Basic References: Hall and Taylor, Chapter 7; Study Guide, Chapter 7. #THE IS-LM MODEL# INTRODUCTION In HT5 we developed money supply and demand relationships, and in HT6 we developed the IS product market relationship. In the current chapter these money and product market relationships are brought together within a single framework---the IS-LM model. This model will allow us to begin to analyze the impact of monetary and fiscal policies on key macroeconomic variables. As a first step in the construction of the IS-LM model, the previous HT6 modellings of investment and net exports will be generalized to permit dependence on the interest rate. INVESTMENT AND THE INTEREST RATE #Behavioral Assumptions for Investment Based on Empirical Observation#: The demand for investment goods (i.e., physical capital goods) depends #negatively# on the expected real interest rate R^e paid on financial assets. That is, investment demand is #low# when R^e is #high# and investment demand is #high# when R^e is #low#. #Intuitive rationale#: High R^e --> high expected cost --> fewer planned investment of borrowing to finance good purchases investment High R^e --> high expected return --> more planned purchases of to lending financial assets #Algebraic Representation for the Investment Demand Function#: I^D = e - dR^e , where R^e = the expected real interest rate; e, d = exogenously given positive coefficients . NET EXPORTS AND THE INTEREST RATE #Key Observation#: An #increase# in the expected HC interest rate R^e tends to cause an expected #appreciation# in the HC currency (hence an expected increase in the exchange rate), which in turn leads to a #decline# in net exports. more attractive for ROW nationals to buy HC assets, that is, to lend to HC firms and households by buying assets denominated in HC currency R higher -> -> relative demand for HC currency increases as ROW nationals try to buy HC assets and to sell ROW assets -> relative demand for HC currency increases less attractive for HC nationals as HC nationals try to to buy ROW assets, more attractive buy HC assets and for HC nationals to put their funds to sell ROW assets into HC assets --> the price of HC currency --> increase in the relative to ROW currency exchange rate increases (ROW currency per unit of HC currency) --> HC goods more expensive to ROW nationals --> EX^D lower and and ROW goods less expensive to HC nationals IM^D higher --> net export demand NE^D = [EX^D - IM^D] declines. #Algebraic Formulation#: These relations are more carefully developed by HT in Chapter 12. For now, we only use the implication that R is #negatively# related to net export demand. Specifically, HT make the behavioral assumption that net export demand is a simple linear function of the (expected) real interest rate R^e as well as of (expected) real income: (*) NE^D = g - mY^e - nR^e , where g, m, and n are exogenously given positive coefficients. Note that (*) implies that net export demand is a decreasing function of both expected income and the expected real interest rate. THE IS-LM MODEL: ALGEBRAIC FORMULATION The objective of this section is to combine the various behavioral assumptions for consumption, investment, net exports, and money demand into an "IS-LM model" explaining how real income might be determined in the short run, taking the general price level P as given (predetermined). The term "IS-LM" will be clarified below. The Basic IS-LM Model Equations for the Economy During Period T Equation Verbal Description Product Market (Spending Balance) Relations: #Supply Side#: (1) Realized income Y = C + I + G + NE Accounting Identity For Realized Income #Demand Side#: (2) Consumption Function C^D = a + bY^e_d Behavioral Assumption (3) Exp. Disp. Income Y^e_d = [1-t]Y^e Definitional Equation (4) Inv Demand Function I^D = e - dR^e Behavioral Assumption (5) NE Demand Function NE^D = g - mY^e - nR^e Behavioral Assumption (6) Aggregate Demand Y^D = C^D + I^D + G + NE^D Definitional Equation #Product Market Equilibrium#: (7) Supply=Demand I = I^D Equilibrium Condition (8) Supply=Demand C = C^D Equilibrium Condition (9) Supply=Demand NE = NE^D Equilibrium Condition (10) Fulfilled Exp's Y^e = Y Equilibrium Condition (11) Fulfilled Exp's R^e = R Equilibrium Condition #Remark#: What about the equality of realized output supply Y and aggregate demand Y^D? The equality Y=Y^D is an implication of equations (1) and (6)-(9) and so does not have to be separately assumed. Money Market Relations: #Supply Side#: (12) Money Supply Function M^S = M Government Monetary Policy Rule #Demand Side#: (13) Money Demand Function M^D/P = kY^e - hR^N^e Behavioral Assumption (14) Exp. Nom. Interest Rate R^N^e = R^e + INF Definitional Equation #Money Market Equilibrium#: (15) Supply=Demand M^S = M^D Equilibrium Condition (16) Fulfilled Exp's R^N^e = R^N Equilibrium Condition REMARK: Equations (10) and (11) are also needed for money market equilibrium, but restating them again here would be redundant. Classification of Variables #Endogenous Variables#: (Variables appearing in the model equations for period T whose solution values are determined by these equations, hence #during# period T) Sixteen equations in sixteen endogenous variables to be solved for: Y^D and Y, C^D and C, I^D and I, NE^D and NE, M^D and M^S, plus Y^e_d, R, R^N, Y^e, R^e, R^N^e #Predetermined Variables#: (Variables appearing in the model equations for period T whose values are determined by model equations relating to periods #prior# to period T) The general price level, P #Exogenous Variables#: (Variables appearing in the model equations for period T whose values are given known quantities determined outside of the model equations for #any# period T) Three government policy variables: t, G, M Plus the coefficients: a, b, e, d, g, m, n, k, h Plus the inflation rate INF (temporary classification) THE IS-LM MODEL: GRAPHICAL REPRESENTATION We will now reduce the relationships (1)-(16) down to just two relationships in the two endogenous variables Y and R---the IS and LM curves---which can be graphically depicted. Key Definitions: The #IS Curve# shows all combinations of the real interest rate R and the level of real income Y which satisfy the spending balance relations (1)-(11). The #LM Curve# shows all combinations of the real interest rate R and the level of real income Y which satisfy the money market relations (10)-(16). THE IS CURVE By definition, the IS Curve is the graph of the spending balance relations (1)-(11) in the Y-R plane after all endogenous variables except Y and R have been substituted out. Intuitively, Y and R should depend #negatively# on each other through these spending balance equations; i.e., the IS Curve should be downward sloping, since an #increase# in the interest rate causes a #decrease# in both investment and in net exports, and hence leads to a decrease in Y through the multiplier process. It is fairly straightforward to establish algebraically that this intuition is correct. Substituting out all endogenous variables from (1)-(11) except Y and R leaves one relation in the #two# unknowns, Y and R: Y = (a + b[1-t]Y) + (e - dR) + G + (g - mY - nR) For our purposes, we want to solve this relation for R as a function of Y, i.e., we want R isolated by itself on the left side. Let A denote the positive quantity [1-b(1-t)+m]. Then, combining terms in Y and R, and solving for R, one obtains the following relation: #IS Equation#: (IS) R = [a + e + G + g]/[d + n] - (A/[d + n])Y . R-intercept slope = dR/dY = -A/[d+n] (Value of R when Y=0) (note the sign is #included#) [Compare Hall and Taylor, equ.(7-5), p. 188.] Since the coefficient terms A, d, and n are all positive, it follows from (IS) that R is a linear function of Y that depends #negatively# on Y. The IS curve is the #graph# of the IS equation (IS). R | | [a+e+G+g] * --------- | [d+n] | IS Curve with slope | | dR - A | -- = ------ | dY [d+n] | | | | | | | -------------------------------------------- Y 0 The IS Curve By construction, the product market is in equilibrium at every point on the IS curve. FOUR DIFFERENT WAYS THE IS CURVE MIGHT BE AFFECTED BY VARIABLE CHANGES: 1. Movements Along the IS Curve: Given fixed values for all exogenous and predetermined variables, a change in Y causes a movement #along# the IS curve as R correspondingly adjusts, since R and Y appear as variables along the axes. 2. Parallel Shifts of the IS Curve: A change in any exogenous or predetermined variable entering into the R-intercept of the IS curve (but not the slope) #shifts the IS Curve in a parallel fashion#. #Examples#: What happens if there is an #increase# in the consumption function intercept term a ("subsistence consumption")? For each given Y, the right hand side of (IS) is #larger# in magnitude, hence the corresponding R on the left must be #larger# in magnitude. In short, for each Y, R is larger; hence the IS Curve #shifts up#. What happens if real government expenditure G #decreases#? For each Y, the right hand side of (IS) is smaller, hence R on the left is smaller. The IS Curve #shifts down#. 3. Rotations of the IS Curve: A change in any exogenous or predetermined variable entering into the slope of the IS curve (but not the R-intercept) #rotates the IS Curve around the R-intercept#. A change in any exogenous or predetermined variable entering into the slope of the IS curve (but not the Y-intercept) #rotates the IS curve around the Y-intercept#. #Example#: What happens if t #increases#? First note that t enters into the slope of the IS curve and into the Y-intercept; but it does not enter into the R-intercept, implying the R-intercept stays fixed. If t increases, then A #increases#; hence, for given Y, the right hand side of (IS) is #smaller#, hence R on the left must be smaller. The IS curve #rotates downward# around the unchanged R-intercept. 4. Simultaneous rotation and shift of the IS Curve: A change in any exogenous or predetermined variable entering into the #slope# of the IS curve #as well as both intercepts# would simultaneously rotate and shift the IS curve. For the model at hand, it happens that no such variables exist for the IS curve. THE LM CURVE By definition, the LM curve is the graph of the money market relations (10)-(16) in the Y-R plane, after all endogenous variables other than Y and R have been substituted out. This substitution out leaves #one# relation in the two endogenous variables Y and R, given by: #LM Equation#: (LM)* M/P = kY - hR - hINF where P, k, h, and c are given predetermined or exogenous variables. Relation (LM)* should be compared with Hall and Taylor, equ.(7-3), p. 186. Recall that, for now, we are retaining the dependence of money demand on the #nominal# interest rate, R+INF, the true opportunity cost of holding money. Hall and Taylor simplify their analysis by assuming money demand depends on the real interest rate R rather than the nominal interest rate R+INF. The LM curve (i.e., the graph of (LM)* in the Y-R plane) slopes #upward#, in the sense that Y and R increase and decrease #together# along the LM curve. The intuitive reason for the upward slope of (LM)* is as follows: Recall that the demand for money (with fulfilled expectations) takes the form M^D/P = kY - hR - hINF. Thus higher Y -> #higher# level of transactions -> demand for money #increases# But the money supply is fixed at M, and (LM)* implies M^D must equal M. Thus, the interest rate R must adjust until the private sector is once again content to hold M; that is, money demand must be #discouraged#. But this requires an #increase# in R, so that people reduce their demand for money holdings because the opportunity cost of holding money has increased. To see this algebraically, let (LM)* be re-expressed as (LM) R = - [ (M/hP) + INF ] + [k/h]Y R-intercept slope = dR/dY = k/h (Value of R when Y=0) [Compare Hall and Taylor, equ.(7-7), p. 189.] Then it is clearly seen that the slope of the LM Curve is k/h, a #positive# number. The R-intercept is negative if the inflation rate INF in nonnegative; otherwise it could be positive. R | | | | LM Curve with slope | | dR k | -- = --- | dY h | 0 -------------*--------------------------------- Y | | [M/kP] + hINF/k | -[M/hP]-INF * | The LM Curve By construction, the money market is in equilibrium at each point on the LM curve. How is the LM curve affected by variable changes? As for the IS Curve: (a) A change in an exogenous or predetermined variable appearing in the R-intercept of the LM Curve (but not the slope) causes the curve to #shift#; (b) A change in an exogenous or predetermined variable appearing in the slope of the LM Curve (but not the R-intercept) causes the curve to #rotate around the R-intercept#; (c) A change in an exogenous or predetermined variable appearing in the slope of the LM curve (but not the Y-intercept) causes the LM curve to #rotate around the Y-intercept#; (d) A change in any exogenous or predetermined variable entering into the slope, the R-intercept, #and# the Y-intercept of the LM curve results in a combined rotation and shift in the LM curve. [Consider, for example, a change in h.] FINDING SHORT-RUN EQUILIBRIUM VALUES Y^o and R^o FOR Y AND R DEFINITION: An economy with income level Y^o and real interest rate R^o is said to be in a "short-run equilibrium" (or "IS-LM equilibrium") if Y^o and R^o represents the intersection of the IS and LM curves in the Y-R plane. Thus, the economy is in a short-run equilibrium if both the product market and the money market are in equilibrium, in the sense that plans are fulfilled (supply = demand) and expectations are realized in both the product and money markets. However, note that labor demand may fail to equal labor supply in a short-run equilibrium---that is, there is no guarantee that the #labor# market is in equilibrium, and hence no guarantee that Y^o equals the full employment level of income Y*. R | | | | | | | E^o R^o |................... | . | . | . | . | . --------------------------------------------- Y 0 Y^o Short Run Equilibrium at E^o How can the short-run equilibrium values for Y and R be determined algebraically? The IS-LM model (1)-(16) has now been reduced down to just two relations in the two unknowns R and Y. Recalling that A denotes the expression (1-b[1-t]+m), these two relations are as follows: (IS) [Product Market Equilibrium] R = [a+e+G+g]/[d+n] - (A/[d+n])Y ; (LM) [Money Market Equilibrium] R = - [ (M/hP) + INF ] + [k/h]Y . The values Y^o and R^o for Y and R which solve the IS-LM model occur at the intersection of the IS and LM Curves in the Y-R plane; i.e., they are the values for Y and R which simultaneously satisfy equations (IS) and (LM). These values are found by using one of the equations to solve for R as a function of Y, and then substituting this value for R into the second equation. For the linear equation model at hand, obtaining the solutions for Y and R by this means is messy but straightforward. For example, use (LM) to solve for R, and substitute this value into (IS). One obtains one equation in the one unknown Y: - [ (M/hP) + INF ] + [k/h]Y = [a + e + G + g]/[d + n] - (A/[d + n])Y . Collecting terms in Y on the left, and putting all other terms on the right, (A/[d+n])Y + [k/h]Y = [ (M/hP) + INF ] + [a+e+G+g]/[d+n] or (A/[d+n] + [k/h])Y = [ (M/hP) + INF ] + [a+e+G+g]/[d+n] . Now divide through by the terms multiplying Y to obtain the short-run equilibrium solution Y^o for Y: Y^o = ( (M/hP) + INF + [a+e+G+g]/[d+n] )/( A/[d+n] + [k/h] ) The short-run equilibrium solution R^o for R is then found by substituting this value Y^o for Y either in the IS equation or the LM equation. Once the solution values Y^o and R^o are obtained for Y and R, solution values for all remaining endogenous variables in equations (1)-(16) can be obtained by substituting the solution values for Y and R back into these equations. For example, given Y^o and R^o, the solution value for consumption C is given by C^o = a + b[1-t]Y^o . THE AGGREGATE DEMAND CURVE DEFINITION: The #aggregate demand curve# is a schedule showing the aggregate spending Y of the economy at each general price level P, assuming the economy is in a short-run equilibrium at that price level. As one would expect, the AD curve is downward sloping---the higher the general price level, the lower the demand. There are, however, major differences between the macro concept of aggregate demand and the concept of a demand curve in microeconomics. The AD curve is derived from the succession of intersection points (Y^o,R^o) of the IS and LM Curves and the general price level P is varied. Specifically, it is the graph of the resulting solution values Y^o against the corresponding P values. Note that P enters only into the LM curve; the IS Curve is not affected by changes in P. P increases ---> M/P decreases --> For each possible Y, R goes [excess demand for money] #up# to dampen money demand --> LM curve shifts #up# --> New intersection point of the IS and LM curves occurs at a #lower# level of Y Consequently, the AD curve is a #downward# sloping curve in the Y-P plane. ALGEBRAIC DERIVATION: Step 1: Consider once again the IS and LM Curves: (IS Curve) R = [a+e+G+g]/[d+n] - (A/[d+n])Y (LM Curve) R = - [ (M/hP) + INF ] + [k/h]Y Step 2: Substitute out for R, leaving one equation in Y and P: [a+e+G+g]/[d+n] - (A/[d+n])Y = - [ (M/hP) + INF ] + [k/h]Y Step 3: Collect terms in Y #and in P#: ( [a+e+G+g]/[d+n] + INF) + (M/hP) = (A/[d+n] + [k/h])Y . Dividing through by the coefficient multiplying Y yields the short-run equilibrium value for Y as a function of P, given by Y = V + B/P = Y^o(P) , where ( [a+e+G+g]/[d+n] + INF) V = ----------------------------- (A/[d+n]) + [k/h] [M/h] B = ------------------- . (A/[d+n]) + [k/h] Alternatively, solving for P as a function of Y, one obtains the "inverse aggregate demand function" P = B/[Y - V] = P^o(Y) , which is defined only for Y greater than V. This latter restriction is necessary for economic meaningfulness. If Y were strictly less than V, note that P would take on negative values. Moreover, if Y were equal to V, the price level would "blow up" because the first term would involve division by zero. QUESTION: When will the AD curve shift and/or rotate in response to a change in some exogenous variable? Answer: Whenever the exogenous variable enters into either V or B. Or equivalently, whenever the exogenous variable appears somewhere in the IS and LM equations which are used to derive the AD curve. Note that changes in the #predetermined# variable P result in movements #along# the AD curve, not in shifts and/or rotations of the AD curve. GRAPHICAL DERIVATION OF THE AGGREGATE DEMAND CURVE: R | | | | | | | | | | | | | | | ------------------------------------------------------ Y 0 Y^o(P_1) Y^o(P_2) Y^o(P_3) . "asymptote" (Y approaches ever closer to V as P increases) . P . | . | . P_1 |........... | . . | . . | . . P_2 |......................... | . . . | . . . | . . . P_3 |......................................... | . . . . ------------------------------------------------- Y 0 V Y^o(P_1) Y^o(P_2) Y^o(P_3) The Aggregate Demand Curve in the Y-P Plane POLICY IN THE IS-LM MODEL: INTRODUCTORY COMMENTS BASIC QUESTION: What #can# government do in the short run to affect Y and R through changes in its monetary policy variable M and its fiscal policy variables G and t? Monetary Policy What happens to the IS curve, the LM curve, and the AD curve if the Fed #decreases# the money supply M? ALGEBRAIC ANSWER: The LM Curve shifts #up#, that is, R is #larger# for each given Y. The IS Curve is not affected. The new IS-LM intersection point is at #higher# R and #lower# Y. Since the predetermined level of P is unaffected by this change in M, this implies a #lower# value of Y for the given P, i.e., the AD curve #moves to the left#. Such a monetary policy change is called a #contractionary# monetary policy change, for obvious reasons. #ECONOMIC INTUITION#: With a #decrease# in the money #supply#, there is more demand for money in the economy than supply---that is, there is an #excess demand# for money in the money market. In order to convince people to demand less money (i.e., to hold more bonds) so that the money market can regain a state of equilibrium, the interest rate (i.e., the opportunity cost of holding money) must #increase# for any given level of Y. The higher interest rate R also discourages investment and net exports, which lowers real income Y through the multiplier process. Conversely, an increase in M would result in a new intersection point at a #lower# R and a #higher# Y, implying a #move to the right# of the AD curve. Fiscal Policy: Government Expenditure What happens to the IS curve, the LM curve, and the AD curve if the government #increases# its expenditure level G? ALGEBRAIC ANSWER: The expenditure level G enters into the numerator of the #R-intercept# of the IS Curve but not the slope of the IS curve. Thus, an increase in G #shifts up# the IS curve. That is, R is higher for each given Y. Since G does not enter into the LM curve, the LM curve is not affected by a change in G. It follows that the new intersection point with the LM curve is at a #higher# value for R and a #higher# value for Y. Since P is unaffected by the change in G, this implies a #higher# Y for the given P; that is, the AD curve #shifts to the right#. Such a policy change is called an #expansionary# fiscal policy change, for obvious reasons. #ECONOMIC INTUITION#: The first-round effect of an increase in G causes Y to increase. This leads to an increase in M^D (hence an #excess demand for money#), and also to an increase in C which tends to further increase Y (although this increase in Y is partially offset by a decrease in net exports in response to the first-round increase in Y). To encourage people to hold less money, the opportunity cost of holding money must increase, i.e., R must increase; but this leads to decreases in investment I and net exports NE which partially offset the initial increase in Y. REMARK: The latter partially offsetting decrease in I in response to the initial increase in G is referred to as the "crowding out effect"---the increase in government expenditures is said to have "crowded out" private investment I. By similar arguments, a #decrease# in G would lead to a #lower# value for R and a #lower# value for Y, and hence a #shift to the left# in the AD curve. Fiscal Policy: Tax Rate What happens to the IS curve, the LM curve, and the AD curve if the government #decreases# the tax rate t? ALGEBRAIC ANSWER: The tax rate t enters into the #slope# and the #Y-intercept# of the IS Curve, but not into the R-intercept of the IS curve. Specifically, a decrease in t causes the negative slope of the IS curve to #decrease# in magnitude (i.e., become less negative) and the positive Y-intercept to #increase# in magnitude. The R-intercept stays fixed. The IS curve thus rotates outward around the R-intercept, implying that R is higher for each given Y. Since t does not enter into the LM curve, the LM curve is not affected by a change in t. It follows that the new intersection point with the LM curve is at a #higher# value for R and a #higher# value for Y. Since the predetermined price level P is unaffected by the change in t in the current period, this implies a #higher# SR-equilibrium value for Y for any given P; that is, the AD curve #shifts to the right#. Such a policy change is called an #expansionary# fiscal policy change, for obvious reasons. #ECONOMIC INTUITION#: The first-round effect of a decrease in t causes C and hence Y to increase. This leads to an increase in M^D (hence an #excess demand for money#), and also to a further increase in C in response to the first-round increase in Y which tends to further increase Y (although this increase in Y is partially offset by a corresponding decrease in net exports). To encourage people to hold less money, the opportunity cost of holding money, R, must increase; but this leads to decreases in investment I and net exports NE which partially offset the initial increase in Y. General Comments About Policy Effects Statements in the financial pages of newspapers and magazines and in T.V. economic commentary concerning the effects of government policy actions often appear to be based on an underlying IS-LM analysis. However, caution must be exercised in applying the IS-LM apparatus to real-world problems. One difficulty is that the behavioral assumptions underlying the IS-LM model can be criticized on the grounds that agents (particularly households) do not exhibit a realistic degree of rationality and are not modelled as solving plausible optimization problems. This is the problem of inadequate "microfoundations" that many economists (particularly of the new Keynesian school of thought) are currently trying to correct. A second difficulty is that the IS-LM model as developed to date is static, in the sense that it does not consider affects on #future# income etc. of government policy decisions taken #now#. It only predicts affects on #current# income. One connection between the current time and the future time comes from a consideration of how the government #finances# its expenditures: #Government Budget#: G = tY + DM/P + DB/P Any part of real government expenditure G which is not financed by an increase in current income taxes must be financed either by new money issue DM/P or by new bond issue DB/P. Changes in money have implications for the future inflation rate (a higher inflation rate means a higher inflation "tax" on private and foreign sector agents holding assets denominated in dollars); and changes in bonds have implications for future tax obligations (the government must somehow raise additional money from future taxpayers to service the new debt). Another connection between the current time and the future time comes from a consideration of how net investment #changes# the size and composition of the current capital stock, and how population trends #change# the size and composition of the current labor force. We will return to these issues later in the course. THE RELATIVE EFFECTIVENESS OF MONETARY AND FISCAL POLICY #When is monetary policy relatively weak, in the sense that changes in M have a correspondingly small impact on real income Y?# Consider the sequence of events which follows upon an expansionary monetary policy (an increase in M) starting from a point of short-run equilibrium (i.e., an intersection point of the IS and LM curves). M #increases# -> #Excess# supply of money develops as M rises above M^D -> #Drop# needed in the opportunity cost R of holding money to get people to hold more of it (i.e., to increase M^D) -> Lower R encourages #more# I and NE -> #Raise# in Y through the multiplier process. An expansionary monetary policy (M increased) might therefore have a relatively #weak# impact on Y if either of the following situations occurs: (1) The drop in the interest rate R that occurs when M increases is #very small# because the money demand M^D is #very sensitive# to changes in R --> h is #very large# in the money demand relation M^D/P = kY - hR - hINF. --> Slope [k/h] of the LM Curve is a #very small positive number# (LM Curve) R = - [ (M/hP) + INF ] + [k/h]Y . and/or (2) Investment I = e - dR and net exports NE = g - mY - nR are #very insensitive# to changes in R --> d and n are #very small positive numbers# --> IS Curve has a #very large negative slope# (IS) R = [a+e+G+g]/[d+n] - (A/[d+n])Y Note that shifts in the LM Curve will tend to have little effect on Y if one or both of these conditions holds. Monetary policy is relatively strong in the reverse case. #When is fiscal expenditure policy relatively weak, in the sense that changes in G result in a correspondingly small change in real income Y?# An expansionary fiscal policy will have a relatively #weak# impact on Y if crowding out effects are significant. Recall the sequence of events in crowding out, starting from a point of equilibrium: G increases -> Y increases (both directly, and through multiplier effects working through increases in C partially offset by decreases in NE) -> M^D increases in response to the increase in Y -> R increases to offset the increase in M^D -> I and NE decrease in response to the increase in R -> increase in Y is partially offset Clearly the overall impact of an increase in G on Y will be #weak# if the offset is #large#. The offset will be large if the following statements hold to a suitable degree: (1) The sensitivity of money demand to the interest rate is #very small# (i.e., h is very small), so that #very large# increases in R are needed to dampen money demand. M^D/P = kY - hR - hINF. --> LM Curve is #very steep# [has a #large positive slope# k/h] (LM Curve) R = - [ (M/hP) + INF ] + [k/h]Y . (2) The sensitivity of investment I = e - dR and/or net exports NE = g - mY - nR to the interest rate R is #very large# (i.e., d and/or n are #very large#) --> IS Curve #very flat# [has a small negative slope -A/[d+n] ] (IS Curve) R = [a+e+G+g]/[d+n] - (A/[d+n])Y In other words, shifts in the IS Curve will tend to have little effect on Y if one or both of these conditions hold. In the case where each of these statements holds in reverse [i.e., the LM Curve is relatively flat and/or the IS Curve is steeply sloped], the overall impact of an increase in G on Y will be #strong#, i.e., fiscal policy will have a significant impact on Y. #Remark#: One might argue that the impact of an increase in G on Y will be #strong# if the government multiplier dY/dG = (1/[1-b(1-t) + m]) is #large#. Note, however, that the inverse of this multiplier is the expression A that appears in the slope term for the IS Curve, with [d + n] in the denominator, where A is bounded below by 0 and (typically) would also be bounded above by 2. Thus, having d and/or n suitably large or small would outweigh any effects on Y through the multiplier process.