Paul Krugman uses elementary Keynesian Macroeconomics to argue that the austerity demanded by the Troika would reduce the Greek debt to GDP ratio, if at all, only by causing deflation and increased Greek net exports. This means that it would take a very long time (or forever) to reduce the Greek debt to GDP ratio that way.
I add that this is also an argument for achieving primary surpluses through tax increases (as proposed by the Greeks) rather than spending cuts (as demanded by the rest of the Eurogroup).
The reason is that the effect of a tax increase on aggregate demand is multiplied by the marginal propensity to consume which is definitely less than one. Typical guesses are that it is about 1/3.
Alternative austerity arithmetic. But what if the 1% surplus were achieved by raising taxes not by cutting spending ? I will be extra super back of the envelope crude and assume that the accelerator effect is equal to the marginal propensity to import so the marginal propensity to consume can be calculated as 1/3 from the 1.5 multiplier . So a 1% of GDP increase in taxes would reduce GDP by (1/3)/(1-1/3) = 0.5% and that would reduce tax revenues by the back of Wren-Lewis’s envelope by 1/6 % so to get to 1% primary surplus taxes would have to be increased by 1.2 % causing GDP to promptly decline 0.6% and the debt to GDP ratio to promptly increase by about 1% so one year to get back to the no austerity debt to GDP ratio.
Your Phillips curve says 1.2*0.23 % less inflation so debt to GDP would fall
(1-(1.7*1.2*0.23)) % per year so it would take about 2 years to get back to where Greece would have been, 2< infinity.
But wait, there’s less. What if the increased taxes were taxes on high incomes (say profits over 100,000 euros per year). That would have a much smaller effect on demand.
Or how about increasing spending 0.5% of GDP and increasing taxes 1.5%. That gives a primary surplus 1% higher and no effect on aggregate demand.
The point is that Keynesians do not have to insist on deficits. The alleged need to choose either fiscal stimulus or low debt is nonsense or in any case has almost nothing to do with Paleo Keynesian macro and less to do with new Keynesian macro.