What dilemma does stagflation present to fiscal and monetary policy makers?
Stagflation is a really bad economic scenario, as it combines both inflation (persistent and generalized increase in prices for all goods in an economy during a period of time) and economic stagnation.
First, in fiscal policy terms, it compromises the government revenue. As inflation grows, money loses its value faster and faster. This, in turn, will lead to an event known as Olivera-Tanzi effect, which consists on the deterioration of the real value of the tax collection.
Once money is losing its value increasingly rapidly, the government faces a gap: the event that generates the tax happens some time before its payment, which means that, as the "price" of the tax is fixed - and as money is losing its value fast -, its real (deflated) value will be lower in the day of the payment than it was in the day of the even that created the liability. Even though money does lose its value across time, its steep downfall is quite a thing to worry about - specially in inflationary - or stagflationary - contexts.
Second, the monetary policy makers face a huge trade-off: as money supply increases in an inflationary scenario, they must control it. However, controlling monetary aggregates - specially currency supply - means counter-cyclical and, therefore, contractionist measures. Now, think of this: he economy is already going back, under a recession - what is the rationale in force it back even harder?