Consider an economy with a real money demand that is dependent upon income (Y)(Y) and the nominal interest rate (i) (MP)

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Consider an economy with a real money demand that is dependent
upon income (Y)(Y) and the nominal interest
rate (i)
(MP)^d=(0.2Y/i)
a) Use this real money demand equation and
the quantity equation (MV=PY)(MV=PY) to derive an
expression for monetary velocity.
b) It can be verified that
the real money demand equation given
above is increasing in income
and decreasing in the nominal interest rate.
∂(MP)d∂Y=0.2i>0∂(MP)d∂Y=0.2i>0
∂(MP)d∂i=−0.2Yi2<0
Describe what these expressions mean in one sentence each.
c) Using the expression for velocity in
part (a), verify that monetary velocity
is increasing in the nominal interest rate.
d) Explain why it is consistent for real
money demand to be decreasing in the nominal interest rate while
monetary velocity is increasing. Hint: it is
assumed that output / income remains constant.
e) Consider the real money demand equation
above where we substitute the nominal interest rate with its
components: the real interest rate and
the expected inflation rate.
i=r+E(π)i=r+E(π)
(MP)d=0.2Yr+E(π)
It can be shown that real money demand
is decreasing in the expected inflation
rate.
∂(MP)d∂E(π)=−0.2Y(r+E(π))2<0
Briefly explain why this makes sense. In other words, why would
an increase in the expected inflation rate result in people
decreasing their demand for real money balances?