Answers to Exam in Macroeconomics, IB and IBP

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1 Coenhagen Business School, Deartment of Economics, Birthe Larsen Question A Answers to Exam in Macroeconomics, IB and IBP 4 hours closed book exam 26th of March 2009 All questions, A,B,C and D are weighted equally Regard the following model for a closed economy: 1. E = C + I + G; 2. C = :5(Y T ); 3. I = b 0 100r 4. Y = E: 5. M d =P = Y 100r 6. M d =P = M=P Where C is consumtion, Y is outut and income, I is investment, G is government sending, T is the tax, E is lanned exenditure; M is money suly and M d is money demand. The variables Y;E;C;I;M d and r are endogenous, T;P;M and G are exogenous. Let G = 200;T = 200;M = 150;P =1and b 0 = 100: 1) Derive and draw the IS curve. We insert equation 1,2 and 3 into equation 4 to obtain: Y = :5(Y 200) r + 200, 0:5Y = r, r = 3 0:005Y: See Figure 1. 2) Derive and draw the LM curve. Insert equation 6 into equation 5 to obtain: 150 = Y 100r, r = 0:01Y 1:5 The LM curve is drawn into Figure 1. 3) Find the equilibrium level of outut and indicate the equilibrium in the IS-LM diagram. 1

2 Insert the LM curve into the IS curve to obtain: 0:5Y = (0:01Y 1:5), Y = = 300 1:5 Then insert the equilibrium outut level into the IS curve (or the LM curve) to obtain: r =3 0: = 1:5 The equilibrium, (Y;r) = (300; 1:5) is indicated in Figure 1. 4) Suose now that the economy faces a recession corresonding to reduction of b 0 to 70. Which curve is shifting? Derive and draw the new curve and Önd the new equilibrium. The IS curve shifts downwards: Y = :5(Y 200) r + 200, 0:5Y = r, r = 2:7 0:005Y: The new equilibrum is then 0:5Y = (0:01Y 1:5), Y new = = 280 1:5 r new = 2:7 0: = 1:3 The new IS curve and the new equilibrium, (Y;r) = (280; 1:3) is indicated in Figure 2. 5) Exlain verbally how the reduction in autonomous investment sending a ects outut: A reduction in b 0 reduces investments for given interest rate (eq. 3) and thereby lanned exenditure (eq. 1) which reduces outut (eq. 3). When outut falls, disosable income falls and thereby consumtion (eq. 2). The decrease is larger the larger the marginal roensity to consume is. In this case it is c 1 =0:5. Reduced consumtion reduces lanned exenditure and thereby outut again, which again reduces disosable income and consumtion. However, lower outut also reduces money demand (eq. 5) and for given money suly, the result is a lower interest rate. The reduced interest rate imlies that investment increases (eq. 3) which again increases lanned exenditure (eq. 1) and outut, modifying the equilibrium reduction of outut. Question B Consider an economy with the roduction function given by Y = F (K; L) = K LE, where K denotes caital, L denotes labour and E denotes labour e ciency. 2

3 1. Derive the er e ective worker roduction function y = f (k). We divide the roduction function by LE in order to obtain: y = Y L = K LE LE = r K LE = k; where k = K=LE denotes caital e ective worker unit. 2. Suose the saving rate is s =0:2, dereciation is =0:08; oulation growth is n =0:01 and growth in E is g =0:01. Derive the steady state level of caital er e ective worker and the steady level of outut er e ective worker acknowledging that the caital accumulation equation is k = sf (k) ( + n + g) k. In a steady state the change in caital er worker is zero, hence k =0. Hence, using the er worker roduction function derived in the revious question gives the steady state caital er worker value: k = s k ( + n + g) k =0, 0:2 k = (0:08 + 0:01 + 0:01) k, k = 0:2 0:1, k = 2, k = 2 2 =4: using the er e ective worker roduction function again to derive the steady state outut er worker level, to obtain: y = k =2: 3. Show the steady state level of caital er worker and outut er worker in a diagram. In order to show the equilibrium, (k ;y )=(4; 2) in a diagram we draw the saving schedule, the break even investment curve and the roduction er e ective worker function. See Figure Suose the saving rate falls to s =0:1. The saving curve thereby shifts downwards. The new curve should be drawn into the diagram and the new equilibrium oints should be marked. They can also be derived: k = s k 0 ( + n + g) k 0 =0, 0:1 k 0 = (0:08 + 0:01 + 0:01) k 0, k 0 = 0:1 0:1, k 0 = 1, k 0 = 1 2 =1: 3

4 using the er worker roduction function again to derive the steady state outut er worker level, to obtain: y 0 = k 0 =1: The new steady state, (k 0 ;y 0 ) = (1; 1) ; is indicated in the diagram in Figure What is the imact of the fall in the saving rate on steady state outut er worker and steady state growth in outut er worker? Steady state outut er worker falls as less money devoted to savings result in lower investment and thereby more caital accumulation. Hence the steady state level of caital er worker falls and as y = k outut er worker also falls. Steady state growth in outut er worker is unchanged equal to g =0:01. Relevant equations could be added. Question C 1. Draw the IS* and LM* curves for an oen economy with erfect caital mobility in an outut-exchange rate diagram and exlain the sloes. The IS curve has a negative sloe for the following reason. A higher exchange rate reduces netexort and thereby outut. The LM curve is vertical as there is only one outut level corresonding to a given exchange rate as erfect caital mobility imlies that the real interest rate is equal to the world real interest rate. See Ögure Exlain the imact of exansive Öscal olicy on outut, the exchange rate and netexort in the short run in an oen economy with áoating exchange rate and erfect caital mobility. When G increases, lanned exenditure increases and thereby outut. This uts and uward ressure on the real interest rate which therefore leads to caital ináow. While reducing the real interest rate again, caital ináow also corresonds to a higher demand for domestic currency, which areciates the currency and therefore reduces exort and increases imort. Consequently, netexort falls. The total imact on outut is therefore equal to zero. 3. Exlain how the result in C.2 changes when the exchange rate is Öxed. When the exchange rate is Öxed, the Central Bank has to increase the money suly to counteract the uward ressure on the domestic currency. The corresonding monetary exansionary imact aggravates the ositive imact of the exansive Öscal olicy on outut. Netexort is unchanged as the exchange rate is unchanged. 4. Give some arguments for and against Öxed and áoating exchange rates. Argument for áoating rates: 4

5 allows monetary olicy to be used to ursue other goals (stable growth, low ináation). Arguments for Öxed rates: avoids uncertainty and volatility, making international transactions easier. discilines monetary olicy to revent excessive money growth & hyerináation. 5. Exlain what characterizes an otimum currency area.a single currency imlies that countries can lower transactions costs. An otimum currency area fulölls: The countries in the area face the same shocks or high factor mobility, thereby the countries can adabt to the shocks. Question D Consider a closed economy and the following long run model 1. Y = C + I + G; 2. C = :5(Y T ) ; 3. I = r; where Y = 400;G= 100 and T = Find the total amount of rivate saving, ublic saving and national saving. Private saving is equal to disosable income deduced consumtion, hence, rivate saving is S = Y T C = :5 ( ) = 50: Public saving is tax revenue minus government sending: S g = T G = = 0: and national saving is then the sum of the rivate saving and ublic saving: S = S + S g =0: 2. The equilibrium interest rate is found by equalizing saving and investment. Hence we obtain by using the derived result and equation 3: S = I () 50 = r eq () 100r eq = 50 () r eq = 0:5: The diagram with the saving and investment schedule and the equilibrium interest rate is given in Figure 6. 5

6 3. Suose autonomous investment falls to b 0 = 70. Derive and show in a diagram what haens to investment, saving, outut and the interest rate? Saving is unchanged as outut is unchanged. We now insert the new value for investment in the equilibrium equations and get the new interest rate: S = I () 50 = r eq () 100r eq = 20 () r eq = 0:2: See Figure 7: The investment curve shifts downwards to I = r () 100r =0:7 0:01I The new equilibrium is indicated in Figure Exlain your result and comare the result you obtained in this question when autonomous investment falls, to the answer you obtained in question A.When b 0, investment demand falls for given interest rate. There is no imact on outut as we are considering the long run and therefore saving is unchanged. The suly of loanable funds is therefore unchanged and the demand for loanable funds has fallen which reduces the interest rate. The interest rate falls as in a closed economy we have that investment is always equal to saving. Therefore the lower demand for loanable funds relatively to the suly will reduce the íriceí of loanable funds, the interest rate. In question A we considered the short run with Öxed rices where demand drives the actual outut sold in the economy. 5. Exlain the adjustment rocess when b 0 falls from 100 to 70 in terms of outut, rices and interest rate. When b 0 falls from 100 to 70, then investments are reduced for given interest rate, which reduces lanned exenditure and outut. This corresonds to a leftward shift of the AD curve. Assume that before the shock, we are at the natural level of outut. As aggregate demand is now lower than aggregate suly, the rice will fall. The reduced rice will increase real money suly and thereby reduce the real interest rate. A lower real interest rate boosts investments and thereby lanned exenditure and outut. This rocess continues until aggregate suly is equal to aggregate demand. This exlanation could be sulemented by relevant grahs. Discuss the relevance of conducting exansive Öscal olicy in the model when b 0 falls. If the government conducts exansive Öscal olicy instead of waiting for lower rices, then it is ossible to shift the AD curve towards the right and thereby get back at the natural level of outut faster and 6

7 without waiting for rices to fall. Getting back at the natural level of outut faster imlies we may avoid long eriods of high unemloyment. Could be illustrated in a diagram. 7

8 Figur 1 Figur 2

9 Figur 3 Figur 4

10 Figur 5 Figur 6

11 Figur 7