The textbook answer, which Bryan gave but rejected, is that interest rates go up, the demand for money falls, and the fall in the demand for money acts like an increase in the supply of money--nominal GDP goes up.
Bryan questioned whether money demand responds to small changes in interest rates. Inelastic money demand (the opposite of a liquidity trap, which would be super-elastic money demand), is a weird case to think about, because it makes the Fed unable to determine the money supply. Suppose that the Fed wants to raise (lower) the money supply. Under Bryan's assumption, the only way to increase (reduce) money demand is to make interest rates fall (rise) by a huge amount. I think that the "inelastic money demand function" is neither theoretically nor empirically interesting.
Hold on, Arnold. A textbook money demand function depends on both interest rates and INCOME. If the interest-elasticity of money demand is zero, the effect of a monetary expansion is to raise nominal income until people are willing to hold the amount of money that exists. Just picture shifting a vertical LM curve to the right. The Fed can raise the money supply as much as it likes - zero interest-elasticity is no obstacle.
Not empirically interesting? I beg to differ. I doubt one non- economist in twenty adjusts his money holdings when the interest rate changes. But lots of people adjust their money holdings when their income goes up.
If you took a look at my financial history for the last twenty years, for example, I'd be amazed if there were any connection between how much money I held and what interest rates were. But there is a clear positive relationship between how much money I held and my income: When I was a poor student, I averaged about $20 in my wallet. Now it's usually ten times higher.