Question

# Assuming output Y is determined exogenously, and demand for real money balances is given by (M/P)...

Assuming output Y is determined exogenously, and demand for real money balances is given by (M/P) d = kY , answer the following:

(a) Suppose k changes from period to period. Using the quantity equation MV = P Y , show how inflation is related to money growth, output growth, and growth in k.

(b) Holding the money supply M and output Y constant, does a fall in k lead to inflation, deflation, or no change in the price level? Explain in words why this is.

(c) Since inflation erodes the purchasing power of money, higher inflation could be expected to cause a fall in demand for real balances. Suppose this is the case. In particular, suppose %∆k = −aπ, where 0 ≤ a < 1, and π is inflation. Under this assumption, show how inflation is related to money growth and output growth (i.e., solve for π in terms of %∆M and %∆Y ).

(d) Suppose the central bank always sets %∆M = %∆Y + x, where x is some constant, with x > 0. Based on your answer from (c), if a increases (but remains less than 1), what will happen to inflation (i.e., will is stay the same, increase, or decrease)? Explain your answer intuitively

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