Within the Phillips curve, how are inflation and unemployment levels related?
Phillips curve states that unempolyment and inflation are inversely related. He drew information from several countries and concluded that decreasing the inflation rate usually results in increasing the unemplyoment rate.
Thus, the economy, according to Philips' curve, faces a permanent trade-off of unemplyoment and inflation (remembering: both are harmful to the economy). The point is, according to Phillips logic, finding a point where the economy is able to balance some level of unemployment and some rate of inflation.
Alternatively, we can draw information from facts, where some underdeveloped countries dragged down high inflation rates (some even hyperinflation cases) resulting, in the short-run, a drastic increase in unemployment.
Inflation is a prolific discussion in Economics, as it can be interpreted in diverse ways (e.g. inflation of demand, inflation of supply, monetary inflation, etc.) and, thus, conducting a policy to undermine inflation rate growth depends on what interpretation has been adopted.
It is also necessary to stress the concept of "natural unemployment", which is a rate attributed conceptually as the lowest level of unemployment achievable in the economy. "Natural unemployment" refers to the frictional unemployment, that is, the one individuals face when changing jobs.
It is possible, then, that the Phillips curve redirect the user to the level where (1) inflation does not destabilize the monetary system and (2) unemployment is as closest to the natural as possible, given the aforementioned inflation constraint.