"A monetary expansion which pushes the economy below the natural rate of unemployment leads to accelerating wage increases and price increases." Explain the argument. Does this mean that there is no distinction between cost and demand inflation?

This argument rests on the analysis that Milton Friedman carried out in 1968 in which he revised the theory Professor A. W. Phillips had first proposed a decade earlier. Phillips believed he had found a correlation between the levels of inflation and unemployment, such that there was always a trade-off between the two (see diagram 1). A high rate of unemployment implied a low level of inflation, and vice-versa. The Phillips curve was thus a menu for governments to choose their positions from - they could choose a level of inflation or a level of unemployment, but not both together, as with a stated level of one, there was a corresponding level of the other. After having chosen their position, they would alter their fiscal and monetary policies to achieve that position.
Throughout the 1970s, there were years where that statistical data for unemployment and inflation didn't fit the pattern identified by Phillips; in these years there were both high rates of unemployment and inflation. This was known as stagflation, and it became apparent that the Phillips curve did not explain all possible situations, and needed to be modified to explain these new situations. This is what Friedman's analysis provided.
To see this, we must first make some assumptions about the economy. Firstly, the level of full employment and output are fixed in the long run; in figure 1, the level of full employment is at U*. This is also known as the natural rate of unemployment, which may not be identical with the absolute full employment level where everyone who wants a job has one, as some members of the labour force may be unwilling to work at the wage level associated with this level of employment. Secondly, there is only sluggish wage and price adjustment, i.e. there is a sticky situation in the associated markets. In response to an aggregate shock, wages and prices only change slowly, and the economy will eventually move back to the full employment level as changes in prices change the real money supply. Thirdly, in the long run the nominal money supply is fixed. When the economy returns to the full employment level, inflation will be zero.
From this initial position of equilibrium, we suppose that there is an increase in the nominal money supply (i.e. in purely numerical terms, the amount of money in the economy increases). Since wages and prices adjust only sluggishly, the initial effect is to increase the real money supply (i.e. the total purchasing power in the economy), and interest rates must be lowered to encourage people to hold a larger quantity of money in real terms (see diagram 2). In the short run, the higher aggregate demand for goods that occurs as a result of the increase in real money causes an increase in the production of goods; more labour is needed to produce this higher output. For this reason, the rate of unemployment falls. In terms of diagram 1, we would move from U* to point A, showing a reduction in unemployment has also been associated with a slight rise in inflation.
This is only the first step in the cycle; the economy does not remain at point A in the long run. Wages will rise as the demand for workers increases, and thus prices also as firms pass in their increased costs to the customer in the form of higher prices. These higher prices will have the effect of reducing the real money supply; if prices rise, a given quantity of money will buy fewer goods. This causes the real money supply in diagram 2 to contract back to the left. Interest rates will rise again, and the demand for real money will start to fall. Aggregate demand for goods in the economy will fall, and hence so will output; unemployment will start to rise again. Secondly, this will reduce upward pressure on prices and wages, eventually reaching a point where there will be no more upward movement. At this point, the economy will have moved back down the Phillips curve in diagram 1 from point A to U*.
Thus the conclusion is that the Phillips curve is not a permanent trade-off between unemployment and inflation; it shows instead that there will be a trade-off in the short run while the economy adjusts to the shock change to aggregate demand caused by an increase in the money supply. In the long run, the economy will tend to its full employment level. Hence the derivation of the long-run vertical Phillips curve (see diagram 3), which reflects the natural rate of unemployment of U* at all price levels.
In the long run, it is not necessary for the nominal money supply to be fixed, as people care about real variables and not nominal ones. In long-run equilibrium with inflation at any rate, the nominal money supply and money wages would be growing at the same rate as prices. The equilibrium level of inflation would be unaffected at any rate other than zero after adjustment to an aggregate demand shock, just as explained above for zero inflation. This can be illustrated by a series of short-run Phillips curves on diagram 3, each at a different level of inflation. With any shock, inflation would remain at the rate it was at initially at U* once adjustment to the shock had occurred. Friedman's explanation showed why stagflation occurred; the short-run Phillips curves had shifted upwards because governments were printing money - the long-run inflation rate had risen.
This monetary inflation that has been considered here is a form of demand-pull inflation. Excess demand that is stimulated by the increase in both the nominal and real money supplies leads to an increase in demand for goods and services. Essentially there is too much money chasing too few goods, and as firms cannot instantaneously increase output in order to meet the increased demand, the market forces of demand and supply cause the equilibrium level of prices to rise in order to ration the level of goods available to those who can afford them. This can be seen in diagram 4, where the AS schedule is an inverted 'L' shape, which represents the homogeneity of labour until the point of full employment, which is U*. If the economy has an initial aggregate demand of ADo, with a price level of po, and then experiences a demand shock that raises demand to AD1, this can initially be accommodated through an increase in the employment level. Prices only rise slowly, to p1. However, when the full employment level is reached (i.e. U*), any increases in demand can not be accommodated merely by increasing the labour force, as there are no more workers available to work at the current wage rate, and thus any rise in demand is purely inflationary. This is shown by the sharp rise in the price level to p2. According to the theory outlined above, when the demand for real money balances contracts again, the aggregate demand schedule will move back to the left to its initial position, which would be at U* in diagram 4. Demand-pull inflation can also be represented by a Keynesian-cross diagram in which the equilibrium level of national income, Ye, is above the full employment level, U*, which leads to an inflationary gap (see diagram 5).
On the other hand, inflation can also occur when there is substantial unemployment, and this is clearly not demand-pull inflation. This is what is known as cost-push inflation, and occurs when firms receive a shock rise in their costs of production, which can be regarded as mainly wages. This in turn pushes up the general price level. This may lead to successive rounds of increases in prices, profits and hence wages, and if international concerns are taken into account, devaluation of the currency. All of this shifts the aggregate supply and demand curves upwards, causing an increase in inflation (see diagram 6).
Therefore, while there are two types of inflation, and while both produce rising prices, the way in which they begin are different. Demand-pull inflation is set in motion by a demand-side shock, caused by a change in the demand for goods and services, whereas cost-push inflation is caused by a supply shock, which changes the costs of employment of the factors of production.