Utopia, you are standing in it!

In the Keynesian pipedream, in a liquidity trap, there is perfect substitutability of money and bonds at a zero short-term nominal interest rate. This renders monetary policy ineffective.

Keynesians claim that the demand for money may be so persistently high that the rate of interest could not fall low enough to stimulate investment sufficiently to raise the economy out of the depression. Allan Meltzer explains:

A liquidity trap means that increases in money by the central bank (monetary base) cannot affect output, prices, interest rates or other variables. Changes in the money stock are entirely matched by changes in the demand to hold money.

With a liquidity trap, the public simply hoards the money the central bank creates rather than attempting to run down additions to their cash balances with increased consumer expenditure. This limitless accumulation of money by the public is not a real world phenomenon. The public will not forever accumulate money.

Auerbach and Obstfeld noted in "The Case for Open-Market Purchases in a Liquidity Trap" that to the extent that long-term interest rates are positive short-term interest rates are expected to be positive in the future, trading money for interest-bearing public debt through open market operations reduces future debt-service requirements.

• A massive monetary expansion during a liquidity trap should improve social welfare by reducing the taxes required in the future to service the now much smaller national debt!!!!
• A quantitative easing during a liquidity trap is, in effect, as good as or even better than a lump sum tax.

Central banks perhaps should contrive liquidity traps because they can then buy back the public debt because of the unlimited demand for money.

The logic of the liquidity trap is people will without limit give up bonds for non-interest bearing cash. If monetary policy is impotent near the zero bound, the central bank should buy trillions of dollars of federal bonds and payoff the public debt. This is a logical implication of liquidity traps for an optimal fiscal policy!!!! Is my reasoning wrong?

In addition to D.H. Robertson, Jacob Viner, Milton Friedman, Philip Cagan, Don Patinkin, Auerbach and Obstfeld, Robert H. Lucas, Greg Mankiw, and Bernanke and Blinder as sceptics about a liquidity trap, Keynes wrote in 1936:

Whilst the limiting case might become practically important in future, I know of no example of it hitherto. Indeed, owing to the unwillingness of most monetary authorities to deal boldly in debts of long term, there has not been much opportunity for a test.

Meltzer, who wrote A History of the Federal Reserve, Vol. 1: 1913-1951 points to several periods when interest rates were at or close to zero:

“In 1954, interest rates were 0.5 percent or below, and we had no problem recovering,” he says. “In 1948 to 1949, we had zero interest rates. Also in 1937 to 1938. We had no problem recovering.”

The Pigou effect states that when there is deflation of prices, employment (and output) will be increased due to an increase in wealth (and thus consumption). The deflation increases the value of cash balances and therefore the wealth of consumers. They spend some of this additional wealth.

After reading the annual reports of the Fed in the 1920s and 1930s, Milton Friedman noticed the following pattern:

In the years of prosperity, monetary policy is a potent weapon, the skilful handling of which deserves the credit for the favourable course of events; in years of adversity, other forces are the important sources of economic change, monetary policy had little leeway, and only the skilful handling of the exceedingly limited powers available prevented conditions from being even worse