As for inflation, monetarists see it even simpler and easier to tackle. This is because in the long term, as Friedman said at the Wincott Memorial Lecture in London in 1970, inflation is always and everywhere a monetary phenomenon. Therefore, what it is needed is that the government, i.e. the central bank, keeps the growth of monetary supply in line with the long term real GDP growth which in turn is determined by the trend of its potential. The central bank may only need to take into account changes in the velocity of circulation of the money stock and adjust the money supply growth accordingly, i.e. slightly increasing the latter when its velocity of circulation decreases and vice-versa.
In summary, the monetarist/neoliberal response is that, yes, it is possible to reduce unemployment without increasing inflation if the government intervention in the labor market is reduced, while monetary policy controls money supply adequately. More in general, monetarist and neoliberals will also response positively to the even bigger challenge of keeping both inflation and unemployment low simultaneously, if the labor market can function freely, without exogenous imposed rigidities and the money supply growth is kept in line with potential GDP growth.
The classical Keynesian approach takes indeed a quite different approach, in particular in relation to the functioning of the labor market. Keynesians do not see the labor market as just another market which left alone, without interferences, will clear the excess of labor supply by adjustment of real wages. J. M. Keynes himself put a lot emphasis in money illusion by which economic agents in general and workers in particular will focus its economic decisions on nominal wages rather than real wages. Moreover, Keynesians firmly belief that wages -both nominal and real- are sticky downwards, i.e. it just an economic reality that wages do not adjust to the excess of labor supply or unemployment. In other words, the labor market is a special market that cannot be compared to the generally more flexible functioning of the rest of the economy.
The key element splitting the view of Keynesians on one hand and monetarist/neoliberals on the other is the degree that the labor market left alone can function to eliminate (involuntary) unemployment. The Keynesian response is indeed negative. And this is the major challenge of macroeconomic policies. Inflation has been seen traditionally by Keynesians as a less relevant macroeconomic problem.
There is a concrete traditional Keynesian response to the question of whether it is possible to keep low both unemployment and inflation: the Phillips Curve. A Professor of Economics at the LSE showed in 1957 that there is an inverse relationship between unemployment and nominal wages using data for UK for a long period. Professor Phillips in fact discovered that there was a stable relationship between annual changes in unemployment and in nominal changes. The higher the unemployment rate was, the lower the nominal wages growth. The economic rational is relatively straightforward: the more unemployment there is, the less bargaining power workers and their trade unions will have to negotiate increases in nominal wages. The same relationship was later on established between unemployment and changes in the general price level. Since then, Keynesians have argued that there is a trade-off between unemployment and inflation and that macroeconomic policies face the dilemma of having to choose between a relatively low level of one of them and -almost unavoidably- a higher level of the other variable. The classical Keynesian view is that the Phillips curve is relatively stable. In other words, the traditional Keynesian response to the question is negative.
However, in 1967 Milton Friedman in a speech to the annual meeting of the American Economic Association explained for the first time that the Phillips curve is not stable and that its position is affected by the phenomenon of inflation expectations. The higher are the expectations of future inflation by the economic agents the higher will be the inflation associated to each unemployment rate in the economy. This was in a revolutionary analysis which confirmed during the economic crisis of the second half of the 1970´s and beginning of the eighties. Thus, even confronted with the existence of this trade-off, the monetarists will answer, yes, if the Phillips curve shifts leftwards as a consequence of lower inflation expectations in the economy. Indeed, the monetarist firmly believed -and somehow were backed by inflation and unemployment developments during the seventies and eighties- that if inflation expectations are low, the Phillips Curve will shift leftwards and downwards within the y/x axis to allow low inflation and low unemployment. How to achieve it? We know it: by a prudent monetary policy as well as no government or trade union interventions in the labor market.
Later on during the eighties, the monetarist developed a new core concept which reflects their (successful) synthesis of the economic debate on the trade-off between unemployment and inflation: they called it the Natural Rate of Unemployment (NARU). This is the rate which happens in the long term and that it is compatible with whatever possible rate of inflation. The later is determined in the long term by the money supply while the natural rate of unemployment is the equilibrium rate in the long term, when there is only voluntary and/or frictional unemployment.
The new Keynesians reacted in the nineties by formulating a very similar concept, the so-called Non-Accelerating Rate of Unemployment (NAIRU). In practice, both concepts are very similar or even identical in some of their features. However, there remains as a key difference that the Keynesians do not consider it as long term equilibrium to the extent that there will be still the possibility for including involuntary unemployment, e.g. structural unemployment.
In conclusion, during the last couple of decades, it is probably right to say that there has been a convergence between monetarists and Keynesians and both approaches will response to the theme of this essay along a mainly common line of arguments. This also applies to a great extent to what macroeconomic policies can do to bring about both low inflation and low unemployment, or reduce unemployment without increasing inflation. There is now almost a unanimous view that long term inflation can only be achieved by a strict monetary policy which control adequately money supply and interest rates in the economy. At the same time, it is also generally admitted that in the long term low unemployment could be achieved by supply side-type policies which allow the efficient functioning of flexible markets, including the labor market. In the latter one, flexible contracts, low minimum wages, training for structural unemployed workers, good education for young workers, tax policies which favor research and development, … all these are policies which can and should contribute to low unemployment in the long term while keeping inflation low.