# Discuss the relationship between inflation and output

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## Abstract:

## Introduction:

## Literature Review:

## Theoretical framework:

## 3.1) Static model

In this section, I discuss the interaction of goods and financial market within a static model. I provide theoretical and analytical discussion of the relationship between inflation and output while using IS-LM and AD-AS general framework. I start using the simplest IS and LM curves, then advancing the discussion to aggregate demand AD curve which is derived from IS-LM equations. Subsequently I introduce the AS curve which is based on the nominal wages in the labour market and price setting equation of the firms. I am aiming to show graphically that how inflation affects the output in short and long run taking other exogenous and behavioural variables to be constant and only one variable to change at a time. Summarizing the first section of static model with graphical presentation, in the later part I will discuss Romer's approach of real variables in Keynesian model. This will help us to understand the effective relationship between inflation and output in a static model.

## 3.1.1) IS-LM Framework

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IS-LM has played a central role in analyzing comparative static relationships between various variables. This framework simplifies the complexities of economics by analyzing the aggregate relationships (Romer 2000, pp. 149). IS-LM synthesis explains the relationship between two variables i.e. output and interest rate. The IS curve is downward slopping and it is derived from the goods market concerning the relation that a higher interest rate reduces the demand for goods at a given level of income, leading to a decrease in the equilibrium level of output (Romer 2000, p. 150). The LM curve is upward slopping and it is derived from the financial or money market. It show that an increase in income leads to an increase in demand for money which causes an increase in interest rate (Blanchard 2009; p, 113)

IS Curve)

LM Curve)

In the above mentioned IS and LM relations, IS curve shows that an increase in the real interest rate reduces the level of output given the value of G and T. Whereas "LM" curve describes the relationship between real balances; M/P and the output; Y at a given rate of interest. An increase in the output increases the demand for money and the interest rate (Blanchard, 2009, p. 161)).

The interaction of IS-LM creates equilibrium between goods and money markets at the initial equilibrium point A; desired level of output at given rate of interest as shown in diagram (1). For the purpose at hand I am interested to know the effects of a change in money supply. Taking into account the fact that changes in money supply will not directly affect the IS curve but affecting LM curve specifically. By increasing the supply of money in the economy, the LM curve shifts downward along the IS curve from LM to LM'. The equilibrium changes from A to B; it means excess in money supply will cause a fall in interest rate which will increase output level (Blanchard 2009; p, 119).

Interest rate

LM

LM'

i A

i' B

IS

Figure 1: Graphically, monetary expansion leads to excess supply of money in the money market therefore interest rate falls and output level increases due increase in investment level (Source: Blanchard 2009, p.119) Y Y' Output

For given level of income/output, an increase in the supply of money will decrease the interest rate in money market therefore a lower rate of interest will give further incentive to investors to invest more. When investment level increases, the level of output will also increase in the economy depending on the slope of the curves. As a result of expansionary monetary policy, interest rate falls and output level increases but it does not affect the price level directly. In IS-LM analysis the price level is not explicitly mentioned and it is assumed to be constant. If this is the case then it cannot unambiguously analyse the effects of inflation on output. In 1960s and 1970s inflation became a core concern of economic policy. Therefore the effect of inflation on output was not clear in IS-LM framework. For this purpose, the AD-AS synthesis was extended in order to endogenise inflation and analyse the effect of price level on output which I am discussing in the following section (Romer 2000 pp. 151).

## 3.1.2) AD-AS Model

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AD (The aggregate demand) curve and price level: The aggregate demand relationship shows the effect of price level on the aggregate quantity of goods demanded (Y) i.e. C + I + G. This relation can be derived from the equilibrium conditions of goods and financial markets; i.e. IS-LM relationship. AD curve is negatively sloped; for a rise in the price level the aggregate demand falls, causing a reduction in output in the economy (Abel and Bernanke, 2008, p. 334).

Suppose the price level is changed what effects will it have on output? Looking at (a) and (b) of figure (2) the equilibrium point is at the intersection point of IS and LM curves i.e. A and B at given level of price and output level along the demand curve. Considering a rise in price level at the given level of nominal stock of money "M" If the price level increases, it will decrease the real stock of money "M/P". This means the stock of real money will decrease therefore the "LM" curve will shift upward, causing a rise in the interest rate. This will reduce the demand for goods therefore the output level is lower than before. On the other hand the aggregate demand level also falls simultaneously due an increase in price level. Considering both the effects into account, as shown in figure (a) and (b) of diagram (2), equilibrium moves from A to A' and B to B'. Summarizing the effect of an increase in the price level, will reduce the real balances of money. The money contraction leads to an increase in interest rate decreases investment which will decrease the output and demand for goods and service; shown in figure (3) (Blanchard 2009; p, 160-162).

Figure 2: The derivation of aggregate demand curve, AD curve shows the relationship between price level and output; source (Blanchard, 2009, p. 161)

Aggregate demand (AD) curve derived from the Keynesian IS-LM framework was based on assumption of fix-price, this ignored effective demand for labour and labour market adjustments and it also could not explain price adjustments in the short-run. Hence, it did not explain the supply side effects of inflation on output. AS curve was extended to IS-LM AD model to develop a model that take flexible wage and price adjustments into consideration in order to determine output and price level in a unified framework (Rao, 2007, p. 416).

AS (Aggregate supply) curve and price level: The aggregate supply curve implies the effect of output on the price level. AS curve is derived from labour market and firm's price setting behaviour. Basic assumptions are made; first, wages in labour market are set according to expected price level and second, expected price level is equal to actual price level. The wage and price setting relations are shown in equation (1) and (2) (Blanchard, 2009, pp 158).

Wage determination equation

And

Price setting equation

Equation (1) indicates that nominal wages depend on the expected price Pe, negatively associate to unemployment level u and positively associated to all other factors affecting the wages in the labour market (minimum wages, unemployment benefits etc). Equation (2) shows that actual price level P depend on the mark-up times nominal wages.

Since I am interested to know the actual price level in the market therefore solving the equations (1) and (2) for "P" actual price shows that

Equation (3) gives us a relationship where the actual price level "P" depends on the expected price level "Pe", on the mark up (), the unemployment rate "u" and other factors that affect the wages and price level.

Now, I would like to know the unemployment rate u in the labour market because unemployment rate is positively associated to output, as it is clear from the production function. We know from the definition that the rate of unemployment u is equal to number of people unemployed U over total labour force L and the number of unemployed people U is equal to total labour force L minus number of people employed N. In addition to this we know from the production function, that to produce one unit of output requires one worker. Hence, N is equal to output Y.

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Examples of our workNow, for the underline purpose to show relation between price level and output, replacing u into equation (3); we get the expression in equation (4).

This equation shows that an increase in output level will lead to an increase in the price level through the positive effects of output on employment level which will increase nominal wages and this will cause an increase in the price level. It also specifies another characteristic that an increase in the expected price level leads to an increase in the actual price level (Blanchard 2009; p, 158-159).

Looking at figure (3), The AS curve is an upward sloping and the equilibrium point is A, it is just because output (Y) equals the natural level of output "Yn" and actual price level P becomes equal to expected price level Pe. Supposing that price expectation is revised and now the expected price level is more than the previous expected price (Pe > Pe'). Ceteris paribus, the effect of increase in the expected price level will shift the AS curve upward, as we can see the below graph.

## Figure 3: shows the effect of an increase in the expectation of price level on AS curve, while the output level is at natural rate of output (Source; Blanchard 2009, p...)

## Short run and the long run equilibrium

The old Keynesian static model was criticized for giving much importance to short-run equilibrium only and ignoring the fact that investment leads to increase in capital stock. Therefore capital accumulation will have an effect on the long-run equilibrium in the economy (Backhouse and Laidler 2003; p. 17). The fact, the traditional static model had a clear shortcoming by ignoring the long-run equilibrium because the aggregate demand has a medium and long-run effects therefore long-run equilibrium was introduced to (Krishna & Skott 2005, p. 11). In the following section I discuss the effects of changes in actual price or price expectations on output in the short-run as well as long-run.

Looking at the economy which is at equilibrium point A shown in figure (4) where the output is equal to natural rate of output and the price level equals to expected price level. Suppose, if the actual price exceeds the expected price level, there will be a new equilibrium B

Price

AS

P B

Pe A

AD

Figure 4: Equilibrium changes when actual price is more than expected price level and the actual output exceeds the natural rate of output in short run (source, Blanchard 2009, p ...) Yn Y Output, Y

Therefore in the short run output exceeds the natural rate of output due to an increase in the price level but now the question arises whether will it remain at new equilibrium or it comes back to natural rate of output. The output eventually in long run will move towards new equilibrium which is at natural rate of output. It is just because when the actual price level is above the expected price level and employers had set nominal wages based on expected price level therefore the nominal wage for the next period will be revised with a higher expectation of an increase in price level. Thus price level will rise from P to Pe and then to Pe'. Since expected price level will go higher and higher therefore the "AS" curve will move up along "AD" curve, depicted in figure (5) (Blanchard 2009; p, 164-165).

Price Level

AS''

AS'

AS

Pe' B''

B'

P B

Pe A

AD

Figure 5: The graph shows revised expectations of price level and economy moves towards natural rate of output in the long run (source, Blanchard 2009, p ...) Yn Y Output, Y

The effect of inflation on output is positive in the short run however, the output gradually moves back to its natural level of output in the long run but price level still remains higher. Now let's analyse a situation where prices are falling or there is deflation in the economy. What can be the effects of deflation on output?

## 3.3.3) David Romer's Approach in Keynesians model

David Romer (2000) constructed a new model by outlining the shortfalls of IS-LM approach. He labelled this as Keynesian macroeconomics without LM curve and presented in framework of IS-MP and AD-IA synthesis where LM is replace by MP (Monetary Policy) and AS is replaced by (IA) inflation adjustment. His assumptions are as; first central banks target real interest rate instead of money supply. Second the price level does not completely and immediately adjust to economic disturbance therefore the lack of perfect nominal adjustments, monetary changes affect the real variables in the short run.

He argued that, though IS-LM is an effective tool in understanding the Keynesians and Monetarist economic policies which is based on basic assumption that central banks target the money supply but this assumption does not solve the problem. Therefore he replaced this assumption by i.e. central banks targets the real interest rate in the economy. This assumption is based on the explanation of IS-LM synthesis. He mentioned that a higher interest rate in a closed economy will reduce the investment demand which will reduce the general consumption level therefore output will decline. In the same manner in an open economy a higher interest rate will appreciate the domestic currency which will reduce net exports. This will decrease the level of output in domestic economy. Thus IS and interest rate relationship shows a negative relation. The next relation in IS-LM framework is the LM curve which shows that the demand for money will increase with a rise in income level. If money supply is assumed to be constant, an increase in income level will increase demand for money therefore the rate of interest is increase. Hence there is a positive relation between interest rate and output (Romer 2000, pp. 149-152).

By stating the assumption that central banks target the real interest rate instead of money supply, the IS-LM and AS-AD synthesis gives realistic results and there are many advantages in solving various issues concerned with the inflation-out relationship. The reasons why this assumption is more realistic; first the central banks frequently revise their nominal interest rate due to usual fluctuation in the expectation of inflation and second in IS-LM framework, for goods market real interest rate is taken but for LM nominal interest rate is considered. This creates complexities due to real and nominal interest rate in the model so to avoid such complications real interest rate is considered for both the markets (Romer 2000, pp. 156).

The modified model of IS-LM and AS-AD i.e. IS-MP and AD-IA by replacing LM curve into monetary policy (MP) and AS into inflation adjustment (IA) gives more realistic approach. The target of interest rate by central banks would the function of interest rate plus inflation and real interest rate is assumed to be an increasing function of inflation r = r (Ï€). It is just because central bank policy is to achieve low inflation and high output mix. If inflation is high the central bank is concerned with increasing interest rate and curbing the inflation (Romer 2000, pp. 155-156).

Now looking at diagram (6) I am interested to evaluate the effect of a change in inflation rate, for the purpose assuming an increase in inflation in IS-MP and AD-AI model. The first effect of an increase in inflation will decrease the output. It means that in the short run inflation will affect the real variables negatively. There is clear evidence that as the price level increase according to model the output level will decrease in the short-run. However, in the long-run equilibrium the economy come back to its natural rate of output.

Figure 6: Negative relation between inflation and output with the real interest rate as an increasing function of inflation rate Source: (Romer 2000, 158)..

Figure 7: Aggregate demand curve and inflation adjustment in the short and long-run. If output level is less than natural level, inflation falls until output reaches to its natural level and vice versa Source: (Romer 2000, 159).

ELR

Y

Yn

IA

IA'

AD

## ï€

ESR

Inflation

OutputSimilarly, IA curve will move along AD curve, it responds to the level of output. If output is below the natural level of output, inflation will decrease and output will increase. However, if output is above the natural rate of output then the inflation will rise and IA curve move upper along the AD curve. It is clearly shown in figure (7)

## ï€

Summarizing the static models discussed in this chapter, it is important to underline the difference and effectiveness of these static approaches in evaluating the relationship between inflation and output. The AD-IA and IS-MP approach is more realistic and simple to understand. It avoids the complexities of nominal and real variables. It is effective for policy making. Though both; ISLM-ASDS and ISMP-ADIA give similar results but there are still differences; first, in the AS-DS model show price-output relationship but any negative demand shock causes a decrease in price lower than it should have been. Thus, in AD-IA inflation is taken endogenously to analyse the relation between inflation and output (Romer 200, p.157). Second, the assumption of inflation adjustment makes the model easier to solve. For example, by assumption it states if output is below natural rate, inflation will fall and vice versa, whereas in the first approach simultaneity of variables makes it difficult (Romer 200, p.159). Third in the Romer's approach the dynamics are simple. For example in IS-LM-AS approach if inflation changes, it affect the LM curve which will shift but as the result of shock in the economy the problem of overshooting its natural rate which produces spiral in inflation-output space (Romer 2000, p. 160) and finally in the new approach the ambiquity of money market is easy to understan. It allows us to understand how money is created and how central bank works to target the supply of money which is based on the real interest rate (Romer 2000, p. 162).