## Transcribed Text

Problem set 1. Part A.
1- Consider the following economy:
Year
Price 1
Quantity 1
Price 2
Quantity 2
Price 3
Quantity 3
2012
3.25
115
5.75
141
9.75
85
2013
3.5
120
6.25
143
11
85
2014
4
122
6.25
145
12
90
2015
4.275
125
6.75
148
12.5
95
2016
4.5
130
7
149
13.25
100
a) b) c)
Year 2012 2013 2014 2015 2016
2- For a)
b)
Y = $4800 + I + $2150 + -$775
c) Calculate the amount of investment I
CalculatetheNominalGDPforeachyear
Calculate the real GDP for each year using 2012 as the base year CalculatetheGDPdeflatorforeachyear.
Nominal GDP 2013.25
2248.75 2474.25 2720.875 2953
Real GDP 2013.25 2041 2107.75 1486.25 2254.25
GDP Deflator 100
110.2
117.4
183.07 131.0
the table below: GDP deflator = 108.9 Calculate the amount of Real Exports X.
Calculate the Real GDP (Y = C + I + G + NX). I= Y- C - G
I= Y- C - G
d) Fill out the rest of the table for nominal values.
Items
Personal Consumption expenditures
Gross Private Domestic I Investments
Gov. Purchases of goods and services
Exports X
Real $4800
$2,150
2,250 -$775
Nominal Values
Imports
Net Exports
GDP
GDP deflator = 108.9
C
G
M NX
10,617.75
Note that NX = net exports= exports - imports
3- Annual growth rates
GDP (2010)= 35,000 ; GDP ( 2011) = 34,900 ; GDP (2012) = 35,750 GDP (2013) = 37,000 ; GDP (2014)= 38,000 ; GDP (2015)= 38,000;
a) Calculatetheannualgrowthratebetween2010-2011.
b) Calculate the annual growth rate between 2010-2012
c) Calculatetheannualgrowthratebetween2013-2015.
d) Calculate the annual growth rate between 2014 and 2015.
4- Please calculate the missing terms: Use the formula for the annual growth rate and apply the properties of the LN (Natural Log) function (or simply use the formula that is already given in the formula sheet).
1. g =1.55
2. g =3.25
3. g =1.15
XZ= 1500 v = 5 calculate Xt =? Xt = 500 XZ = 600 calculate v = ?
Xt = 900 v = 4 calculate XZ = ?
Problem Set 1 Part B
1. Considerthefollowingeconomy
Ca = 1800 – 15 R; c= 0.65 ; Ta = 1,750 ; t = 0
G = 2,100 ; X = 1,800 ; NX = -1,275 . Assume nx = 0.
a) Compute the marginal propensity to save
b) Calculate the amount of imports for this country
c) Compute the multiplier
d) Derive the equation of the autonomous spending and compute its
value for R = 3.25
e) Derive the IS curve and compute its value for R= 3.25.
2. Considerthefollowingeconomy
C = Ca + 0.80 (Y – T); Ca = 500 – 25 R ; T = 300 + 0.245 Y; IP = 1800 – 35 R ; G=1800; NX=750–0.08Y.
a) What are the values of the autonomous net export NXa and the autonomous taxes Ta (hint: see the formulas and compare)
b) Compute the multiplier
c) Derive the equation of the autonomous spending.
d) Derive the equation of the IS curve
e) Compute the values of the AP and YIS for r =17/4
f) Compute the values of the Ca, C, T, IP, and NX for income
Y = 20,000 and R = 4.25 . Is this country a net importer or net
exporter?
3. Consider the following economy
Ca = 1,780; c = 0.55; T = 1400 + 0.175 Y; IP = 1800; G = 1600; NX = 750 – 0.0075 Y.
; IP = 20 (150 – R ) ;
a) What is the value of the autonomous Tax Ta (Hint: see the formula and compare)
b) Compute the value of the multiplier
c) Derive the equation of the autonomous spending and calculate its value.
d) Derive the equation of the IS curve and calculate its value.
e) Compute the value of the new IS when government spending increases by
155. What is the difference between the two IS values?
4. Consider the following economy: Ca = 10 (32.5 – 1.5R); c = 17/20 ;
T = 240 + (3/20) Y; IP = 10 (12.75 – 2.5 R) ; G = 2,500; NX = 800 – 0.08 Y.
a) What are the values of the autonomous net exports and autonomous
Tax Ta (Hint: see the formula and compare)
b) Compute the value of the multiplier
c) Derive the equation of the autonomous spending
d) Find the equation of the IS curve
e) Graph the autonomous Spending using the points for R = 2, 4, 6, 8,
10, 12, 14, 16, 18, 20, 25, 30 (Excel will be best).
f) From e, graph the IS curve.
Problem Set2
The most important thing is that you show the equilibrium point both on the P axis and the Y axis and how graphs shift in case of policy implementation.
1- Consider the following economy with:
RealMoneydemand (𝑀)𝑑 =–15R+0.35Y
𝑃
Real Money supply (𝑀𝑠)= 5800 𝑃
a) Derive the LM curve
b) Find the value of money demanded when income Y = 25,000 and interest rate R = 2.55. Is this equilibrium? Why? Why not?
c) Derive the LM curve when the money supply increases by 3000.
d) Derive the LM curve when money supply decreases by 25%
e) Compare the LM curves from a, b and c by graphing them using any
graphing tool (excel preferably). Comment on the differences.
2- Consider the following economy with :
IScurveYIS =k(AP –250R); LMcurve YLM =4(𝑀𝑠)+500R; c=0.85;t=10%;nx=0.08; 𝑃
AP=4500; MS=3500 .
a) Calculate the multiplier k
b) Derive the IS and the LM curves for P = 0.8.
c) Find the interest rate and the output at equilibrium (In this exercise, a negative interest
rate can be found. Example R = - 3% means no lending at the corresponding price level).
d) Find the equilibrium interest rates and outputs for the following price levels: Find the
equilibrium interest rates and outputs for the following price levels
P1 =1.0;P2 =1.2;P3 =1.5;P4 =2;P5 =3(hint:repeatstepsbandcforeachpricelevel; however, you will notice that the price change only affects the LM curve and not the IS curve).
e) Plot the aggregate demand (AD curve) based on your findings in c. 3- Consider the following economy
C=Ca +0.85(Y–T) Ca =500–12R T=825+0.125Y (𝑴𝑷)𝒅=0.20Y–25R
(𝑀𝑠) =3000. ThismeansthatMs =3000. Ip =2750–25R G=3200 NX=765–0.08Y
𝑃𝑃
a) Clearly define and compute the multiplier for this economy.
b) Clearly define and derive the equation of the autonomous spending Ap and the IS curves.
c) Clearly define and derive the equation of the LM curve as function of R and P. [Hint: equalize the
demand and supply for money (𝑀𝑠) = (𝑴)𝒅] 𝑃𝑷
d) Find the equilibrium interest rate equation for YIS = YLM. This should be a function of P.
Questions Below are Optional ( But Recommended)
e) Derive the equation of the aggregate demand curve AD. [Hint: Replace the equilibrium interest rate in either the IS or LM function. This should give you the AD curve in the form:
YAD= Constant + 𝑪𝒐𝒏𝒔𝒕𝒂𝒏𝒕 . 𝑷
f) Now consider the following aggregate supply curve YAS = 15,000 - 25 W + 250 P. For W = 50, derive the aggregate supply YAs.
g) Find the equilibrium levels of price and output for which YAD=YAS.
h) Graph the estimate of the AD and the AS curves clearly showing the equilibrium point indicating
the price on the vertical axis and the output on the horizontal axis.
i) Based on the last graph, please give an example and the impact of the following policy decisions
or events on a separate graph. Use arrows to clearly show how the respective curve (s) shifts in each case. Indicate and describe the resulting equilibrium point:
A. Expansionary fiscal policy.
B. Contractionary monetary policy.
C. Increase in real wage rate in the labor market.
D. Simultaneous decrease in the real wage rate and increase in the real money supply.

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1. a) Compute the marginal propensity to save

s+c=1

s+0.65=1

s=1-0.65

s=0.35

b) Calculate the amount of imports for this country

NX=X-M

-1275=1800-M

M=3075

c) Compute the multiplier

k=1/((1-c)(1-t)+t+nx)=1/((1-0.65)(1-0)+0+0)=2.86

d) Derive the equation of the autonomous spending and compute its value for R = 3.25

Ap=Ca-C*Ta+I+G+NXa=1800-15r-0.65*1750+20(150-R)+2100-1275=4487.5-35R

Ap(R=3.25)=4487.5-35*3.25=4601.25

e) Derive the IS curve and compute its value for R= 3.25.

YIS=k* Ap=2.86*(4487.5-35R)=12834.25-100.1R

YIS(R=3.25)=12834.25-100.1*3.25=12508.925

2. a) What are the values of the autonomous net export NXa and the autonomous taxes Ta (hint: see the formulas and compare)

NXa=750

Ta=300

b) Compute the multiplier

s=1-c=1-0.80=0.2

k=1/(0.2*(1-0.245)+0.245+0.08)=2.10

c) Derive the equation of the autonomous spending.

Ap=500-25R-0.8*300+1800-35R+1800+750=4610-60R

d) Derive the equation of the IS curve

YIS=k*Ap=2.10*(4610-60R)=9681-126R

e) Compute the values of the AP and YIS for r =17/4

r=17/4=4.25

Ap=4610-60*4.25=4355

YIS=9681-126*4.25=9145.5...