Question 1: Aggregate Demand and Aggregate Supply (This question is worth 20 points if correctly answered.) Assume the U.S. economy is in long-run equilibrium. Analyze each of the following events independently and include answers to the following in your analysis: (1) Explain whether AD or SAS changes and why the change occurred. (2) Explain what happens to the equilibrium price level and equilibrium output in the U.S. in the short run. (3) Describe the type of gap facing the economy. (4) Draw a graph to illustrate your answer. a. The bubble in the housing market bursts, and prices of houses quickly begin to fall. b. With plenty of slack in the labor market, firms lower wages. c. Anticipating the possibility of war, the government increases its purchases of military equipment. d. Productivity in the U.S. continues to increase. Question 2: More Aggregate Demand/Aggregate Supply (This question is worth 10 points if correctly answered.) a. Suppose the United States’ economy is in short run equilibrium producing RGDP equal to $150 billion. Potential GDP equals $250 billion. The marginal propensity to consume in the U.S. is 0.5. Draw a graph illustrating the U.S. economy. Is the economy characterized by a recessionary gap or an inflationary gap? What problems does the gap present for United States? b. You are an economic advisor to the President. He asks you to design a fiscal policy to close the gap. What fiscal policy do you propose? Why did you choose this particular policy? Explain how your policy works. Draw a graph illustrating your answer. c. Describe any costs the United States may bear in the long run due to the implementation of the policy you designed in part (b). d. If your policy is not acceptable to Congress, describe the self-correction mechanism by which the economy could return to long-run equilibrium. Draw a graph illustrating the self-correction process. Describe any costs the United States may pay with self-correction. Question 3: The Federal Reserve System (the Fed). (This question is worth 10 points if correctly answered.) a. Describe the structure of the Federal Reserve System. b. The government of Turtleville uses measures of monetary aggregates similar to the United States, and the central bank of Turtleville imposes a required reserve ratio of 10%. Given the following information, answer the questions below. Bank deposits at the central bank = $200 million Currency held by the public = $150 million Checkable bank deposits = $500 million Currency in bank vaults = $100 million Traveler’s checks = $10 million 1. M1 = _____________ 2. The Monetary Base = _____________ 3. Excess Reserves = _______________ 4. The amount by which commercial banks in Turtleville can increase checkable deposits: _____________ 1 Solving Differential Equations: 1. Solve the following diffe ...

1. Question 1: Aggregate Demand and Aggregate Supply (This
question is worth 20 points if correctly answered.)
Assume the U.S. economy is in long-run equilibrium. Analyze
each of the following events independently and include answers
to the following in your analysis: (1) Explain whether AD or
SAS changes and why the change occurred. (2) Explain what
happens to the equilibrium price level and equilibrium output in
the U.S. in the short run. (3) Describe the type of gap facing the
economy. (4) Draw a graph to illustrate your answer.
a. The bubble in the housing market bursts, and prices of houses
quickly begin to fall.

2. b. With plenty of slack in the labor market, firms lower wages.
c. Anticipating the possibility of war, the government increases
its purchases of military equipment.
d. Productivity in the U.S. continues to increase.
Question 2: More Aggregate Demand/Aggregate Supply (This
question is worth 10 points if correctly answered.)

3. a. Suppose the United States’ economy is in short run
equilibrium producing RGDP equal to $150 billion. Potential
GDP equals $250 billion. The marginal propensity to consume
in the U.S. is 0.5. Draw a graph illustrating the U.S. economy.
Is the economy characterized by a recessionary gap or an
inflationary gap? What problems does the gap present for
United States?
b. You are an economic advisor to the President. He asks you to
design a fiscal policy to close the gap. What fiscal policy do
you propose? Why did you choose this particular policy?
Explain how your policy works. Draw a graph illustrating your
answer.

4. c. Describe any costs the United States may bear in the long run
due to the implementation of the policy you designed in part
(b).
d. If your policy is not acceptable to Congress, describe the
self-correction mechanism by which the economy could return
to long-run equilibrium. Draw a graph illustrating the self-
correction process. Describe any costs the United States may
pay with self-correction.

5. Question 3: The Federal Reserve System (the Fed). (This
question is worth 10 points if correctly answered.)
a. Describe the structure of the Federal Reserve System.
b. The government of Turtleville uses measures of monetary
aggregates similar to the United States, and the central bank of
Turtleville imposes a required reserve ratio of 10%. Given the
following information, answer the questions below.

6. Bank deposits at the central bank = $200 million
Currency held by the public = $150 million
Checkable bank deposits = $500 million
Currency in bank vaults = $100 million
Traveler’s checks = $10 million
1. M1 = _____________
2. The Monetary Base = _____________
3. Excess Reserves = _______________
4. The amount by which commercial banks in Turtleville can
increase checkable deposits: _____________
1
Solving Differential Equations:
1. Solve the following differential equations using the Laplace
Transform method:
a) & ; ( ) sin( ), ( )y y x x t t y+ = = =4 3 2 0 1
b) && & & ; ( ) ( ), ( ) , & ( )y y y x x x t u t y y+ + = − = = =4
20 2 0 0 0 1
c) && & ; ( ) ( ), ( ) , & ( )y y y x x t u t y y+ + = = = = −7 12

7. 6 0 0 0 2
d) && & ( ), ( ) , & ( )y y y x t y y+ + = = = −9 20 0 1 0 2 , x(t)
= 2u(t)
Laplace Transforms
1. Compute the Laplace Transforms of the following functions:
a) x t t u t( ) sin( ) ( )= 4 100
b) x t t u t( ) sin( ) ( . )= − −4 100 10 0 1
c) x t u t t t u t( ) ( ) ( ) cos( ) ( )= + − −2 4 5δ
d) x t tu t t u t t u t( ) ( ) ( ) ( ) ( ) ( )= − − − + − −2 2 2 3 3
e) x t u t e tt( ) ( ) cos( )= − −2 10 u(t)
2. Compute the inverse Laplace Transforms of the following
functions:
a) X s
s
s s
( )
( )
=
+
+ +
10 1

8. 4 32
b) X s
s
s s
( )
( )
=
+
+ +
10 1
4 82
c) X s
s
s s s
( )
( )( )( )
=
+
+ + +
2 100
1 8 10
d) X s
s

9. s s
e s( )
( )
=
+
+ +
−10 1
4 32
2
e) X s
s s s
( )
( )
=
+ +
20
10 162
f) X s
s
s s s
( )
( )

10. ( )
=
+
+ +
10 1
4 82
3. Find the limit as t→∞ of x(t) (if the limit exists)
a) X s
s
s s s
( )
( )
( )
=
+
+ +
10 1
4 32
b) X s
s
s s s

11. ( )
( )
( )
=
+
+ +
10 1
4 82
c) X s
s
s s s
( )
( )
( )
=
+
+ −
10 1
2 32
4. Give the general form of x(t) (do not solve for the
coefficients explicitly).

12. a) X s
s
s s s
( )
( )( )( )
=
+
+ + +
2 100
2 6 10
b) X s
s
s s s s
( )
( )( )( )
=
+
+ + −
2 100
1 8 4
c) X s
s

13. s s s
( )
( )( )( )
=
−
+ + +
40
1 8 10
d) X s
s
s s s
( )
( )
( )
=
+
+ +
10 1
4 32
e) X s
s
s s s

14. ( )
( )
( )
=
+
+ +
10 1
4 82
f) X s
s
s s s
( )
( )( )
=
+
+ +
1
4 82
g) X s
s
s s s

15. ( )
( )
( )(( ) )( )
=
+
+ + + +
20 1
16 4 25 12 2
Transfer Functions:
1. Find the transfer functions of the following systems:
a) &y y x+ =4 3
b) && & &y y y x x+ + = −4 20 2
c) &&& && & && &y y y y x x x− + + = − +3 4 8 4 2
2. Find the transfer function of
+
-
R1 R2
C1 C2
x(t) y(t)

16. +
-
Give the result for C1=C2=100µf, R1 =R2 =2000Ω
3. Find the transfer function of the following circuit where
R1=R2=1000Ω and C=100µf.
a)
4. For the system given below,
&& &y y y x+ + =8 116 116
a) Find the transfer function.
b) Give the poles and zeros.
c) Give the general form of the response y(t) to a step input (do
not solve explicitly).
d) Use MATLAB to plot the step response (put your name in the
title of the plot).
5. Repeat Problem 4 for the system given below. In addition,
compare the types of poles of this system
to those in Problem 4 and use this to explain the resulting
behavior seen in the step response plots.
&& &y y y x+ + =8 12 12
R2
+ +
y(t)
R1 C
-

17. x(t)
-
6. Simplify the block diagram to find the transfer function
X(s) Y(s)
H1(s)
H2(s)
H4(s)
H3(s)
+
+
+ -
Give the transfer function H(s)=Y(s)/X(s) for H1(s)=2,
H2(s)=10/s, H s
s3
01
20
( )
.
=
+
, H s

18. s4
2
4
( ) =
+
7. Reduce the block diagram to one block.
8. Find the transfer function of the following circuit in terms of
R1, R2, C, and L. Now, suppose that
R1=R2=2000Ω, C = 100µf, L = 10mH. Determine the poles of
the circuit.
H3(s)
H4(s)
H1(s)
H2(s)
X(s) Y(s)
-
+
+
+
+
y(t)
-

19. R1
C
+
x(t)
-
R2
L
· Read Chapter 3 in the textbook Signals and Systems Using
MATLAB.
· Read the Lecture “W4 Lecture 2 – Laplace Transform”.
· Download and review the supplemental questions.
· Work the following six problems below for submission.
· Submit homework solutions via Assignment Upload Tool.
Show all work for full credit.
1. The Laplace transform of e-10t u(t) is?
2. The Laplace transform of (t2cos ωt ) u(t) is?
3. By using the Laplace transform, compute the convolution x(t)
* v(t) of the two signals?
where x(t)= e-3t u(t) and v(t) = (5sin t )u(t)
4. Compute the inverse Laplace transform of X(s) =
3s2+2s+1s3+5s2+8s+4 ?
5. Use Laplace transforms to compute the solution to the
differential equation given below?

20. Where y(t)=0 ;y(t)=1
6. Determine the final value of X(s)= 3s2+4s+1s4+3s3+3s2+2s
?