UNIVERSITY OF TORONTO SCARBOROUGH ...
UNIVERSITY OF TORONTO SCARBOROUGH DEPARTMENT OF MANAGEMENT MGEC06: Topics in Macroeconomic Theory Winter 2014
Instructor: A. Mazaheri Test-1 (Saturday February 15, 1-3) Instructions: This is a closed book test.
You have 2 Hours. Good Luck! Last Name: First Name:
ID
FOR MARKERS ONLY: Q1
Q2
Q3
Q4
Total
40
20
20
12
92
Marks Earned Maximum Marks Possible
The University of Toronto's Code of Behaviour on Academic Matters applies to all University of Toronto Scarborough students. The Code prohibits all forms of academic dishonesty including, but not limited to, cheating, plagiarism, and the use of unauthorized aids. Students violating the Code may be subject to penalties up to and including suspension or expulsion from the University.
Answer all following questions: Question-1 [40 Points] Answer the following questions: a) (8 Points) An economy is characterized by the following:
AD SRAS LRAS Supply of capital Supply of labour Okun’s Law Natural rate of unemployment
Y = 400 + (MS/P) Y = Y + 10(P – Pe) Y = K0.5L0.5 K = 500 L = 500 (Y – Y )/ Y = –2.0(u – un) un = 0.06 (6%)
Suppose that the money supply has been constant for many years at MS = 1000. Now suppose there is an unexpected fall in autonomous consumption such that the AD curve becomes Y = 250 + (MS/P) Use the AS-AD model to find the short-run equilibrium values of Y, P, Pe, and u? What are the values of cyclical unemployment? What are the new long-run values of Y, P, Pe, and u? Show your answers in one AS-AD diagram making sure to label all the critical points. Solution: There is no shock as the money supply has been constant for many years therefore expected price will be equal to the actual price and:
Y = 500 0.550.5 = 500 1000 YD = 400 + = 500 P => P = P e = 10, Y = 500 Now there is a shock but the expectation does not adjust therefore in the short run:
Page 2 of 15
P e = 10 1000 = YSRAS = 500 + 10( P − 10) P => P = 5, Y = 450
Y AD = 250 +
Y − Y 450 − 500 = = −2(u − 0.06) Y 500 u = 0.11 In the long Run:
1000 = YLRAS = 500 P => P = 4 = P e u = 0.06
Y AD = 250 +
c)
LRAS
SRAS
10 AD 5 4 AD’ 450
500
Page 3 of 15
b) (8 Points) Consider two economies A and B. A operates according to the sticky-wage model and B operates under the sticky-price model. Aggregate demand unexpectedly falls in both countries, leading to a recession and an unexpected decline in price level and the demand for output. Use a graph of the labor market in each economy to illustrate the impact of the recession on the level of employment and the real wage.
Solution:
Sticky Wage Model: Because the nominal wage W is sticky, a decrease in the price level from P1 to P2 increases the real wage from W/P1 to W/P2. As a result, the quantity of labor demanded falls from L1 to L2 and the fall in labor demand decreases output. Note: that in the sticky wage model the labor market does not clear.
LS (W/P)1 Sticky-Price Model (W/P)2
L1D L2D
Labor
W/P
Sticky Price Model: Because the nominal price is sticky, when a decrease in the price level from P1 to P2 occurs only firms with flexible prices will reduce their demand for labor and therefore the overall demand D
for labor declines to L2 . The real wage declines from W/P1 to W/P2 and the quantity of labor demanded falls from L1 to L2 and the fall in labor demand decreases output. Note: that in the sticky price model the labor does not clear.
Page 4 of 15
c) (4 Points) Use a DAD-DAS curve diagram to illustrate the short-run and long-run effect of an unexpected negative supply shock on output, price level, unemployment rate, and inflation rate. Solution:
π DAS
A
B
DAD
Y Y A negative supply shock that (lasts for one period) will shift DAS leftward from point A towards point B. Inflation rises and output falls as a result inflation expectation starts to fall but not as rapidly. In period (t+1) the supply shock has ended but the inflation expectation does not return to its original level a fast. As a result the DAS moves towards the original equilibrium of A but only slowly. That assumes that the central Bank does not take any action. If in the process the central Bank monetizes the stagflation by increasing the inflation target then the DAD will shift rightward and the economy will move to a permanently higher inflation level.
Page 5 of 15
d) (4 Points) Use the Philips curve diagram with adaptive expectation to illustrate the short-run and long-run effect of an unexpected negative supply shock on output, price level, unemployment rate, and inflation rate. Assume an accommodating monetary policy. Solution:
The negative supply shock shifts up the short-run Phillips curve. The stagflation means that the new short run equilibrium is to the right of full employment. The expansionary monetary policy moves the short run equilibrium towards long run full equilibrium but at a new inflation rate.
Page 6 of 15
e) (10 Points) Suppose Canadian economy follows the Phillips curve
π = π −1 − 0.5(u − u n )
and that the natural rate of unemployment is given by the average of the past two years’ unemployment: u n = 0.5(u−1 + u−2 ) .
Suppose the natural rate of unemployment (un) has been historically at 6%. The Bank of Canada follows a policy to reduce inflation by 2% permanantly. i) (6 Points) Show the impact of this policy on the natural rate of unemployment over time. Solution:
π − π −1 = −0.5(u − u n ) − 0.02 = −0.5(u − u n ) => u − u n = 0.04 => u = 10% u0 = 6%, u1 = 10% 0.10 + 0.06 = 0.08 2 u + u1 0.08 + 0.10 u3 = 2 = = 0.09 2 2 u + u2 0.09 + 0.08 u4 = 3 = = 0.085 2 2 u + u3 0.085 + 0.09 u5 = 4 = = 0.0875 2 2 u2 =
ii) (4 Points) What is the sacrifice ratio for this disinflation? Briefly explain your answer. Solution: Because unemployment is always higher than it started, output is always lower than it would have been. => the sacrifice ratio is infinite. This is called hysteresis: we find that there is a long-run tradeoff between inflation and unemployment: to reduce inflation, unemployment must rise permanently.
Page 7 of 15
f) (6 Points) Start by briefly explaining the role of the monetary policy in the DAD framework. Then explain the difference between the conventional aggregate demand and the dynamic aggregate demand. Make sure to explain why the DAD is downward sloping. Solution: In the DAD framework the monetary policy is endogenized through the monetary rule. For instance, a decrease in the inflation rate forces the Bank of Canada to reduce the overnight rate and as a result the real interest rate will fall and the investment rises leading to a rise in the output. A surprise change in the parameters of the monetary rule such as an increase in the target inflation rate will shift the DAD rightward. The primary difference between the conventional demand and the DAD is the fact that in DAD framework, instead of price, incorporates the inflation. As explained above, in DAD framework, a movement along the curve represents a change in the Bank of Canada overnight rate (Federal Rate) accompanied by a change in the investment. For instance, a move down along the curve represents a decline in the inflation accompanied by a reduction in the overnight rate. The resulting decline in the real interest rate leads to an increase in the investment and hence an increase in the output. As one can see, while in the conventional aggregate demand framework the supply of money is constant, in the DAD framework the supply of money in endogenous to fit the Bank of Canada interest rate rule.
Page 8 of 15
Problem-2: [20 Points] Consider an economy in its long-run equilibrium with an inflation
rate, π, of 6% per year and a natural unemployment rate, un, of 4%. The expectationsaugmented Phillips curve is:
π = πe – 0.5(u – un), Assume that Okun’s law holds so that a 1% increases in the unemployment rate maintained for one year reduces output by 2% of full-employment output. Now consider a four-year disinflation according to the following table:
Year π
T+1 4%
T+2 2%
T+3 2%
T+4 2%
In this economy, agents use adaptive expectations to generate expected inflation rate. To be precise, agents use the average of the inflation rate from the previous two years to form the expected inflation. a) [10 Points] What is the unemployment rate in each of the four years? Illustrate your solution using a Phillips curve graph. b) [5 Points] By what percentage does output fall short of full-employment each year? What is the sacrifice ratio of this disinflation process? c) [5 Points] Use your graph of part (a) and clearly explain what would have happened if the expectation was rational rather than adaptive. What would have been the sacrifice ratio of this disinflation process?
Solution: Year πe u
T+1 6% 4% = 6%– 0.5(u – un) (u – un) = 4% => u = 8%
T+2 5% 2% = 5%– 0.5(u – un) (u – un) = 6% => u = 10%
T+3 3% 2% = 3%– 0.5(u – un) (u – un) = 2% => u = 6%
T+4 2% 2% = 2%– 0.5(u – un) (u – un) = 0% => u = 4%
6%
2%
un Page 9 of 15
b) Using Okun ratio of 2
2*Cyclical unemployment 2*4% = 8%, 2*6% = 12%, 2*2% = 4%, 2*0%=0 Sacrifice Ratio = (8%+12%+4%)/4=6 c) Under rational expectation the inflation would have adjusted instantly and therefore the sacrifice ration would have been zero.
6%
2%
un
Page 10 of 15
Problem-3 [18 Points] Suppose the loss function of the central bank is given by: L(u, π) = u2 + γ(π)2 The Phillips curve of this economy is: u = un − α(π − πe) a) (5 Points) What is the actual inflation and the expected inflation if the Bank adopts a credible rule? b) (8 Points) What is the actual inflation under policy discretion? What is the expected inflation and why? Briefly explain your results. c) (5 Points) Holding all else constant, what happens to actual inflation when γ increases and why? What does this suggest as to who should be appointed as the central banker? Solution: a) If rule is chosen
π =πe => u = u n The optimal rule would be: π = 0 b) The first step is to solve for the Bank choice of inflation, for any given inflationary expectations. Substituting the Phillips curve into the loss function to get:
L(u, π ) = (u n − α (π − π e ) ) + γ (π ) 2 2
Differentiate with respect to inflation π, and set this first-order condition equal to zero:
dL(u , π ) = −2α u n − α (π − π e ) + 2γπ = 0 dπ α 2 π e + αu n π= α2 +γ
(
)
Of course, rational agents understand that the Bank will choose this level of inflation.
π e = π , therefore the above equation simplifies to: αu n π= γ
=>
Page 11 of 15
Since the inflation is expected the unemployment will stay at the natural rate. The outcome of the discretionary policy is higher inflation and no change in the output. The phenomenon is called Time-inconsistency. If the policy makers use their discretion, rational consumers will expect the higher inflation and the policy maker will have no choice but to accommodate. This results into higher inflation which is costy to the policy maker. the natural rate of unemployment rises, the inflation rate also rises. c) Higher γ means more dislike for inflation relative to unemployment and therefore lower inflation and therefore lower loss. This suggests appointing a conservative central banker (higher γ).
Page 12 of 15
Problem – 4 (12 Points): Suppose the DAD and DAS equations are as follows and that the economy has been in equilibrium:
Yt = Yt − A(π t − π t* ) + Bε t
π t = π t −1 + φ (Yt − Yt ) + ν t where:
A=
αθπ 1 > 0, B = >0 1 + αθY 1 + αθY
Furthermore, suppose:
Y = 300, π t* = 2, α = 2.0, ρ = 1.0, φ = 0.2, π θ = 0.5, π Y = 0.5 In period t, the Bank of Canada decreases the inflation target from 2 to 1 permanently. What would be the impact on the output and inflation. To answer this question make sure to show your solution clearly then fill up the following table and at the end use a DAD/DAS framework to graph your solution.
Period
Supply shock
Demand Shock
t-2 t-1 t t+1 t+2 t+3 t+4
0 0 0 0 0 0 0
0 0 0 0 0 0 0
Inflation in Preceding period
Output
Inflation
Page 13 of 15
Solution:
Period
Supply shock
Demand Shock
t-2 t-1 t t+1 t+2 t+3 t+4
0 0 0 0 0 0 0
0 0 0 0 0 0 0
Inflation in Preceding period 2 2 2 1.94 1.88 1.82 1.77
Output
Inflation
300 300 299.545 299.58 299.62 299.65 299.69
2 2 1.909 1.82 1.748 1.678 1.62
1 1 Yt = 300 − (π t − 1) + ε t 2 2 π t = π t −1 + 0.2(Yt − 300) + ν t 1 Yt = 300 − (π t −1 + 0.2(Yt − 300) − 1) 2 1 0 .2 Yt = 330.5 − π t −1 − Y 2 2 2 .2 1 Y = 330.5 − π t −1 2 2 1 Yt = 300.45 − π t −1 2 .2 1 Yt = 300.45 − = 299.545 2 .2 => π t = π t −1 + 0.2(Yt − 300) = 2 + 0.1( 299.545 − 300) = 1.909 1 (1.909) = 299.58 Yt +1 = 300.45 − 2 .2 => π t +1 = 1.909 + 0.2(299.58 − 300) = 1.82 1 (1.82) = 299.62 2 .2 = 1.82 + 0.2(299.62 − 300) = 1.748
Yt + 2 = 300.45 − => π t + 2
Page 14 of 15
π DAS
π =2
π =1 DAD
Y Y = 300
Page 15 of 15
Instructor: A. Mazaheri Test-1 (Saturday February 15, 1-3) Instructions: This is a closed book test.
You have 2 Hours. Good Luck! Last Name: First Name:
ID
FOR MARKERS ONLY: Q1
Q2
Q3
Q4
Total
40
20
20
12
92
Marks Earned Maximum Marks Possible
The University of Toronto's Code of Behaviour on Academic Matters applies to all University of Toronto Scarborough students. The Code prohibits all forms of academic dishonesty including, but not limited to, cheating, plagiarism, and the use of unauthorized aids. Students violating the Code may be subject to penalties up to and including suspension or expulsion from the University.
Answer all following questions: Question-1 [40 Points] Answer the following questions: a) (8 Points) An economy is characterized by the following:
AD SRAS LRAS Supply of capital Supply of labour Okun’s Law Natural rate of unemployment
Y = 400 + (MS/P) Y = Y + 10(P – Pe) Y = K0.5L0.5 K = 500 L = 500 (Y – Y )/ Y = –2.0(u – un) un = 0.06 (6%)
Suppose that the money supply has been constant for many years at MS = 1000. Now suppose there is an unexpected fall in autonomous consumption such that the AD curve becomes Y = 250 + (MS/P) Use the AS-AD model to find the short-run equilibrium values of Y, P, Pe, and u? What are the values of cyclical unemployment? What are the new long-run values of Y, P, Pe, and u? Show your answers in one AS-AD diagram making sure to label all the critical points. Solution: There is no shock as the money supply has been constant for many years therefore expected price will be equal to the actual price and:
Y = 500 0.550.5 = 500 1000 YD = 400 + = 500 P => P = P e = 10, Y = 500 Now there is a shock but the expectation does not adjust therefore in the short run:
Page 2 of 15
P e = 10 1000 = YSRAS = 500 + 10( P − 10) P => P = 5, Y = 450
Y AD = 250 +
Y − Y 450 − 500 = = −2(u − 0.06) Y 500 u = 0.11 In the long Run:
1000 = YLRAS = 500 P => P = 4 = P e u = 0.06
Y AD = 250 +
c)
LRAS
SRAS
10 AD 5 4 AD’ 450
500
Page 3 of 15
b) (8 Points) Consider two economies A and B. A operates according to the sticky-wage model and B operates under the sticky-price model. Aggregate demand unexpectedly falls in both countries, leading to a recession and an unexpected decline in price level and the demand for output. Use a graph of the labor market in each economy to illustrate the impact of the recession on the level of employment and the real wage.
Solution:
Sticky Wage Model: Because the nominal wage W is sticky, a decrease in the price level from P1 to P2 increases the real wage from W/P1 to W/P2. As a result, the quantity of labor demanded falls from L1 to L2 and the fall in labor demand decreases output. Note: that in the sticky wage model the labor market does not clear.
LS (W/P)1 Sticky-Price Model (W/P)2
L1D L2D
Labor
W/P
Sticky Price Model: Because the nominal price is sticky, when a decrease in the price level from P1 to P2 occurs only firms with flexible prices will reduce their demand for labor and therefore the overall demand D
for labor declines to L2 . The real wage declines from W/P1 to W/P2 and the quantity of labor demanded falls from L1 to L2 and the fall in labor demand decreases output. Note: that in the sticky price model the labor does not clear.
Page 4 of 15
c) (4 Points) Use a DAD-DAS curve diagram to illustrate the short-run and long-run effect of an unexpected negative supply shock on output, price level, unemployment rate, and inflation rate. Solution:
π DAS
A
B
DAD
Y Y A negative supply shock that (lasts for one period) will shift DAS leftward from point A towards point B. Inflation rises and output falls as a result inflation expectation starts to fall but not as rapidly. In period (t+1) the supply shock has ended but the inflation expectation does not return to its original level a fast. As a result the DAS moves towards the original equilibrium of A but only slowly. That assumes that the central Bank does not take any action. If in the process the central Bank monetizes the stagflation by increasing the inflation target then the DAD will shift rightward and the economy will move to a permanently higher inflation level.
Page 5 of 15
d) (4 Points) Use the Philips curve diagram with adaptive expectation to illustrate the short-run and long-run effect of an unexpected negative supply shock on output, price level, unemployment rate, and inflation rate. Assume an accommodating monetary policy. Solution:
The negative supply shock shifts up the short-run Phillips curve. The stagflation means that the new short run equilibrium is to the right of full employment. The expansionary monetary policy moves the short run equilibrium towards long run full equilibrium but at a new inflation rate.
Page 6 of 15
e) (10 Points) Suppose Canadian economy follows the Phillips curve
π = π −1 − 0.5(u − u n )
and that the natural rate of unemployment is given by the average of the past two years’ unemployment: u n = 0.5(u−1 + u−2 ) .
Suppose the natural rate of unemployment (un) has been historically at 6%. The Bank of Canada follows a policy to reduce inflation by 2% permanantly. i) (6 Points) Show the impact of this policy on the natural rate of unemployment over time. Solution:
π − π −1 = −0.5(u − u n ) − 0.02 = −0.5(u − u n ) => u − u n = 0.04 => u = 10% u0 = 6%, u1 = 10% 0.10 + 0.06 = 0.08 2 u + u1 0.08 + 0.10 u3 = 2 = = 0.09 2 2 u + u2 0.09 + 0.08 u4 = 3 = = 0.085 2 2 u + u3 0.085 + 0.09 u5 = 4 = = 0.0875 2 2 u2 =
ii) (4 Points) What is the sacrifice ratio for this disinflation? Briefly explain your answer. Solution: Because unemployment is always higher than it started, output is always lower than it would have been. => the sacrifice ratio is infinite. This is called hysteresis: we find that there is a long-run tradeoff between inflation and unemployment: to reduce inflation, unemployment must rise permanently.
Page 7 of 15
f) (6 Points) Start by briefly explaining the role of the monetary policy in the DAD framework. Then explain the difference between the conventional aggregate demand and the dynamic aggregate demand. Make sure to explain why the DAD is downward sloping. Solution: In the DAD framework the monetary policy is endogenized through the monetary rule. For instance, a decrease in the inflation rate forces the Bank of Canada to reduce the overnight rate and as a result the real interest rate will fall and the investment rises leading to a rise in the output. A surprise change in the parameters of the monetary rule such as an increase in the target inflation rate will shift the DAD rightward. The primary difference between the conventional demand and the DAD is the fact that in DAD framework, instead of price, incorporates the inflation. As explained above, in DAD framework, a movement along the curve represents a change in the Bank of Canada overnight rate (Federal Rate) accompanied by a change in the investment. For instance, a move down along the curve represents a decline in the inflation accompanied by a reduction in the overnight rate. The resulting decline in the real interest rate leads to an increase in the investment and hence an increase in the output. As one can see, while in the conventional aggregate demand framework the supply of money is constant, in the DAD framework the supply of money in endogenous to fit the Bank of Canada interest rate rule.
Page 8 of 15
Problem-2: [20 Points] Consider an economy in its long-run equilibrium with an inflation
rate, π, of 6% per year and a natural unemployment rate, un, of 4%. The expectationsaugmented Phillips curve is:
π = πe – 0.5(u – un), Assume that Okun’s law holds so that a 1% increases in the unemployment rate maintained for one year reduces output by 2% of full-employment output. Now consider a four-year disinflation according to the following table:
Year π
T+1 4%
T+2 2%
T+3 2%
T+4 2%
In this economy, agents use adaptive expectations to generate expected inflation rate. To be precise, agents use the average of the inflation rate from the previous two years to form the expected inflation. a) [10 Points] What is the unemployment rate in each of the four years? Illustrate your solution using a Phillips curve graph. b) [5 Points] By what percentage does output fall short of full-employment each year? What is the sacrifice ratio of this disinflation process? c) [5 Points] Use your graph of part (a) and clearly explain what would have happened if the expectation was rational rather than adaptive. What would have been the sacrifice ratio of this disinflation process?
Solution: Year πe u
T+1 6% 4% = 6%– 0.5(u – un) (u – un) = 4% => u = 8%
T+2 5% 2% = 5%– 0.5(u – un) (u – un) = 6% => u = 10%
T+3 3% 2% = 3%– 0.5(u – un) (u – un) = 2% => u = 6%
T+4 2% 2% = 2%– 0.5(u – un) (u – un) = 0% => u = 4%
6%
2%
un Page 9 of 15
b) Using Okun ratio of 2
2*Cyclical unemployment 2*4% = 8%, 2*6% = 12%, 2*2% = 4%, 2*0%=0 Sacrifice Ratio = (8%+12%+4%)/4=6 c) Under rational expectation the inflation would have adjusted instantly and therefore the sacrifice ration would have been zero.
6%
2%
un
Page 10 of 15
Problem-3 [18 Points] Suppose the loss function of the central bank is given by: L(u, π) = u2 + γ(π)2 The Phillips curve of this economy is: u = un − α(π − πe) a) (5 Points) What is the actual inflation and the expected inflation if the Bank adopts a credible rule? b) (8 Points) What is the actual inflation under policy discretion? What is the expected inflation and why? Briefly explain your results. c) (5 Points) Holding all else constant, what happens to actual inflation when γ increases and why? What does this suggest as to who should be appointed as the central banker? Solution: a) If rule is chosen
π =πe => u = u n The optimal rule would be: π = 0 b) The first step is to solve for the Bank choice of inflation, for any given inflationary expectations. Substituting the Phillips curve into the loss function to get:
L(u, π ) = (u n − α (π − π e ) ) + γ (π ) 2 2
Differentiate with respect to inflation π, and set this first-order condition equal to zero:
dL(u , π ) = −2α u n − α (π − π e ) + 2γπ = 0 dπ α 2 π e + αu n π= α2 +γ
(
)
Of course, rational agents understand that the Bank will choose this level of inflation.
π e = π , therefore the above equation simplifies to: αu n π= γ
=>
Page 11 of 15
Since the inflation is expected the unemployment will stay at the natural rate. The outcome of the discretionary policy is higher inflation and no change in the output. The phenomenon is called Time-inconsistency. If the policy makers use their discretion, rational consumers will expect the higher inflation and the policy maker will have no choice but to accommodate. This results into higher inflation which is costy to the policy maker. the natural rate of unemployment rises, the inflation rate also rises. c) Higher γ means more dislike for inflation relative to unemployment and therefore lower inflation and therefore lower loss. This suggests appointing a conservative central banker (higher γ).
Page 12 of 15
Problem – 4 (12 Points): Suppose the DAD and DAS equations are as follows and that the economy has been in equilibrium:
Yt = Yt − A(π t − π t* ) + Bε t
π t = π t −1 + φ (Yt − Yt ) + ν t where:
A=
αθπ 1 > 0, B = >0 1 + αθY 1 + αθY
Furthermore, suppose:
Y = 300, π t* = 2, α = 2.0, ρ = 1.0, φ = 0.2, π θ = 0.5, π Y = 0.5 In period t, the Bank of Canada decreases the inflation target from 2 to 1 permanently. What would be the impact on the output and inflation. To answer this question make sure to show your solution clearly then fill up the following table and at the end use a DAD/DAS framework to graph your solution.
Period
Supply shock
Demand Shock
t-2 t-1 t t+1 t+2 t+3 t+4
0 0 0 0 0 0 0
0 0 0 0 0 0 0
Inflation in Preceding period
Output
Inflation
Page 13 of 15
Solution:
Period
Supply shock
Demand Shock
t-2 t-1 t t+1 t+2 t+3 t+4
0 0 0 0 0 0 0
0 0 0 0 0 0 0
Inflation in Preceding period 2 2 2 1.94 1.88 1.82 1.77
Output
Inflation
300 300 299.545 299.58 299.62 299.65 299.69
2 2 1.909 1.82 1.748 1.678 1.62
1 1 Yt = 300 − (π t − 1) + ε t 2 2 π t = π t −1 + 0.2(Yt − 300) + ν t 1 Yt = 300 − (π t −1 + 0.2(Yt − 300) − 1) 2 1 0 .2 Yt = 330.5 − π t −1 − Y 2 2 2 .2 1 Y = 330.5 − π t −1 2 2 1 Yt = 300.45 − π t −1 2 .2 1 Yt = 300.45 − = 299.545 2 .2 => π t = π t −1 + 0.2(Yt − 300) = 2 + 0.1( 299.545 − 300) = 1.909 1 (1.909) = 299.58 Yt +1 = 300.45 − 2 .2 => π t +1 = 1.909 + 0.2(299.58 − 300) = 1.82 1 (1.82) = 299.62 2 .2 = 1.82 + 0.2(299.62 − 300) = 1.748
Yt + 2 = 300.45 − => π t + 2
Page 14 of 15
π DAS
π =2
π =1 DAD
Y Y = 300
Page 15 of 15
