1/4, saving rate s = 0.3, depreciation rate δ = 0.05 and no growth in productivity.
(a) Calculate the growth rates of output and capital. How do the growth rates depend
on s and δ? (2 points)
(b) What is the steady-state capital/output ratio? How does it depend on s and δ?
(2 points)
The above AK model is the simplest model of endogenous growth. Now we consider an alternative model that also generates endogenous growth. Suppose that the economy has two sectors, which we call manufacturing firms and research universities. Firms produce goods, which are used for consumption and investment in physical capital. Universities produce a factor of prodution called ”knowledge,” which is then freely used in both sectors.
The production function for firms in period t is Yt = Kt(α)[(1 - γ)NEt](1-α), where Kt is the stock of physical capital, Et is the stock of knowledge and N is the constant amount of labor input. There are two parameters in the production function: 0 < α < 1 as in the standard Solow model and γ is the fraction of employment in universities. Therefore, 1 - γ is the fraction of employment in manufacturing. The knowledge accumulation equation is Et+1 - Et = g(γ)Et , where g(γ) is an increasing function of γ that shows how the growth of knowledge depends on the fraction of employment in universities. Lastly, the capital accumulation equation is Kt+1 - Kt = sYt - δKt .
(c) Consider the balanced growth path where the growth rate of physical capital equals the growth rate of knowledge. What are the growth rates of physical capital and knowledge? (2 points)
(d) Derive an expression that shows how output Yt depends on physical capital Kt . What is the capital/output ratio in this economy? How does it depend on parameters such as s, δ and γ? (2 points)
(e) Following part (d), what is the growth rate of output in this economy? How does the
growth rate of output depend on parameters such as s, δ and γ? In what sense is this an endogenous growth model? Explain. (2 points)
[Total: 10 marks]
(a) In the AK model, the growth rate of output and capital is g = sA - δ = 0.3/4 - 0.05 =
0.025. A higher s or a lower δ contributes to a higher growth rate.
(b) The steady-state capital/output ratio is K/Y = 1/A = 4. This ratio does not depend
on s and δ .
(c) On the balanced growth path, both knowledge and physical capital grow at the same rate. From the knowledge accumulation equation, we can find the growth rate of knowledge is g(γ). It follows that the growth rate of physcial capital is also g(γ).
(d) From the physical capital accumulation equation, we find
g(γ)Kt = sYt - 6Kt
It follows that
g(γ) + 6
s
The capital output ratio is therefore s/[g(γ) + 6]. This ratio depends positively on s and negatively on γ and 6 .
(e) The growth rate of output is the same as the growth rate of physical capital which
is g(γ). This growth rate does not depend on the saving rate and depreciation rate. It depends only on the parameter γ . This is an endogenous growth model because the production function collapse into an ”AK” production function. The growth in output is not driven by productivity growth, but is driven by knowledge accumulation and the function g(γ).
2022-10-31