## DADSAS and Mundell Fleming a look behind the scene

Let us pause to look at what is going on beneath the surface of the DAD-SAS model as displayed in the p-Y diagram. The purpose of this interlude is to emphasize that whatever happens in the DAD-SAS model can be traced back to the Mundell-Fleming model, and vice versa. We look at the immediate response to an increase in money growth first, which moves the economy up along SAS j.

The short-run response in DAD-SAS and IS-LM-FE representation In Figure 8.8 the economy is in equilibrium at point A. The upper panel shows this in the DAD-SAS model. The lower panel depicts it in the Mundell-Fleming model.

For convenience, suppose the initial equilibrium is non-inflationary, that is pq = mo = 0. In period ! the money supply growth rate increases from 0 to !0%, so that the nominal money supply rises by !0%. In the Mundell-Fleming model, where prices are considered fixed, the real money supply also increases by !0%. This shifts LM to the right into the broken blue position. If the price level really did not respond, the exchange rate would depreciate just enough to shift IS right into the broken blue position, raising income to Yc. In the upper

Figure 8.8 (Flexible exchange rates.) An acceleration of money growth shifts DAD to the right. In the Mundell-Fleming model this shifts LM and, through endogenous depreciation, IS to the right into the broken blue positions. Since insufficient supply at the old price level triggers inflation, the economy moves from C to B along DADi in the upper panel. In the lower panel the rising price level reduces the real money supply and the real exchange rate. LM and IS move back into the solid light blue position. Income has increased from Y* to YB, and not to YC as it would have if the SAS curve was horizontal.

panel, income would also have risen to Yc if inflation had stayed at 0. However, this would have required the SAS curve to be horizontal.

Now SAS is not horizontal, but positively sloped. This means that the labour market is not prepared to supply output Yc at unchanged prices. Only as prices rise (or inflation goes up) and real wages fall, will output increase along SASi. Given DADi, period 1 equilibrium in the upper panel is at B. How does this translate into the lower panel? Well, the increase of inflation from 0 to pi nibbles away at the real money supply increase. As a result, LM shifts back left into the light blue position, bringing the economy to point B. At the same time, inflation reduces the real exchange rate, shifting IS back left into the light blue position.

So, after taking into account the price changes required to bring aggregate supply up to meet aggregate demand, the Mundell-Fleming model gives the same income response to the money supply increase as the DAD-SAS model. The drawback of the Mundell-Fleming model is that it does not tell us what price changes do indeed occur as we move from one equilibrium to another.

The long-run response in DAD-SAS and IS-LM-FE representation Let us now look at how the long-run adjustment from A to A' is reflected in the MundellFleming diagram (Figure 8.9). First, note some properties of A'. In the new equilibrium, the movements of LM and IS that occurred during the transition from A to A' have ended. So the real money supply, which determines the position of LM, remains constant, meaning that money and prices grow at the same rates: p = m. The real exchange rate, which determines the position of IS, must be constant as well, meaning that depreciation equals inflation (supposing world inflation is 0): e = p. So p, m and e are all 10%. If our currency depreciates by 10% period after period, the market sooner or later expects this. Financial investors are then only prepared to hold domestic bonds if these carry interest rates 10% higher than the world interest rate -as compensation for the anticipated loss in value through depreciation. So the new position of FE is at iW + 10, which identifies the new long-run equilibrium A' in the lower panel of Figure 8.9. The fact that both LM and IS pass through A' offers two new insights:

SAS,

SAS,

SASa

No-inflation * equilibrium

No-inflation * equilibrium

SASa

Expected | |

inflation of | |

10% shifts | |

IS up |
Reduction of real money supply shifts LM up Reduction of real money supply shifts LM up Expected depreciation of 10% shifts FE up Expected depreciation of 10% shifts FE up Income Figure 8.9 (Flexible exchange rates.) After inflation has adjusted, DAD and SAS are in the light blue positions and the economy has moved from A to A' (upper panel). Inflation is at 10% permanently, and e also is 10%. In equilibrium this depreciation must be expected. This shifts the FE curve up by ten percentage points in the lower panel. The intersection between this new FE line and the vertical line over potential income marks A'. To shift LM up to pass through A', the real money supply must have fallen. IS shifts up because it must go up by ten percentage points to keep the real interest rate unchanged. The real interest rate is the nominal interest rate (as observed in the market) minus the inflation rate. It deducts from nominal interest payments the purchasing power lost due to price increases. Maths note. Repeating the derivation of the IS curve in Chapter 5 with the new investment function I = I - b(i - p) gives the new IS curve for an inflationary environment Since di/dp = 1,a one percentage point rise in p shifts IS up by 1 percentage point. 1 Since LM has shifted up compared with where it was when the equilibrium was A, the real money supply has fallen. Do not confuse this with the fact that once we are at A', inflation equals money growth and M/P remains constant. During the transition from A to A' the sum of all price changes must have been larger than the sum of all changes in the money supply. The resulting reduction of the real money supply is needed, since individuals want to hold less (real) money when interest rates are at 10% (as at A') than at interest rates of 0% (that applied at A). 2 It is tempting, but wrong, to think that for similar reasons the real exchange rate must have depreciated to shift IS out and make it go through A'. To see why this is wrong, we now need to stress the distinction between the nominal interest rate i and the real interest rate r k i — p that results after we deduct inflation from the nominal interest rate. This distinction was not important in earlier chapters in which the price level was considered fixed. There i was both the nominal and the real interest rate. Now, with inflation brought into the picture, we need to recognize that the interest rate that determines investment decisions of firms is the real interest rate. Suppose a bank lends £100 for one year to a firm that wants to invest. At a 5% interest rate the bank will have £105 at the end of the year. If prices have remained the same, the purchasing power of the £100 lent out has increased by 5%. Therefore, the real return, or the real interest rate, is 5%. Now assume that same scenario, except that prices rose by 5%. Then the £105 which the bank has at the end of the year only buys what the £100 would have bought at the beginning of the year. Everything costs 5% more. The bank has not received any real compensation for lending the money. The real interest rate is 0. To receive the same real compensation that the bank received when there was no inflation, the nominal interest rate would have to be 10%. Then the real interest rate would be r = 10% — 5% = 5%. With the same argument, the firm that borrows the money also knows that, in the face of inflation, the pounds it gives back to repay the loan will be worth less than the pounds it received. Thus, what is relevant for firms deciding how much to borrow and which investment projects to undertake is the real interest rate which takes account of inflation. Rewriting the investment schedules as I = I — b(i — p), the IS curve shifts up one by one if inflation goes up. The increase of inflation from 0 to 10% shifts the IS curve up into A', since the nominal interest rate needs to be 10 percentage points higher to make firms undertake the same level of investment as at A. No change in the real exchange rate is needed. The decomposition of the nominal interest rate into the real interest rate and inflation is known as the Fisher equation. Augmented with the assumption of an approximately constant normal real interest rate r, it constitutes a theory of the behaviour of nominal interest rates: Fisher equation (8.7) Keep in mind, however, that this version of the Fisher equation only holds in equilibrium, on EAS. During booms the interest rate falls below what equation (8.7) says; during recessions it rises above what equation (8.7) says. The Fisher equation (named after the American economist Irving Fisher, 1867-1947) says that interest rates change if either the real interest rate or inflation changes.The implication that a one percentage point increase in inflation raises the nominal interest rate by one percentage point is called the Fisher effect. The key reason for this is that firms and banks do not know inflation when they agree on the interest rate for a loan, but need to base decisions on inflation expectations. Equation (8.7) does not qualify as a short-run relationship because inflation may differ from expected inflation, and because income may be above or below normal levels for a while. |

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