 # Problem set 1. Part A. 1- Consider the following economy: Year ...

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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...

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