Understanding the dual mandate

Both the RBA and the Fed have a "dual mandate", to keep both inflation and unemployment down. A way to think about that in monetary policy terms is that the central bank, as the monopoly provider of money, is expected to keep the value of money stable (not changing greatly across time) and the level of transactions high (keeping production up around capacity). Keeping the value of money stable minimises the cost of inflation (or deflation) while keeping transactions up so that production is up around capacity means that it is not leaving a lot of labour capacity unused (i.e. unemployed).

If we think of it in terms of the equation of exchange:
MV = Py

(Money supply x Velocity  = Price level x output)

then we want changes in P to be low and y on to be on a stable growth path. Which, to put it another way, means Py on a stable growth path. In economic-speak, that means targeting NGDP, GDP in money terms--which is P x y. (Or, to be more precise, targeting expected NGDP.)

The trouble with just targeting changes in P (inflation-targeting) is that, if there is a fall in y, then the money supply (and so income) has to follow y down, exacerbating the effect of the fall in output (given that prices, and debt obligations, are "sticky"). (Unless one is the RBA and one's target is an average change in P over the business cycle, so can lean against changes in y.)

To put in another way, rigid inflation targeting sacrifices keeping the level of transactions up in order to keep the value of money stable. Conversely, targeting (expected) NGDP involves a commitment by the central bank to respond to changes in the demand for money so that the level of transactions can be maintained (if the demand for money increases) and changes in P are stable (if the demand for money falls).

As Lars Christensen clearly points out, the current crisis comes from central banks, particularly the Fed, not responding to changes (specifically increases) in the demand for money. As Scott Sumner points out, it represents the failure of inflation targeting. (Evan Soltas has some good arguments for NGDP targeting here.)

ADDENDA: One of the tragedies of the illusory appeal of "Austrianism" (popularised Austrian economics) is that it diverts energy from useful critique of the performance of central bankers to an obsessive irrelevance. The historical record shows that it is the periodic propensity for central bankers to undersupply money, to fail to match money demand, which is the most economically disastrous failure of central banking. So it is periodic money-droughts, not hyperinflation, which is the dangerous failure-risk of central banking. (A propensity that is more in line with the normal problem of monopoly-providers, which is to undersupply.) Any serious analysis of central banking must grapple with that, not obsess over over-supply as the "real" or "underlying" problem.