## Quantity theory of money , Econometrics

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Suppose an economy has the following Real money demand Function:

L(Y,i) = 1000 + 0.3Y - 4000i,

where   i is the nominal interest rate paid on non-monetary (financial) assets,

P s the nominal price level, Y is real income (GDP),

and monetary assets such as cash earn no interest.

A) For P = 110, Y = 2000 and i = 0.05, find the money market equilibrium levels of real money demand, nominal money demand and the velocity of money (V).  Hint: Think about how the quantity equation helps us to see or determine V.

B) Assume real income increases by 5% and the nominal interest rate increases by 15% (this does not mean that i jumps by 15 percentage points to 0.20 or 20%).  Find the new equilibrium levels of real money demand, nominal money demand and velocity.

C) Now assume that Y falls by 10% from part (A) levels, and i falls by 30% from part (A) levels.  Find the new equilibrium level of real money demand, nominal money demand and velocity.

D) Does the Quantity Theory of Money hold (in any/all time frame(s)) with this real money demand function?  Explain when it does or does not hold AND why this is the case?  Find a functional relationship between Y and i, expressed as a function where Y depends on i (i.e. Y(i) ), such that the Quantity Theory of Money would hold.  (6 points)

Hint: Remember in the QTM the V term is constant.

E) If the central bank influences the nominal interest rate in such a way as to make the Quantity Theory of Money hold true (given your answer in the previous section), then what level of i (as a percentage) would they target in part (B) given they could perfectly foresee the 5% increase in the level of real GDP?  (Hint:  Take the derivative of the Y(i) function with respect to i).

What would be the new nominal level of money supplied in the economy in the short-run?  If the central bank controls the money supply directly, assuming the economy is in equilibrium with prices stuck at 110, by what percentage would the central bank need to change the nominal money supply to achieve their target level of i?  If prices are fixed in the short-run, what relationship does the Quantity Theory of Money suggest between the equilibrium nominal money supply and the nominal interest rate?

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