http://www.princeton.edu/~pkrugman/debt_deleveraging_ge_pk.pdf
From the paper's assumptions:
"Imagine a pure endowment economy in which no aggregate saving or investment is possible, but in which individuals can lend to or borrow from each other. Suppose, also, that while individuals all receive the same endowments, they differ in their rates of time preference."
Imagine all that indeed; we trust fund baby/individuals all roll out of bed each morning and 'receive the same endowments.'
Krugman and his fellow cargo cult scientists have front end rigged the analysis by modeling 'bizarro world' and then compound their inartfullness by crudely mixing dynamic with static analysis. Second year engineering students are slapped up the side of the head for doing that.
SD curves are static; changes/shifts in SD curves are dynamic.
The hand waving explanations of the positive slopes of those static curves are based on dynamic arguments. Krugman's ultimate conclusions depend on a static analysis of the resulting -aggregate- curves.
Imagine we were a pure endowment economy indeed...and then come up with a model of aggregate supply and demand both with positive slopes instead of opposite signed slopes.
Krugman's argument relies on an assertion that aggregate demand (AD) and aggregate supply (AS) curves during the current liquidity trap (non-response of economic circulation to further reductions in interest rates) have the same sign slope—both respond in the same sense to price changes.
His argument, in a nut-shell: When 'real' interest rates are negative (interest rate minus inflation rate), folks will want to buy more of things as their prices rise, because of the inflationary pressure of ever more worthless money that can be borrowed at negative real interest rates. He is confusing the slope of the AD curve with the response of people during times of hyperinflation (a constant pressure to move right in the AD curve, a willingness to every day pay more for the same thing because of the hyperinflation).
But, during such times of hyperinflation the AS curve will shift left—at the same Q suppliers will demand more of the ever-worthless $. The net result is fluctuating Q and ever-rising prices, hyperinflation.
Not, as his theory demands, an AD curve ( a static non-shifting curve) that represents folks' desire to buy more of something as its price increases, and less of something as its price decreases!!!
He's mixing static analysis (AD and AS curves) with a dynamic ("Minsky Moment/Shock") condition -- hyperinflation, or it precursor -- negative interest rates. That is his uncalibrated, non-uncertainty-analyzed, mathematical subterfuge/sleight-of-hand. It is pure technical barbarism in the name of political science uber alles.
What Krugman et. al. self servingly describe as a 'liquidity trap', where the carrot and stick of interest rates lose all impact even near '0' is really a complete loss of faith in the economic game, precisely because of the painless remote 'the economy' running in our non-centrally planned, not centrally controlled 'the economy', as if we, too, were the failed USSR.
'The Economy' today is owned by the shed-risk parasites, not the once beast builders.
They make up words like 'liquidity trap' to avoid facing up to what a 'liquidity trap' really is.
The failure of the economies to respond to lowering interest rates are a symptom of something, and that something panics the alternate easy floggers/prodders of the economies. That failure is an indictment of economic political leadership, a collapse of faith that those regulating the economic game have the first f'n clue what they are doing.
During such periods of tribal insanity, the real pumps and engines that drive circulation in the economies take a time out, and pause, and the economies contract and no longer respond to the little witch doctor dances going on at the base of the volcano by the witch doctors. The real pumps and engines of the economies hold back, do not borrow money and take risk and instead wonder when the tribal insanity is going to pass.
And in such times, the parasites and witch doctors panic, and throw every constructivist cheap trick they can at the economies, and hope and pray that the rains will someday come again, so the tribe doesn't get such a good look at them dancing like fools and sweating in front of the volcano.
In our new economies of waiting, there are few fools taking on risk and building business and pumping value through out economic pipes. Instead, what is left of 'capitalism' is largely crony capitalism, trying to hang around the waterfalls of effortless water falling from above, waiting for the government truck to show up with the latest load of unpumped water and do their best to get wet without breaking an actual sweat.