Suppose our closed economy has a money demand function given by the following equation:

Md=[300+0.5Y-500i]*P ,

Md is nominal money demanded

P is the nominal price level

i is the nominal interest rate ( i = r + e) r is the real interest rate

e is the expected inflation rate

Y is real GDP

where

For all of the sub-questions below show your calculations do not simply provide a single number answer.

a)Suppose the central bank has been successfully pursuing an inflation targeting policy that seeks to maintain a zero-inflation rate. As a result, the inflation rate has been zero for several years. Also suppose that in long-run equilibrium real GDP & nominal GDP are both equal to 1000 and the real rate of interest is equal to 0.10. Determine the long-run equilibrium level of the nominal money supply. Using this answer, determine the velocity of money in this economy.

b)Determine the real income elasticity of money demand at the long-run equilibrium level of nominal money (balances) from part a.

c)The rate of inflation can be defined as the growth rate of the nominal money supply minus the product of the income elasticity of money demand times the growth rate of real output.

Assume that the real income elasticity is equal to your answer from part b, that real income is expected by grow by 4.5% over the next year, and that the real interest rate is expected to remain constant over the next year. As noted, before the inflation rate has been zero for several years. The central bank has been pursuing an inflation targeting policy that seeks to maintain a zero-inflation rate next year, then by how much should the central bank increase the money supply? Show your calculations.

d)One version of the quantity theory of money assumes that the velocity of money is constant. Does this version of the quantity theory of money hold in the example here/above? Explain why or why not.