Two macroeconomic objectives that a government would like to achieve are: a low and stable rate of inflation and a low level of unemployment. Unemployment is defined as the people of working age who are without work, available for work and actively seeking employment according to ILO, while inflation is defined as a persistent increase in the average price level in the economy. Phillips curve suggests that there is a trade-off between those two macroeconomic problems. This means that the increase in the unemployment rate from 10.6 in December 2011 to 10.7 in January 2012 in the Euro Zone should cause a fall in the unemployment rate, according to Alban Williams Philips' theory. The Euro Zone is an economic and monetary union of 17 European Union member states that have adopted the euro as their common currency and sole legal tender. 
Taking a deeper look at Phillips' theory, it is implied that there is an inversely proportional relationship between the inflation and unemployment rate. A hypothetical Phillips Curve is demonstrated below.
Inflation Rate %
Unemployment Rate %
It is observed that as inflation falls from 6% to 2% unemployment increases from 3% to 5%. This trade-off can be used by governments to reduce either unemployment or inflation but at the cost of allowing the other rate to increase. This fact can also be explained by an aggregate demand/aggregate supply analysis.
Aggregate price level
Real Output (Y)
If the economy is initially in equilibrium at with a Price level of and the government feels there is too much undesired unemployment, then it might use Keynesian demand management polices to increase the aggregate demand, from to. That is a shift to the right of the aggregate demand. If such a policy is implemented then the real output will increase from to and therefore it is assumed that firms start employing more workers to meet increased aggregate demand. Unemployment falls but the price level has increased from to. This means higher inflation. Thus, this theory agrees with the Phillips curve hypothesis, since decreased unemployment is achieved by higher inflation.
Inflation Rate %
Unemployment Rate %
In the Euro Zone, however the rise in unemployment led to an increase in inflation too. If inflation brings about a negative growth and unemployment remains steadily high, then this will cause the phenomenon known as stagflation. However, "the economic slowdown is not having quite the downward influence that we anticipated" and there is no trade-off. Something different takes place here that may be explored by the use of the Long-run Phillips curve.
It may be argued that the Euro Zone is in a long-run equilibrium on a (A) and the only unemployment that it faces is its natural rate of unemployment. People expect the inflation rate to remain at 2.6% (percent) so they may negotiate pay increases taking advantage of the trade union power that they might posses. If however, the government wants to reduce unemployment then it will adopt expansionary demand-side policies, increasing government spending. This subsequently, would cause an increase in inflation from 2% to 2.6%. In the short-run, unemployment might be reduced since employers are attracted by what they think are higher wages. However, workers have suffered from money illusion as their real wages have not risen. When they realize that, they leave their jobs and therefore, unemployment returns to its previous level. However, inflation remains at 2.6% and the economy will be on new short-run Phillips curve (C). People may again expect the inflation to remain at this level and may start negotiating increases in their wages. If the government intervenes again with demand-side policies to reduce the current level of unemployment this will result in higher inflation. So inflation moves from 2.6% to 2.7% and the economy moves to another short-run Phillips curve(E). So inflation seems to rise because of government intervention.
These facts show that if governments do not use expansionary policies inflation will not accelerate at the natural rate of unemployment. However, in the Euro Zone the jobless rate in the 17 euro nations is calculated as an average of the unemployment rate of all member countries. This means that "flagging economies like Italy and Greece were responsible for much of the increase." The natural rate of unemployment is presumably high in these economies and government intervention enough to accelerate inflation. A possible rise in the unemployment rate in any of these flagging economies has an effect on Euro Zone's jobless rate and that may be a reason why unemployment rose by 0.1% more, reaching 10.7%.