3. Nominal interest rates are at a record low level in Japan, leading to concerns that the economy is in a liquidity trip, making short-run monetary expansion ineffective. Explain precisely how long-term monetary expansion may nonetheless be effective in stimulating the economy.

When an economy is in a liquidity trap, increases in the money supply fail to reduce the nominal interest rate. If the nominal interest rates does not fall, consumption and investment cannot be stimulated and output does not rise. The trick, then, is to find a way to increase consumption and investment without any drop in nominal interest rates. 
You will recall that both consumption and investment depend on the expected real rate of interest, defined as the difference between the nominal rate of interest and the expected rate of inflation. So, if you can't get the expected real rate of interest down by dropping nominal interest rates, the only other way to get the expected real rate of interest down is by raising expected inflation.
Long-term monetary expansion will cause a steady increase in the price level -- i.e. inflation. (You can explain this in two ways. First you can appeal to the quantity theory of money, MV=PY. Alternatively, you can use the AS-AD framework of the Keynesian model to show that each increase in the money supply is associated with an increase in the price level, so ongoing increases in the money supply will cause with inflation).
An increase in expected inflation implies, for any given nominal intrerest rate, a reduction in the expected real interest rate.This stimulates investment and consumption and causes an increase in output. But note the kicker here. Ongoing increases in the money supply cause inflation, but consumption and investment depend on expected inflation. In order for this trick to work, then, the central bank must make sure everyone understands that it is committed to ongoing money supply increases. That is, the central bank must promise the inflation publicly.