IS-LM-BP model
The IS-LM-BP model (also known as IS-LM-BoP or Mundell-Fleming model) is an extension of the IS-LM model, which was formulated by the economists Robert Mundell and Marcus Fleming, who made almost simultaneously an analysis of open economies in the 60s. Basically we could say that the Mundell-Fleming model is a version of the IS-LM model for an open economy. In addition to the balance
in goods and financial markets, the model incorporates an analysis of the balance of payments.
Even though both economists researched about the same topic, at about the same time, both have different analyses. Mundell’s paper “Capital Mobility and Stabilization Policy under Fixed and Flexible Exchange Rates”, 1963, analyses the case of
perfect mobility of capital, while Fleming´s model, depicted in his article “Domestic Financial Policies under Fixed and under Floating Exchange Rates”, 1962, was more realistic as it assumed imperfect capital mobility, and thus made this one a more rigorous and comprehensive model. However, nowadays, his model has lost cogency, as the actual world situation has more resemblance with total capital mobility, which corresponds better to Mundell’s view.
In order to understand how this model works, we’ll first see how the IS curve, which represents the equilibrium in the goods market, is defined. Secondly, the LM curve, which represents the equilibrium in the money market. Thirdly, the BP curve, which represents the equilibrium of the balance of payments. Finally, we’ll analyse how the equilibrium is reached.
IS curve: the market for goods and services
In an open economy, the equilibrium condition in the market for goods is that production (Y), is equal to the demand for goods, which is the sum
of consumption, investment, public spending and net exports. This relationship is called IS. If we define consumption (C) as C = C(Y-T) where T corresponds to taxes, the equilibrium would be given by:
We consider that investment is not constant, and we see that it depends mainly on two factors: the level of sales and interest rates. If the sales of a firm increase, it will need to invest in new production plants to raise production; it is a positive relation. With regard to interest rates, the higher they are, the more expensive investments are, so that the relationship between interest rates and investment is negative. Now, in addition to what we have in the IS-LM model, since we have net exports, we have also to take into account the exchange rates, which directly affect net exports. Let’s say e is the domestic price of foreign currency or, in other words, how many units of our own currency have to be given up to receive 1 unit of the foreign currency. The new relationship is expressed as follows (where i is the interest rate):
Y = C (Y- T) + I (Y, i) + G + NX(e)
If we keep in mind the equivalence between production and demand, which determines the equilibrium in the market for goods, and observe the effect of interest rates, we obtain the IS curve. This curve represents the value of equilibrium for any interest rate.
An increasing interest rate will cause a reduction in production through its effect on investment. Therefore, the curve has a negative slope. The adjacent graph shows this relationship.
As stated before, we also need to analyse changes in exchange rates (here, e). If e decreases, then we’ll be able to buy more foreign currency with less of our own
depreciation under flexible exchange rates or a devaluation under fixed exchange rates), domestic residents will pay more for the same goods. To sum up, an increase in e causes net exports to increase (IS curve shifts to the right) and a decrease in e causes net export to decrease (IS curve shifts to the left).
LM curve: the market for money
The LM curve represents the relationship between liquidity and money. In an open economy, the interest rate is determined by the equilibrium of supply and demand for money: M/P=L(i,Y) considering M the amount of money offered, Yreal income and i real interest rate, being L the demand for money, which is function of i and Y. Also, the exchange rate must be analysed since it affects money demand (investors may decide buy or sell bonds in a country depending on the exchange rate).
The equilibrium of the money market implies that, given the amount of money, the interest rate is an increasing function of the output level. When output increases, the demand for money raises, but, as we have said, the money supply is given. Therefore, the interest rate should rise until the opposite effects acting on the demand for money are cancelled, people will demand more money because of higher income and less due to rising interest rates.
BP curve: the balance of payments
The BP curve shows at which points the balance of payments is at equilibrium. In other words, it shows combinations of production and interest rates that guarantee that the balance of payments is viably financed, which means that the volume of net exports that affect total production must be consistent with the volume of net capital outflows. It will usually slope up since the higher the production, the higher the imports, which will disturb the equilibrium of the balance of payments, unless
interest rates rise (which would cause capital inflows to maintain the equilibrium). However, depending in how great the mobility of capital is, it will have a greater or smaller slope: the higher the mobility, the flatter the curve.
Once the BP curve is derived, there is an important thing to know about how to use it. Any point above the BP curve will mean a balance of payments surplus. Any points below the BP curve will mean a balance of payments deficit. This is important since depending where we are, different things may affect the interest rates.
The IS-LM-BP model
1 Perfect capital mobility
1.1 Fixed exchange rate
An expansionary monetary policy will shift the LM curve to LM’, which makes the
equilibrium go from point E0 to E1. However, since we are below the BP curve, we know the economy has a balance of payments deficit. Since exchange rates are
fixed, government intervention is required: the government will purchase domestic currency and sell foreign currency, which will drop the money supply and therefore shift the LM’ curve to its original position (which makes the equilibrium go to E2). Monetary policy has therefore no effect under these circumstances.
This will increase the money supply, shifting the LM curve to the right. The final equilibrium is reached at point E2 where, at the same interest rate, production has increased greatly: fiscal policy works perfectly under these circumstances.
1.2 Flexible exchange rate
An expansionary fiscal policy will shift the IS curve to IS’, moving the equilibrium from point E0to point E1. The economy will therefore have a balance of payments surplus, which in this case of flexible exchange rate will appreciate the domestic currency. This will decrease net exports, since we are able to import more goods and services with less money, while foreigners will import less of our products because of our appreciated domestic currency. This drop in net exports will shift the IS’ curve back to its original position. Since now the final equilibrium E2 corresponds to the initial equilibrium, we know fiscal policy is no good in this case.
It is easy to see why Mundell devised what is known as the impossible trinity. In a few words, no economy can have the following three: perfect capital mobility, fixed
2 Imperfect capital mobility
2.1 Fixed exchange rate
Here we have the exact same situation as before: an expansionary monetary policy will shift the LM curve to LM’, which makes the equilibrium go from point E0 to E1. However, since we are below the BP curve, we know the economy has a balance of payments deficit. Since exchange rates are fixed, the government will purchase domestic currency and sell foreign currency, which will drop the money supply and therefore shift the LM’ curve to its original position (which makes the equilibrium go to E2). Monetary policy has again no effect, no matter how great or small capital mobility is.
payments surplus (high capital mobility, BP+ curve) or a balance of payments deficit (small capital mobility, BP- curve). Since exchange rates are fixed, government will need to intervene: its acquisitions and disposals of both domestic and foreign currency will shift the LM curve to either LM’ or to LM* (you can review what happens above: a balance of payments surplus is the same scenario as in a fiscal policy with perfect capital mobility and fixed exchange rates, while the balance of payments deficit
corresponds to the monetary policy scenario). Under these circumstances, fiscal policy is completely efficient. It’s actually the more efficient the higher capital mobility is.
2.2 Flexible exchange rate
An expansionary fiscal policy will shift the IS curve to IS’, moving the equilibrium from point E0to point E1. Now, depending on capital mobility, we’ll either have a balance of payments surplus (high capital mobility, BP+ curve) or a balance of payments deficit (small capital mobility, BP- curve). In the case of a balance of payments surplus, and considering flexible exchange rates, there will be an appreciation of the domestic currency. This will decrease net exports, which will shift the IS’ curve to the left. Also, since domestic assets are more expensive, the BP+ curve will shift to the left. The final equilibrium will therefore be at point E2. If there is a balance of payments deficit (the case for the BP- curve), the result will be the same one as in the monetary policy case (being E2* the final equilibrium). In this scenario, fiscal policy will be more efficient the smaller capital mobility is.
The Mundell-Fleming model is a very useful tool when dealing with the analysis of open economies. A great deal of textbooks and papers argue for or against each of these models. However, there’s no denying the world is moving towards
Attempts at incorporating the foreign sector into the Keynesian model were pursued famously by James Meade (1951) and Jan Tinbergen (1952) - largely in response to the elasticity-absorption debate that was then raging in balance of payments theory.
However, the most successful attempt at integrating the foreign sector into the Neo-Keynesian system has been the "Mundell-Fleming Model", the outcome of the research conducted by Robert Mundell (1962, 1963) and J.M. Fleming (1962) while at the
International Monetary Fund (IMF).
The "Mundell-Fleming" model extends of the IS-LM apparatus to incorporate balance of payments considerations, which has proved quite useful in analyzing international macroeconomic policy. To begin with, let us take the simplest open economy model. In this case, aggregate demand can be defined as:
Yd = C + I + G + NX
where NX are net exports (exports minus imports). We can break NX into the following:
NX = X0 - mY
where X0 are exports and mY are imports. This form implies that a particular economy's exports are exogenous (X0) but that its imports are a function of its own national
income, Y. Note that m is the marginal propensity to import out of income and we assume that 0 < m < 1. We obtain goods market equilibium when aggregate supply meets aggregate demand, Y = Yd or, assuming the simplest consumption function C = C0 + cY, investment function I = I0 + I(r) and assume exogenous government spending G = G0, we obtain in equilibrium:
so exports enter as an autonomous term (X0) whereas the marginal propensity to import is incorporated in the multiplier. In order for this equilibrium to exist, we must assume that 0 < c - m < 1, so that the sum of the marginal propensity to import and the marginal propensity to consume is a fraction. Notice that the open economy multiplier, 1/(1-c-m) is smaller than the closed economy one, 1/(1-c). In relative terms, the IS curve is steeper in an open economy than in a closed economy.
However, these relations are far too simplistic: domestic actions, by affecting interest rates, exchange rates and foreign income levels, may affect net exports in more ways. The Mundell-Fleming model incorporates some of these effects into the IS-LM model. Let us define the balance of payments surplus as the sum of the current account surplus and capital account surplus, or:
BP = NX + KA
where NX is the current acount (i.e. net exports) and KA is the capital account (domestic assets owned by foreigners minus foreign assets owned by domestic citizens). If BP > 0 then we have a balance of payments surplus; conversely, if BP < 0 we have a balance of payments deficit. Balance of payments equilibrium is achieved when BP = 0.
To enrich the relationships, let us argue that net exports are a function of the real exchange rate, eP/P* where e is the nominal exchange rate (domestic country's
currency units per foreign country's currency unit, e.g. dollars per yen), P the domestic price level and P* the foreign/world price level as well as income. Thus we can express net exports as a function:
NX = T(Y, eP/P*)
real exchange rate rises, net exports fall due to the lower "competitiveness" of exports). Note that the famous "Marshall-Lerner" conditions must be met in order for this last statement to be true. Assuming P, P* are fixed then we can write this relationship simply as NX = T(Y, e).
In contrast, the capital account is a function of the difference between domestic interest rates and foreign interest rates, specifically:
KA = k(r - r*)
where dk/d(r-r*) > 0 so that if domestic interest rates rise relative to foreign interest rates, then the domestic capital account increases as the greater relative attractiveness of domestic assets implies that domestic and foreign citizens will buy up domestic assets and drop foreign assets.
In Figure 8 we have superimposed the external balance locus BP on the IS-LM model. Every point on the BP locus represents a balance of payments equilibrium, BP = 0. Let us assume that exchange rates and price levels are fixed (thus e, P and P* are
exogenous) and foreign interest rates are fixed (r* exogenous). Thus, only r and Y are allowed to fluctuate. As a result, a given Y will yield a particular NX whereas a given r will yield a particular KA. So a point on the BP locus is a combination of r and Y that yields BP = NX + KA = 0.
mobility (kr = 0), then the BP curve will be completely vertical whereas if there is perfect capital mobility (kr = ï½¥ ), then the BP curve will be horizontal.
Under a fixed exchange rate regime, there is no obvious reason that we will necessarily be at BP = 0. In other words, the IS-LM equations will yield a particular (Y*, r*) that may or may not be where BP = 0. If equilibrium (Y*, r*) is to the right of the BP curve (e.g. at point F in Figure 8), then we have a balance of payments deficit (BP < 0); if (Y*, r*) is to the left of the BP curve (e.g. at point G in Figure 8), then we have a balance of
payments surplus.
The implications for fiscal and monetary policy are obvious. Beginning at the equilibrium point E in Figure 8 where BP = 0 prevails, we can immediately notice that a monetary policy expansion (a rightward shift in LM to LMï½¢ ) will yield a new equilibrium F which is below the BP curve, thus we obtain a balance of payments deficit. In other words, from the money supply increase, the consequent rise in Y has driven the current account towards deficit and the fall in r has driven the capital account towards deficit - thus the balance of payments is now in deficit. In contrast, starting from E, a fiscal policy expansion (rightward shift in IS to ISï½¢ ) will drive the economy to a balance of
payments surplus at point G. Here the reasoning is more subtle: the rise in Y has driven the current account towards deficit but the rise in r has driven the capital account
towards surplus. The net result depends on the relative slopes of the LM and BP curves. If LM is steeper than BP, then the net result is a balance of payments suplus; if LM is flatter than BP, then the net result is a balance of payments deficit. Thus, the relative sensitivity of international capital flows and income sensitivity of imports are the crucial factors in determining whether an expansionary fiscal policy leads to external deficits or surpluses.
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Although fiscal and monetary policy can lead to balance of payments surpluses and deficits, the implication of the Mundell-Fleming model is that one can use a combination of fiscal and monetary policy to increase output without inducing a balance of payments deficit or surplus. This is obvious again in Figure 8 where beginning at E, we can
undertake both a fiscal and monetary policy expansions (say, IS to ISï½¢ and LM to LMï½¢ ) in such a manner that the resulting equilibrium will be a balance of payments equilibrium (e.g. H in Figure 8).
Of course, things are never quite this simple. A balance of payments surplus corresponds to an excess supply of foreign currency which must be bought by the Central Bank; similarly, a balance of payments deficit implies there is an excess
demand for foreign currency which must be provided by the Central Bank. However, the Central Bank pays for its purchase of foreign currency with domestic currency and when it sells its foreign currency, it withdraws domestic currency from circulation. Thus, a balance of payments surplus/deficit will increase/decrease the money supply of the economy because the central bank must purchase/sell foreign exchange. As a result, balance of payments surpluses and deficits are not sustainable on their own.
For example, suppose there is a monetary policy expansion such that we obtain a balance of payments deficit (as at point F in Figure 8) and thus an excess demand for foreign exchange. The consequent fall in the supply of domestic money as the
government sells foreign exchange will gradually shift the LMï½¢ back to LM and thus equilibrium will return to E. In order to maintain the position at F, the Central Bank must conduct what are known as "sterilization policies". This means that by open market operations or some other domestic tool, the Central Bank increases the domestic money supply exogenously by exactly the same amount as it that money supply was decreased by the foreign exchange sales required to maintain the balance of payments deficit. Thus, the Central Bank "sterilizes" the monetary effects of balance of payments disequilibrium with monetary policy. To sustain a balance of payments surplus, the Central Bank's sterilization policy works in reverse.
maintain the assumption of fixed exchange rates and no sterilization policies, then it is obvious that fiscal policy is more effective than monetary policy. To see this, examine Figure 8 again. Beginning at E, a monetary expansion will shift LM to LMï½¢ and thus achieve a balance of payments deficit at point F. However, without sterlization, money supply will decline and consequently LM will shift leftwards back to LM and we return from F to E. Thus, monetary policy was completely ineffective at increasing output. In contrast, suppose that, beginning at E, we undertake a fiscal expansion and shift IS to ISï½¢ and therefore have a balance of payments surplus at point G. Without
sterilization, a balance of payments surplus implies that the money supply will increase, therefore shifting LM rightwards to LMï½¢ . The new equilibrium, at point H, is the resulting long-run position. Thus, output has increased tremendously in this case because the money supply movements in the absence of sterilization reinforce the original fiscal expansion. Thus, under fixed exchange rates, fiscal policy is highly effective and monetary policy is ineffective.
Of course, the effectiveness of fiscal policy depends on the degree of capital mobility. If there is no capital mobility so that BP is a vertical line, then notice that both
expansionary fiscal and monetary policies are completely ineffective in increasing output. This is because all expansions yield balance of payments deficits and thus lead to reductions in the money supply that bring output back down. In contrast, under perfect capital mobility, when the BP curve is horizontal, monetary policy is again ineffective, but fiscal policy is fully effective, i.e. output rises the full amount of the fiscal expansion as the consequent increase in money supply in the absence of sterilization implies that there will be absolutely no rise in interest rates.
We should note here that James Meade (1951) only considered the "no capital mobility" case (vertical BP). Consequently, in order for fiscal or monetary expansion to affect output, Meade argued that the BP locus must be shifted outwards by means of a different and often complicated class of policies seeking to affect net exports, e.g. exchange rate changes, subsidies, quotas, tariffs, etc. The analysis of the impact of such "expenditure-switching" policies were pursued by economists in the 1950s,
means of an optimal mix of fiscal and monetary policy without requiring any delicate and complicated expenditure-switching policies.
The analysis gets quite different under flexible exchange rates. Recall that if the real exchange rate rises, then NX falls for any level of income. As a result, there are two effects of a rise in exchange rates: the BP curve shifts upwards and the IS curve shifts leftwards. Conversely, a fall in the real exchange rate implies a rise in NX and thus a rightward shift in the BP curve and a rightwward shift in the IS curve. Under a flexible exchange rate regime, there will be none of the rises and falls in money supply due to balance of payments surpluses or deficits. Rather, balance of payments
surpluses/deficits result in rises/falls in the real exchange rate and thus movements in the BP and IS curves rather than the LM curve.
The implications of flexible exchange rates for fiscal and monetary policies can be visualized in Figure 9. Suppose we begin at E = (r*, Y*) at the intersection of the curves IS, LM and BP and suppose there is a monetary policy expansion from LM to LMï½¢ . As a result, we move from E to F, where we are in a balance of payments deficit. At F, there is excess demand for foreign currency and excess supply of domestic currency on the foreign exchange market. Under a flexible exchange rate regime, this implies that the real exchange rate will fall, therefore shifting BP rightwards to BPï½¢ and IS rightwards to ISï½¢ so that we are now at point J - at a higher equilibrium output level YJ*. Notice that external and internal balance obtain at point J as we have the
intersection of ISï½¢ , LMï½¢ and BPï½¢ . Thus, under a flexible exchange rate regime (and unlike a fixed exchange rate regime), monetary policy is quite effective in
increasing output.
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In contrast, fiscal policy under flexible exchange rates is more ambiguous. In Figure 9, beginning at point E, suppose we have a fiscal policy expansion that drives our IS curve to ISï½¢ ï½¢ at point G. However, at point G, we have a balance of payments surplus and thus there will be a rise in the exchange rate which, in turn, shifts BP upwards to BPï½¢ ï½¢ and IS backwards from ISï½¢ ï½¢ to ISï½¢ . A new equilibrium is achieved at point K, the intersection of ISï½¢ , LM and BPï½¢ ï½¢ . Obviously, in relative terms, such a fiscal expansion is less powerful under a flexible exchange rate regime than under a fixed exchange rate regime.
However, appropriate modifications to this story must be made if fiscal policy
The classical model:
Determination of Output and Employment • Output and employment are determined by the production function and the demand for labour and the supply of labour in the economy. • This is shown in the form of the following production function: • Q=f (K, T, N) where total output (Q) is a function (f) of capital stock (K), technical
knowledge (T), and the number of workers (N)
Dn • The demand for labour Dn and the supply of labour Sn determine the level of output and employment • The demand for labour as the function of the real wage rate: Dn =f (W/P) • Where Dn = demand for labour, W = wage rate and P = price level. • Dividing wage rate (W) by price level (P), we get the real wage rate (W/P)
Dn • The demand for labour is a decreasing function of the real wage rate, as shown by the downward sloping Dn curve in Fig. 2. • It is by reducing the real wage rate that more workers can be employed.
Sn • The supply of labour also depends on the real wage rate: Sn =f (W/P), where Sn is the supply of labour. • But it is an increasing function of the real wage rate, as shown by the upward sloping Sn curve in Fig. 2. • It is by increasing the real wage rate that more workers can be employed.
Equilibrium • When the Dn and Sn curves intersect at point E, the full
employment level Nf is determined at the equilibrium real wage rate W/P0. • If the wage rate rises from WP0 to WP1 the supply of labour will be more than its demand by ds.
unemployment • Now at W/P1 wage rate, ds workers will be involuntary
unemployed because the demand for labour d) is less than their supply (W/P1-s). • With competition among workers for work, they will be willing to accept a lower wage rate. Consequently, the wage rate will fall from W/P1 to W/P0.
The complete classical model of income and employment determination in an economy in Fig. 3.7. In panel (a) of this figure labour market equilibrium is shown wherein it will be seen that the intersection of demand for and supply of labour determines the real wage rate (W0/P0 ).
At this equilibrium real wage rate the amount of labour employed is N1; and, as explained above, this is full employment level. As depicted in panel (b) of the figure this full employment level of labour N1 produces Y1 level of output (or income).
In panel (c) of Figure 3.7 we have drawn 45° line that is used to transfer the level of output on the vertical axis in panel (b) to the horizontal axis of panel (c). In panel (d) we have shown the determination of price level through intersection of the curves of aggregate demand for and aggregate supply of output, as explained by the quantity theory of money. In the classical theory, aggregate supply curve AS is a vertical straight line at full-employment level of output YF.
Determination of Income and Employement: Complete Classial Model
Thus, given constant velocity of money V, the quantity of money M0 will determine the expenditure or aggregate demand equal to M0V according to which aggregate demand curve (with flexible prices) is AD0. It will be seen from panel (d) of Fig. 3.7 that intersection of vertical aggregate supply curve AS at fully-employment level output YF and aggregate demand curve AD0 determines the price level P0. With price level at P0, the money wage rate is W0 so that W0/P0 is the real wage rate as
determined by the intersection of demand for and supply of labour [see panel (a) of Fig. 3.7].
employed, the output cannot increase. Therefore, as depicted in panel (d) following the increase in money supply to M1, aggregate demand or expenditure will increase to M1 V and thereby causing aggregate demand curve to shift to AD1. As a result, price level rises from P0 to P1.
However, as explained above, with the given money wage rate W0, the rise in price level from P0 to P1 will cause a fall in real wage rate. As will be seen from panel (a), with the rise in price level to P1 real wage rate falls to W0/P1.
