"Super Neutrality" and Changes in Money Growth in the RBC Macro Model.
Consider the basic flexible-price, market-clearing model (which satisfies the Classical Dichotomy) in which r and Y are constant as long as there are no shocks to preferences or technology. The nominal stock of money is growing at rate μ so that:
Mt = Mt-1(1+μ), μ > 0.
Show the money-market clearing condition which determines the price level (P) at any time t.
For r and Y constant, what is the equilibrium rate of inflation and the equilibrium nominal interest rate? Explain.
In a diagram with ln(P) and ln(M) on the vertical axis and time on the horizontal axis, show the time paths of ln(P) and ln(M). (Hint: The nice thing about graphing ln(x) -- the natural log of x -- is that a constant rate of growth of x means that ln(x) is linear.)
Suppose that at time t* there is an unanticipated (but fully recognized as soon as it happens) increase in the rate of money growth to μ' (μ' > μ) which everyone expects to persist indefinitely. Explain in detail any changes in the path of the price level, the rate of inflation, the nominal interest rate and real money balances.
Explain why the increase in inflation from (d) leads to a reduction in real money demand.
This question was posed within the context of a flexible-price, market-clearing macro model. Discuss in detail why the change in μ which takes place in part (d) should be expected in this setting to lead to no change in r or Y.
Suppose now that the change at t* was announced (and believed) at time t' where t' < t*. Explain why the price level would rise instantly at time t', even though nominal money growth at t' had not yet changed.
In the world of part (d), there is a clear relationship between nominal money growth and inflation-indeed the relationship is one-to-one. But in the world of part (g), this relationship breaks down: measured inflation changes before the increase in nominal money growth. In both worlds we have perfectly flexible prices and markets clearing.
Reconcile these differences. Use this to explain why many economists choose to look at long-term averages in inflation and money growth rather than year-to-year changes. What would you expect the year-to-yearempirical relationship between inflation and money growth to be in the real world?