I want to know the explanation of Phillips relation, the relation seen in type Ia supernovae(SN Ia with broader light curve is brighter). More Ni-56 implies a larger luminosity at peak but what about broader light curve?
Check this paper: http://adsabs.harvard.edu/abs/2001ASPC… 229… 287M
LargerNi-56 directly implies brighter at peak, since it is the dominant source of radiation energy at early times.
The broadness of a light curve depends on the light curve timescale, which depends on ejecta mass, opacity, and kinetic energy. Since SNe Ia are from WD progenitors, there are not much different in ejecta mass. From simulations, kinetic energy is roughly the same across broad parameters. This leaves opacity to be the origin of the broadness. Since Fe-group elements have higher opacity than intermediate mass elements (IME), and more Ni-56 implies more Fe-group/IME, it is to be expected that high Ni-56 implies high opacity that implies broader light curve.
The slide, that someone provided in your comment, explains the same idea here (with more references).
The Phillips curve is an economic concept developed by A. W. Phillips stating that inflation and unemployment have a stable and inverse relationship. The theory claims that with economic growth comes inflation, which in turn should lead to more jobs and less unemployment. However, the original concept has been somewhat disproven empirically due to the occurrence of stagflation in the 1970s, when there were high levels of both inflation and unemployment.
- The Phillips curve states that inflation and unemployment have an inverse relationship. Higher inflation is associated with lower unemployment and vice versa.
- The Phillips curve was a concept used to guide macroeconomic policy in the 20th century, but was called into question by the stagflation of the 1970's.
- Understanding the Phillips curve in light of consumer and worker expectations, shows that the relationship between inflation and unemployment may not hold in the long run, or even potentially in the short run.
The Phillips Curve (Explained With Diagram)
The Phillips curve given by A.W. Phillips shows that there exist an inverse relationship between the rate of unemployment and the rate of increase in nominal wages.
A lower rate of unemployment is associated with higher wage rate or inflation, and vice versa. In other words, there is a tradeoff between wage inflation and unemployment.
Reason: during boom, demand for labour increases. Due to greater bargaining power of the trade union, wage increases.
Thus, decrease in unemployment leads to increase in the wage (Fig. 13.6). But when wage increases, the firms cost of production increases which leads to increase in price. Therefore it is also called wage inflation, that is, decrease in unemployment leads to wage inflation. (Fig. 13.6)
This show that there exists inverse relationship between the rate of unemployment and growth rate of money wages.
The Phillips Curve shows that wages and prices adjust slowly to changes in AD due to imperfections in the labour market.
e.g. Assume: Initially, the economy is in equilibrium with stable prices and unemployment at NRU (U * ) (Fig. 13.7)
If Money supply increases by 10%, with price level constant, real money supply (M/P) will increase. This will lead to decrease in interest rate and thus increase in AD which in turn will lead to an increase in both wages and prices by 10% so that the economy reaches back to the full employment equilibrium level (U * ) i.e. at NRU.
Thus, Phillips curve shows that when wage increases by 10%, unemployment rate will fall from U* to U1. This will cause the wage rate to increase, but when wage increases, prices will also increase and eventually the economy will return back to the full-employment level of output and unemployment.
Rewriting equation 1 which shows Relation between wage inflation to unemployment
Equation shows that wages will increase only if U < U *
Since Phillips curve shows a trade off between inflation and unemployment rate, any attempt to solve the problem of inflation will lead to an increase in the unemployment. Similarly, any attempt to decrease unemployment will aggravate inflation. Thus, the negative sloped Phillips Curve suggested that the policy makers in the short run could choose different combinations of unemployment and inflation rates.
In the long run, however, permanent unemployment – inflation trade off is not possible because in the long run Phillips curve is vertical. Since in the short run AS curve (Phillips Curve) is quite flat, therefore, a trade off between unemployment and inflation rate is possible. It offers the policy makers to chose a combination of appropriate rate of unemployment and inflation.
I. Wage – Unemployment Relationship:
(Relationship between gw and the level of employment)
Why are wages sticky? Or Why nominal wages adjust slowly to changes in demand?
According to the Neo-Classical theory of supply, wages respond and adjust quickly to ensure that output is always at full-employment level. This is because wages and prices are completely flexible. Therefore, the economy will always produce full employment output but the Phillips curve suggests that wages adjust slowly in response to changes in unemployment to ensure that output is at full employment level.
The wages are sticky and therefore they move slowly over the time. They are not fully and immediately flexible, to ensure full employment at every point in time. To understand wage stickiness, the Phillips curve relationship is translated into a relationship between the rate of change of wages (gw) and the level of employment.
Wage employment relation shows that:
Wages in this period = wages in the last period but with adjustment in the level of employment.
There exists positive relationship between wages and employment because according to Phillips curve any attempt to decrease unemployment will lead to increase in wages. Decrease in unemployment means increase in employment. Therefore, when employment increases wages increase. Thus, the positively sloped WN curve shows that the wage rate paid by firms is higher when more hours are worked.
Joint points A, e0, and C, we get the wage employment line which is positively sloped. However, the extent to which wage responds to employment depends on e (response of money wage growth to change in unemployment).
If є is large — Unemployment has large affects on wage and WN line is steep.
Electronically Assisted Astronomy (EAA) with just a camera and Apple iPad. Why isn't there a real option out yet?
More than anything this is a question of why or why not?
I started back into the hobby and got more serious back in 2014 and my current telescope is an 8" Celestron Evolution. I joined a club and was very involved. I joined the board, but most of all I focused my attention on the outreach aspect of astronomy. Eyepiece observing has been my focus and im a keep it simple kind of guy. I saw folks persuing astrophotography as almost a natural progression of the hobby, but I stuck to eyepieces. I simply did not need any more stress in my life. I figured I could just appreciate other folk's images. Some folks in our club started focusing on EAA which seemed a little simpler as there were a lot less challenges and pieces of equipment and at outreach events I saw that visitors were gravitating to checking out the monitors of EAA observers as much as looking into eyepieces. I'm also in a state with not a lot of dark areas so imaging brings out a lot more detail than the eyepiece does especially on nebulae and galaxies.
Why in the world hasn't someone developed a hub box that regular ZWO or other popular cameras can plug into and then also plug into a tablet device? The hub could have conversion software built in or it could transmit to an app and be converted there. Why aren't there EAA options that work with a basic iPad? If someone did this you'd have to think the business model would be lucrative. I know image files and raw data that comes out of these cameras is large and stacking software is required, but ipads support stacking software in certain apps already so one would have to think this is doable.
Why hasn't something "reasonable" been brought to market as of yet..I know there are some expensive options out there probably or screen mirroring options, but again simple things that do their job sell well in most spaces.
What if the Phillips Curve is just ‘missing’?
Alternatively, some argue that the Phillips Curve is still alive and well, but it’s been masked by other changes in the economy: Here are a few of these changes:
Inflation expectations are well anchored.
Consumers and businesses respond not only to today’s economic conditions, but also to their expectations for the future, in particular their expectations for inflation. As then Fed Chair Janet Yellen noted in a September 2017 speech:
“In standard economic models, inflation expectations are an important determinant of actual inflation because, in deciding how much to adjust wages for individual jobs and prices of goods and services at a particular time, firms take into account the rate of overall inflation they expect to prevail in the future. Monetary policy presumably plays a key role in shaping these expectations by influencing the average rate of inflation experienced in the past over long periods of time, as well as by providing guidance about the FOMC’s objectives for inflation in the future.”
Inflation expectations have generally been low and stable around the Fed’s 2 percent inflation target since the 1980s. This stabilization of inflation expectations could be one reason why the Phillips Curve tradeoff appears weaker over time if everyone just expects inflation to be 2 percent forever because they trust the Fed, then this might mask or suppress price changes in response to unemployment. This is indeed the reason put forth by some monetary policymakers as to why the traditional Phillips Curve has become a bad predictor of inflation.
The labor market isn’t as tight as the low unemployment rate suggests:
Some argue that the unemployment rate is overstating the tightness of the labor market, because it isn’t taking account of all those people who have left the labor market in recent years but might be lured back now that jobs are increasingly available. Indeed, the long-run slide in the share of prime age workers who are in the labor market has started to reverse in recent years, as shown in the chart below.
If the labor market isn’t actually all that tight, then the unemployment rate might not actually be below its long-run sustainable rate. Another way of saying this is that the NAIRU might be lower than economists think. Proponents of this argument make the case that, at least in the short-run, the economy can sustain low unemployment as people rejoin the workforce without generating much inflation.
Some economists argue that the rise of large online stores like Amazon have increased efficiency in the retail sector and boosted price transparency, both of which have led to lower prices. Because this phenomenon is coinciding with a decline in the unemployment rate, it might be offsetting the increases in prices that would otherwise be forthcoming. But that doesn’t mean that the Phillips Curve is dead.
German wages, the Phillips curve and migration in the euro area
This post studies why wages in Germany have not borne strong increases despite a relatively strong labour market. I list four reasons why announcing the death of the Phillips curve – the negative relationship between unemployment and wage growth – is premature in Germany. One of the reasons I report is substantial immigration from the rest of the EU.
By: Guntram B. Wolff Date: November 29, 2017 Topic: European Macroeconomics & Governance
An important debate in the blogosphere concerns the possible death of the Philipps curve – i.e. the empirical relationship between inflation or wage growth on the one hand and the amount of slack in the labour market on the other hand. European Central Bank president Mario Draghi has recently confirmed his conviction that euro-area inflation rates will pick up as the slack in the labour markets closes. He expressed confidence that with sufficient patience, we will see an increase in inflation.
In this blog post, I analyse one important aspect of the debate for the euro area: wage developments in Germany. If Germany’s Phillips curve was dead and wages remained low, it would have far-reaching implications for inflation in the euro area as a whole. I find that the Phillips curve correlation is weaker after the crisis but is still present. Recent wage demands in collective bargaining and wage settlements have increased, while the substantial increase in immigration from the EU towards Germany could have contributed to the more muted recent wage rise. Germany already has a higher participation rate than the euro-area average, suggesting that labour force increases may be more muted. As the slack falls, wages should increase.
Germany’s wage developments have continuously outperformed those of the rest of the euro area since 2010
Germany’s wage developments have continuously outperformed those of the euro area since 2010, while the opposite was true before 2010. The same is also roughly true for real wages. Yet, wage developments have still been low and disappointing in Germany since 2010, hardly surpassing the 2% inflation goal of the ECB. Since there is productivity growth, German inflation rates have been mostly below 2% since the beginning of the 2009 crisis. And of course, arithmetic rules require German inflation to be well above 2% if the euro area is to achieve a 2% inflation average, as several countries will still need to run lower inflation rates to regain relative price competitiveness.
Reasons why declaring the Phillips curve in Germany dead may be premature
If the Phillips curve was strong and alive, shouldn’t we see much higher inflation rates in Germany, given that Germany’s unemployment rate is only around 3.7%? This question is particularly relevant in the euro area as higher inflation rates in Germany facilitate relative price adjustment between Germany, France and Italy. If Germany runs an inflation rate of below 2%, some southern European countries may have to run lower inflation rates in order to adjust their level of competitiveness relative to Germany. Will the break-down in Germany’s Phillips curve lead to deflation in the South?
Here are four reasons why this worry is, at least, exaggerated.
For a start, Germany’s Phillips curve seems to continue to exist as Figure 2 shows. Nominal wage growth is negatively correlated with the unemployment rate. The relationship also holds for the more recent period since the beginning of the crisis, though it is less evident (i.e. the fit is lower). This suggests that as the unemployment rate falls further, nominal wage growth should increase. This, in turn, should eventually push companies to also increase prices. The Phillips curve also exists for real wage growth, which suggests that German workers also see their real income increase.
Figure 2: Nominal wage growth Phillips curve, 1999Q1-2017Q3
Source: Bruegel, Statistisches Bundesamt, Eurostat
Second, the tighter labour market seems to gradually also lead to stronger increases in wage agreements in collective wage bargaining. One obvious example is the recent demand by the IG Metall union to increase wages by 6%, combined with demands for more flexibility on working hours. The increased demands are also starting to be visible in the economy-wide collectively agreed monthly earnings in Germany. As can be seen in Figure 3, in the second quarter of 2017 these have reached the highest increase since 2011.
Third, there has been one major labour supply effect that may have dampened short-term wage increases for some time: immigration. A basic mechanism for adjustment to wage differences and unemployment differences in a monetary union should be immigration. Accordingly, one would expect immigration in Germany to have increased since the start of the crisis, as the German labour market was doing relatively well.
The table below shows that total net immigration from the EU into Germany has increased from negative numbers in 2008 to well above 300,000 in 2015. Gross immigration has more than doubled and reached more than 900,000. We are focusing here on intra-EU migration as it is for a great part directly linked to the labour market, while immigration numbers from outside the EU are heavily influenced by motives other than access to the labour market. Immigrants coming for family reunification or refugees and asylum seekers are often not integrated into the labour market immediately.
We also look at immigration from the entire EU, as the EU has free movement of labour – i.e. labour mobility can occur from any EU country and is not solely restricted to the euro area. In fact, it is well established that often workers from eastern Europe’s non-euro-area countries move to different countries in the ‘West’ but then are more quick to move away. For example, a Romanian may have moved in the housing boom to Spain before the crisis only to now work on a German construction side. The break-down across countries shows that much of the increase has originated from Poland, Romania and Bulgaria. Yet, the numbers of immigrants with Italian, Greek and Spanish nationality have also risen substantially.
The numbers therefore suggest that a still somewhat slow wage growth in Germany can at least in part be attributed to immigration.
Fourth, labour force participation in Germany is already quite high and certainly significantly higher than the euro-area average. That suggests that further labour supply increases resulting from rising participation may be more muted in Germany than elsewhere. In turn, this could lead to higher inflation rates in Germany than elsewhere.
In conclusion, German wage and inflation developments are still quite low but there are encouraging signs that wage growth will pick up – and, with it, inflation rates. The slack in the German economy is certainly lower than elsewhere in the euro area. Immigration to Germany has played part of the role of adjustment to unemployment rates elsewhere, thereby also reducing the slack there and providing the ground for new wage increases. Overall, however, the adjustment is slow and wage settlements in Germany are certainly rather cautious. Yet, the Phillips curve is still alive and wages do adjust.
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A common reason given for low inflation in the post-crisis period is an influx of cheap goods, mainly from China, holding back prices.
But DePratto said this explanation fails to explain why prices for services haven’t increased, since you can’t import them. And it explain why inflation stalled after 2008, considering the price effects of China’s 2001 entry into the WTO had mostly faded by then.
Another common explanation is that e-commerce, which has lower overhead costs, is keeping prices low. But while online sales growth is outpacing that of traditional channels, digital retail sales still only account for about 2 per cent of total retail spending, TD says.
Though changes in the type of work have undoubtedly curbed bargaining power, TD noted, the sluggishness in wage growth is standard for both part time precarious sectors and full-time work.
Shapley was arguing in favor of the Milky Way as the entirety of the universe.  He believed that "spiral nebulae" such as Andromeda were simply part of the Milky Way. He could back up this claim by citing relative sizes—if Andromeda were not part of the Milky Way, then its distance must have been on the order of 10 8 light years—a span most contemporary astronomers would not accept. Adriaan van Maanen was also providing evidence to Shapley's argument. Van Maanen was a well-respected astronomer of the time who claimed he had observed the Pinwheel Galaxy rotating.  If the Pinwheel Galaxy were in fact a distinct galaxy and could be observed to be rotating on a timescale of years, its orbital velocity would be enormous and there would clearly be a violation of the universal speed limit, the speed of light. Shapley also backed up his claims with the observation of a nova in the Andromeda "nebula" that had briefly outshone the entire nebula, constituting a seemingly impossible output of energy were Andromeda in fact a separate galaxy.
Curtis on the other side contended that Andromeda and other such "nebulae" were separate galaxies, or "island universes" (a term invented by the 18th-century philosopher Immanuel Kant, who also believed that the "spiral nebulae" were extragalactic).  He showed that there were more novae in Andromeda than in the Milky Way. From this he could ask why there were more novae in one small section of the galaxy than the other sections of the galaxy, if Andromeda were not a separate galaxy but simply a nebula within Earth's galaxy. This led to supporting Andromeda as a separate galaxy with its own signature age and rate of nova occurrences. He also cited dark lanes present in other galaxies similar to the dust clouds found in Earth's own galaxy.
Curtis stated that if van Maanen's observation of the Pinwheel Galaxy rotating were correct, he himself would have been wrong about the scale of the universe and that the Milky Way would fully encompass it.
Later in the 1920s, Edwin Hubble showed that Andromeda was far outside the Milky Way by measuring Cepheid variable stars, proving that Curtis was correct.  It is now known that the Milky Way is only one of as many as an estimated 200 billion ( 2 × 10 11 )  to 2 trillion ( 2 × 10 12 ) or more galaxies,   proving Curtis the more accurate party in the debate. Also, astronomers generally accept that the nova Shapley referred to in his arguments was in fact a supernova, which does indeed temporarily outshine the combined output of an entire galaxy. On other points, the results were mixed (the actual size of the Milky Way is in between the sizes proposed by Shapley and Curtis), or in favor of Shapley (Curtis's galaxy was centered on the Sun, while Shapley correctly placed the Sun in the outer regions of the galaxy). 
It later became apparent that van Maanen's observations were incorrect—one cannot actually see the Pinwheel Galaxy rotate during a human lifespan.
The format of the great debate has been used subsequently to argue the nature of fundamental questions in astronomy. In honor of the first "Great Debate", the Smithsonian has hosted three more events. 
How does aggregate demand affect the phillips curve?
The Phillips curve is pretty closely related to aggregate demand - any change in the latter thus has reflections on the former.
The Phillips curve illustrates the inverse relationship between the rate of unemployment and the rate of inflation in a graphical manner. In simpler terms, a lower rate of unemployment (which means more people are without jobs) will correspond to a higher rate of inflation for an economy.
When output is relatively lower, fewer workers get employment thus shooting up the rate of unemployment. When the aggregate demand in an economy shoots up, output increases and GDP in real terms thus shoots up. This brings about two types of changes - a) more people get employed, so the employment rate moves up (or in other words, unemployment comes down) and b) prices rise. This translates into an upward movement along the Phillips curve.
(Source : http://www.swlearning.com/economics)
Stability of regional Phillips curves
Once an active central bank is incorporated into the analysis, it becomes clear that national data on inflation and unemployment are not useful for exploring whether a structural, or stable, Phillips curve relationship exists. In order to account for the complications raised by incorporating a central bank, we make use of regional data on unemployment and inflation.
We imagine an economy composed of numerous regions and a single central bank. Regional shocks make inflation rates and unemployment rates vary across regions. To simplify, we assume that regions are the same for the most part, but each faces different local disturbances, or shocks.
As before, the central bank aims to stabilize the inflation rate, which, for the central bank, is the average rate over all regions. Policy will therefore move to stabilize average national inflation. Monetary policymakers will react strongly to national shocks that affect inflation in all regions, but react very little to a shock that increases inflation in one region only, since this has little impact on the average. In the absence of central bank response to local conditions, a regional shock that affects unemployment in just a single region can therefore help identify the existence and size of a structural relationship between current labor market conditions and future inflation.
To frame the analysis graphically, consider Figure 3, which plots the regional-national differences for future inflation and current unemployment. Thus, the vertical axis displays the gap between future inflation in a given region and the inflation target set by the central bank the difference between current unemployment in the same region and average national unemployment is plotted on the horizontal axis.
The PC curve in Figure 10 is the Phillips curve which relates percentage change in money wage rate (W) on the vertical axis with the rate of unemployment (U) on the horizontal axis. The curve is convex to the origin which shows that the percentage change in money wages rises with decrease in the employment rate.
In the figure, when the money wage rate is 2 per cent, the unemployment rate is 3 per cent. But when the wage rate is high at 4 per cent, the unemployment rate is low at 2 per cent. Thus there is a trade­off between the rate of change in money wage and the rate of unemployment. This means that when the wage rate is high the unemployment rate is low and vice versa.
The original Phillips curve was an observed statistical relation which was explained theoretically by Lipsey as resulting from the behaviour of labour market in disequilibrium through excess demand. Several economists have extended the Phillips curve analysis to the trade-off between the rate of unemployment and the rate of change in the level of prices or inflation rate by assuming that prices would change whenever wages rose more rapidly than labour productivity.
If the rate of increase in money wage rates is higher than the growth rate of labour productivity, prices will rise and vice versa. But prices do not rise if labour productivity increases at the same rate as money wage rates rise.
This trade-off between the inflation rate and unemployment rate is explained in Figure 10 where the inflation rate (P) is taken along-with the rate of change in money wages (W). Suppose labour productivity rises by 2 per cent per year and if money wages also increase by 2 per cent, the price level would remain constant.
Thus point B on the PC curve corresponding to percentage change in money wages (M) and unemployment rate of 3 per cent (AO equals zero (O) per cent inflation rate (P) on the vertical axis. Now assume that the economy is operating at point B. If now, aggregate demand is increased, this lowers the unemployment rate to OT (2%) and raises the wage rate to OS (4%) per year.
If labour productivity continues to grow at 2 per cent per annum, the price level will also rise at the rate of 2 per cent per annum at OS in the figure. The economy operates at point C. With the movement of the economy from B to C, unemployment falls to T (2%). If points B and C are connected, they trace out a Phillips curve PC.
Thus money wages rate increase which is in excess of labour productivity leads to inflation. To keep wage increase to the level of labour productivity (OM) in order to avoid inflation. ON rate of unemployment will have to be tolerated.
The shape of the PC curve further suggests that when the unemployment rate is less than 5 per cent (that is, to the left of point A), the demand for labour is more than the supply and this tends to increase money wage rates.
On the other hand, when the unemployment rate is more than 5½ per cent (to the right of point A), the supply of labour is more than the demand which tends to lower wage rates. The implication is that the wage rates will be stable at the unemployment rate OA which is equal to 5½ per cent per annum. It is to be noted that PC is the “conventional” or original downward sloping Phillips curve which shows a stable and inverse relation between the rate of unemployment and the rate of change in wages.
Friedman’s View: The Long-Run Phillips Curve:
Economists have criticised and in certain cases modified the Phillips curve. They argue that the Phillips curve relates to the short run and it does not remain stable. It shifts with changes in expectations of inflation. In the long run, there is no trade-off between inflation and unemployment. These views have been expounded by Friedman and Phelps in what has come to be known as the “accelerationist” or the “adaptive expectations” hypothesis.
According to Friedman, there is no need to assume a stable downward sloping Phillips curve to explain the trade-off between inflation and unemployment. In fact, this relation is a short-run phenomenon. But there are certain variables which cause the Phillips curve to shift over time and the most important of them is the expected rate of inflation.
So long as there is discrepancy between the expected rate and the actual rate of inflation, the downward sloping Phillips curve will be found. But when this discrepancy is removed over the long run, the Phillips curve becomes vertical.
In order to explain this, Friedman introduces the concept of the natural rate of unemployment. In represents the rate of unemployment at which the economy normally settles because of its structural imperfections. It is the unemployment rate below which the inflation rate increases, and above which the inflation rate decreases. At this rate, there is neither a tendency for the inflation rate to increase or decrease.
Thus the natural rate of unemployment is defined as the rate of unemployment at which the actual rate of inflation equals the expected rate of inflation. It is thus an equilibrium rate of unemployment toward which the economy moves in the long run. In the long run, the Phillips curve is a vertical line at the natural rate of unemployment.
This natural or equilibrium unemployment rate is not fixed for all times. Rather, it is determined by a number of structural characteristics of the labour and commodity markets within the economy. These may be minimum wage laws, inadequate employment information, deficiencies in manpower training, costs of labour mobility, and other market imperfections. But what causes the Phillips curve to shift over time is the expected rate of inflation.
This refers to the extent the labour correctly forecasts inflation and can adjust wages to the forecast. Suppose the economy is experiencing a mild rate of inflation of 2 per cent and a natural rate of unemployment (N) of 3 per cent. At point A on the short-run .2 4 Phillips curve SPC1 in Figure 11, people expect this rate of inflation to continue in the future. Now assume that the government adopts a monetary-fiscal programme to raise aggregate demand in order to lower unemployment from 3 to 2 per cent.
The increase in aggregate demand will raise the rate of inflation to 4 per cent consistent with the unemployment rate of 2 per cent. When the actual inflation rate (4 per cent) is greater than the expected inflation rate (2 per cent), the economy moves from point A to B along the SPC1 curve and the unemployment rate temporarily falls to 2 per cent. This is achieved because the labour has been deceived.
It expected the inflation rate of 2 per cent and based their wage demands on this rate. But the workers eventually begin to realise that the actual rate of inflation is 4 per cent which now becomes their expected rate of inflation. Once this happens the short-run Phillips curve SPC1 shifts to the right to SPC2. Now workers demand increase in money wages to meet the higher expected rate of inflation of 4 per cent.
They demand higher wages because they consider the present money wages to be inadequate in real terms. In other words, they want to keep up with higher prices and to eliminate fall in real wages. As a result, real labour costs will rise, firms will discharge workers and unemployment will rise from B (2%) to C (3%) with the shifting of the SPC1 curve to SPC2. At point C, the natural rate of unemployment is re-established at a higher rate of both the actual and expected inflation (4%).
If the government is determined to maintain the level of unemployment at 2 per cent, it can do so only at the cost of higher rates of inflation. From point C, unemployment once again can be reduced to 2 per cent via increase in aggregate demand along the SPC2 curve until we arrive at point D. With 2 per cent unemployment and 6 per cent inflation at point D, the expected rate of inflation for workers is 4 per cent.
As soon as they adjust their expectations to the new situation of 6 per cent inflation, the short-run Phillips curve shifts up again to SPC3, and the unemployment will rise back to its natural level of 3 per cent at point E. If points A, C and E are connected, they trace out a vertical long-run Phillips curve LPC at the natural rate of unemployment.
On this curve, there is no trade-off between unemployment and inflation. Rather, any one of several rates of inflation at points A, C and E is compatible with the natural unemployment rate of 3 per cent. Any reduction in unemployment rate below its natural rate will be associated with an accelerating and ultimately explosive inflation. But this is only possible temporarily so long as workers overestimate or underestimate the inflation rate. In the long-run, the economy is bound to establish at the natural unemployment rate.
There is, therefore, no trade-off between unemployment and inflation except in the short run. This is because inflationary expectations are revised according to what has happened to inflation in the past. So when the actual rate of inflation, say, rises to 4 per cent in Figure 11, workers continue to expect 2 per cent inflation for a while and only in the long run they revise their expectations upward to 4 per cent. Since they adapt themselves to the expectations, it is called the adaptive exceptions hypothesis.
According to this hypothesis, the expected rate of inflation always lags behind the actual rate. But if the actual rate remains constant, the expected rate would ultimately become equal to it. This leads to the conclusion that a short-run trade off exists between unemployment and inflation, but there is no long run trade-off between the two unless a continuously rising inflation rate is tolerated.
The accelerationist hypothesis of Friedman has been criticised on the following grounds:
1. The vertical long-run Phillips curve relates to steady rate of inflation. But this is not a correct view because the economy is always passing through a series of disequilibrium positions with little tendency to approach a steady state. In such a situation, expectations may be disappointed year after year.
2. Friedman does not give a new theory of how expectations are formed that would be free from theoretical and statistical bias. This makes his position unclear.
3. The vertical long-run Phillips curve implies that all expectations are satisfied and that people correctly anticipate the future inflation rates. Critics point out that people do not anticipate inflation rates correctly, particularly when some prices are almost certain to rise faster than others.
There are bound to be disequilibria between supply and demand caused by uncertainty about the future and that is bound to increase the rate of unemployment. Far from curing unemployment, a dose of inflation is likely to make it worse.
4. In one of his writings Friedman himself accepts the possibility that the long-run Phillips curve might not just be vertical, but could be positively sloped with increasing doses of inflation leading to increasing unemployment.
5. Some economists have argued that wage rates have not increased at a high rate of unemployment.
6. It is believed that workers have a money illusion. They are more concerned with the increase in their money wage rates than real wage rates.
7. Some economists regard the natural rate of unemployment as a mere abstraction because Friedman has not tried to define it in concrete terms.
8. Saul Hyman has estimated that the long-run Phillips curve is not vertical but is negatively sloped. According to Hyman, the unemployment rate can be permanently reduced if we are prepared to accept an increase in inflation rate.
James Tobin in his presidential address before the American Economic Association in 1971 proposed a compromise between the negatively sloping and vertical Phillips curves. Tobin believes that there is a Phillips curve within limits.
But as the economy expands and employment grows, the curve becomes even more fragile and vanishes until it becomes vertical at some critically low rate of unemployment. Thus Tobin’s Phillips curve is kinked-shaped, a part like a normal Phillips curve and the rest vertical, as shown in Figure 12.
In the figure Uc is the critical rate of unemployment at which the Phillips curve becomes vertical where there is no trade-off between unemployment and inflation. According to Tobin, the vertical portion of the curve is not due to increase in the demand for more wages but emerges from imperfections of the labour market.
At the Uc level, it is not possible to provide more employment because the job seekers have wrong skills or wrong age or sex or are in the wrong place. o Regarding the normal portion of the Phillips curve which is negatively sloping, wages are sticky downward because labourers resist a decline in their relative wages.
For Tobin, there is a wage-change floor in excess supply situations. In the range of relatively high unemployment to the right of Uc in the figure, as aggregate demand and inflation increase and involuntary unemployment is reduced, wage-floor markets gradually diminish. When all sectors of the labour market are above the wage floor, the level of critically low rate of unemployment Uc is reached.
Like Tobin, Robert Solow does not believe that the Phillips curve is vertical at all rates of inflation. According to him, the curve is vertical at positive rates of inflation and is horizontal at negative rates of inflation, as shown in Figure 13.
The basis of the Phillips curve LPC of the figure is that wages are sticky downward even in the face of heavy unemployment or deflation. But at a particular level of unemployment when the demand for labour increases, wages rise in the face of expected inflation. But since the Phillips curve LPC becomes vertical at that minimum level of unemployment, there is no trade-off between unemployment and inflation.
The vertical Phillips curve has been accepted by the majority of economists. They agree that at unemployment rate of about 4 per cent, the Phillips curve becomes vertical and the trade-off between unemployment and inflation disappears. It is impossible to reduce unemployment below this level because of market imperfections.