Solutions To Problem Set Five

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Marcia Maxwell
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1 Lecture 6 <5> Simultaneous equilibrium in both goods and financial markets in the IS LM model () Idea: Any point on the IS curve represents the equilibrium level of output at an interest rate in the goods market. Any point on the LM curve represents the equilibrium interest rate for a level of output in the financial markets There is only one combination of output and the interest rate that simultaneously maintain equilibrium in both the goods and financial markets. (2) Algebra: IS : Y = C (Y,T)+I (Y,i)+G M LM : P = Y L (i) Solving the above set of two equations with two unknowns yields a solution (Y,i) as the overall equilibrium, with (T,G, M ) being the shifting parameters. P In fact, (c o,c ) are also shifting parameters, but omitted from consideration since we are only interested in fiscal and monetary policies. (3) Graph: Figure 6-7: The overall equilibrium is the point (Y,i)atwhichthe IS and LM curves intersect each other. Any factor(s) that causes (cause) a shift in the IS or the LM or both curves will change the overall equilibrium. <6> The impact of changes in fiscal policy on the overall equilibrium via shifts in IS () Two policies: Fiscal expansion: government spending G rises or/& taxes T are cut Fiscal contraction: government spending G is cut or/& taxes T rise (2) An example: contraction Figure 6-8 (c): add arrows Graph: T T 0 IS shifts left (by 4Y = c λ4t ) yielding a new overall equilibrium Y Y 0 and i Economics: T T 0 Z D firms cut production Y Y C to restore equil. in the goods mkt (moving left gradually onto IS 0 ) M d {=$Y L (i)} i to restore equil. in the financial mkt s (moving along IS 0 gradually onto LM). Question: Y falls to Y 0 but not to Y C,why?NotethatY 0 >Y C.Answer:Asi, some of the initial big drop in Y to Y C is offset by the positive effect of the lower i on I and hence on Y.{i I Z D Y } (3) Results: A fiscal expansion will cause: in Y, in i, in (C and S) via in Y D ; have ambiguous effect on I since i causes I while Y causes I.

2 A fiscal contraction will cause: in Y, in i, in (C and S) via in Y D ; have ambiguous effect on I since i causes I while Y causes I. where, Y T = Y D and Y T = Y D when G. <7> The impact of changes in monetary policy on the overall equilibrium via shifts in LM () Two policies: Monetary expansion: the money supply M is increased by the central bank through buying bonds Monetary contraction: the money supply M is decreased by the central bank through selling bonds (2) An example: expansion Figure 6-9: add arrows Graph: M M 0 LM shifts down yielding a new overall equilibrium Y and i i 0 Economics: M M 0 creating an excess money supply i i 00 to induce M d for restoring equil. in the financial mkt (jumping down to LM 0 ) while causing I Z D Y to restore equil. in the good mkt (moving along LM 0 gradually onto IS). Question: i falls to i 0 but not to i 00,why? Notethati 0 >i 00. Answer: As Y, some of the initial big drop in i to i 00 is offset by the positive effect of the higher Y on i. { M 0 = Y L (i): Y L (for the permanent change of M to M 0 ) i } P (3) Results: Amonetaryexpansion will cause: in Y, in i, in (C and S) via in Y D,and in I via ( in Y and in i). Amonetarycontraction will cause: in Y, in i, in (C and S) via in Y D,and in I via ( in Y and in i). where, changes in the private banks reserve ratio θ, in the individuals currencydeposit ratio c, or/& in the central bank s monetary base H will cause changes in the money supply M, thus leading to shifts in LM. <8> The fiscal (F-) and monetary (M-) policy mix A combination of changes in M- and F- policies is called the M-F policy mix, which causes both the IS and LM curves to shift. () There are 4 possible cases of the policy mix: case : Expansionary M- policy and expansionary F- policy LM shifts down and IS shifts right case 2: Expansionary M- policy and contractionary F- policy LM shifts down and IS shifts left case 3: Contractionary M- policy and contractionary F- policy LM shifts up and IS shifts left 2

3 case : Contractionary M- policy and expansionary F- policy LM shifts up and IS shifts right (2) The results: Unclear In each case, the effects of the policy mix on one of the endogenous variables (Y,i,C,S,I) may be ambiguous (unless the exact magnitude of policy changes is known). But, the effect on some other endogenous variable(s) may be known; e.g., case 2 in figure 6-0. Figure 6-0: we only know that i unambiguously falls Figure 6-: we only know that i unambiguously rises <9> The dynamics of the IS LM model The real sector of an economy adjusts slowly to the exogenous shocks while the financial sector adjusts very quickly. () As the IS curve shifts, Y will gradually and slowly adjust to its new equilibrium because: production will respond with a lag to changes in demand consumption will respond with a lag to changes in disposable income investment will respond with a lag to changes in sales Come back to figure 6-8c: From the discussion in Chapter 4, we know that production adjustment following a change in demand cannot be completed right away, and so the economy takes time to move from point A to point F in figure 6-8c. Point F is off the LM or financial equilibrium, and interest rate adjustments cannot be finished soon, either, even if financial adjustment itself is very fast. This is because drops in the interest rate between point F and point A lead to investment adjustments that take place slowly. (2) Financial markets will adjust rapidly to changes in supply and demand, and the LM will shift fast. Figure 6-2: M- contraction: LM shifts upwards to LM 0 instantaneously, whereas production adjustment from A to A takes place over time. From now on, we assume that the adjustment of the interest rate to any change in money demand or supply is so fast that the economy is always on the LM curve. Under this assumption, we can re-state the adjustment process associated with shifts in the IS curve. See a figure on page 7 in Study Guide, where the economy is thought of as moving along the LM after the IS has shifted to IS 0. <0> Assignments Questions, 2, 3, 4, 5 on page 23. Solutions To Problem Set Five 3

4 Chapter 6, Page 23, Textbook (Blanchard and Melino, 999 ). Question : omitted Investment decisions are made depending on whether or not the projects are profitable. If a firm borrows to invest in a project, it must consider if profits on the project are higher than its cost including the borrowing cost. If a firm can finance a project using its own fund such as retained earnings, it also has to compare profitability from the project with income from investing this fund in other assets such as lending it. In this case, higher interest rates will make lending more attractive and thus discourage investing in projects. Question 2: As discussed in the text, a decrease in the budget deficit may cause investment spending to increase or decrease. If you were asked by the prime minister to determine which way investment would change after a deficit reduction, what specific information would you need to give him an answer? Solution: Using the IS (Keynes) approach to the determination of equilibrium income, we have: Investment = private saving + public saving I = S +(T G) or I = S (G T ) where (G T ) is budget deficit. If private saving is constant and if there is a fall in budget deficit, one can expect investment to rise. However, we cannot keep private saving constant when governments reduce budget deficits. There are two ways to reduce budget deficit: decreasing G and raising T,whichbothinfluence the goods market equilibrium. () For in G and 4T =0, 4I = 4S 4G Suppose that I (Y,i) =b o + b Y b 2 i. Look at equil condition: Y = Z, Y = C + I + G, Y = c o + c (Y T )+b o + b Y b 2 i + G This yields: Y = c b (c o c T + b o b 2 i + G) Then, 4Y = c b 4G Private saving: S = Y T C = c o +( c )(Y T ) Then, 4S =( c ) 4Y = c c b 4G Thus, 4I = 4S 4G = h c c b i 4G = b c b 4G The sign of c b is unclear. So, in order to know if this fiscal contract increases I or not, we need information on MPC and MPI (The above has omitted the financial equilibrium for simplicity). (2) For in T and 4G =0, 4I = 4S + 4T Since Y = c b (c o c T + b o b 2 i + G), 4Y = c c b 4T Since S = c o +( c )(Y T ), 4S =( c )(4Y 4T ) So, 4I =( c )(4Y 4T )+4T = c b c b 4T It is the same as above that one has to know about MPC and MPI in order to find out how a rise in taxes affects investment even in this partial equil (without considering financial equil) Question 3: Consider the following numerical version of the IS LM model: Y = Y D, I = i +0.Y, G = 200, T =200; 4

5 (M/P) d =0.5Y 7500i, (M/P) s = 500 (a) find the equation for the IS curve (b) find the equation for the LM curve (c) solve for the equil real output (d) solve for the equil interest rate (e) solve for the equil values of consumption and spending, and verify the value you obtained for Y by adding up C, I, G. (f) now suppose that government spending increases by 500 to 700. Solve again for Y,i,C,I, and once again verify that Y = C + I + G in equil (g) summarize the effects of the expansionary fiscal policy in part f by stating what has happened to Y,i,C,I. (h) set all variables back to their initial values. Suppose that the money supply increases by 500. Solve again for Y,i,C,I. Once again, verify that Y = C + I + G in equil (i) summarize the effects of the expansionary monetary policy in part h by stating what has happened to Y,i,C,I. Solution: (a) IS curve: Equil condition: Y = C + I + G Y = (Y 200) i +0.Y Y = i Y = i Ex (): i = Y (b) LM curve: Equil.. condition: 500 = 0.5Y 7500i Ex (2): i = + Y (c) (d) Overall equil: Put Ex () and Ex (2) together: Y = Solve this for Y =2200 Substitute Y back to Ex () or Ex (2) to have i =8% (e) Plug (Y,i )inc and I functions to yield: C = ( ) = 400 I = % = 600 C + I + G = = 2200 = Y (f) Only IS shifts after G = Then, Y = (Y 200) i +0.Y Y = i Y = i Ex () : i = Y Put Ex () and Ex (2) together: Y = + Y Solve it for the new overall equil: Y 0 = 2950 and i 0 =3% C 0 = ( ) = 775 I 0 = % = 475 C 0 + I 0 + G 0 = = 2950 = Y 0 (g) Y by 750, i by 5%, C by 375, I by 25 + Y

6 (h) Only LM shifts after M = Then, 000 = 0.5Y 7500i Ex (2) : i = 2 + Y Put Ex () and Ex (2) together: Y = 2 Solve it for the new overall equil: Y 0 = 2600 and i 0 =4% C 0 = ( ) = Y I 0 = % = 800 C 0 + I 0 + G 0 = = 2600 = Y 0 (i) Y by 400, i by 4%, C by 200, I by 200 Question 4: suppose that policy makers want to decrease the deficit while guaranteeing that there will be no decrease in either output or investment spending. Is there any monetary-fiscal policy mix that can achieve this goal? Solution:Yes, there exists some policy mix that can achieve the goal of fiscal deficit reduction while keeping output unchanged. The fiscal policy is now contractionary;thiscanbecombinedwithanexpansionmonetarypolicy(suchas M) that shifts the LM down. In this case, the equil interest rate is reduced and investment must be increased given output is constant. It is better to use a figure for illustration. Question 5: Omitted An expansionary fiscal policy shifts the IS right. As output cannot be adjusted rightaway,andastheeconomyisalwaysonthelm curve, there would be a slow increase in interest rate, coupled with a slow increase in output. This adjustment process continues until Y and i reach the new LS LM intersection. Draw many small arrows along the LM from Y to Y. 0 6

Business Fluctuations. Notes 05. Preface. IS Relation. LM Relation. The IS and the LM Together. Does the IS-LM Model Fit the Facts?

Business Fluctuations. Notes 05. Preface. IS Relation. LM Relation. The IS and the LM Together. Does the IS-LM Model Fit the Facts? ECON 421: Spring 2015 Tu 6:00PM 9:00PM Section 102 Created by Richard Schwinn Based on Macroeconomics, Blanchard and Johnson [2011] Before diving into this material, Take stock of the techniques and relationships