Question

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

Answer #1

Assume the real money demand function is
L(Y;i)=2000+0.3Y-5000i
where Y is real output, P is the price level, i is the nominal
interest rate on non-monetary assets and monetary assets earn no
interest.
a) Assuming that the asset market is in equilibrium at i=0.05.
Find equilibrium levels of real money supply, nominal money supply,
and the velocity of money if P=100, and
Y=2000.
b) Find the real income elasticity of money demand at the
equilibrium level of money balances found...

In Freedonia the real demand for money is L = (M/P)d
= kY, k a constant. The money supply is growing at 12% per year and
real income, Y, is growing at 4% per year.
(a) What is the income velocity of money in Freedonia?
(b) What is Freedonia’s annual inflation rate?
(c) Suppose the income velocity of money is growing at the rate
of 1%. What is Freedonia’s annual rate of inflation.

Suppose that the money demand function takes the form
(M/P)d = L (i, Y) = Y/(5i)
a. If output grows at rate g and the nominal interest rate is
constant, at what rate will the demand for real balances grow?
b. What is the velocity of money in this economy?
c. If inflation and nominal interest rates are constant, at what
rate, if any, will velocity grow?
d. How will a permanent (once-and-for-all) increase in the level
of interest rates...

In Freedonia the real demand for money is d = (M/P)d
= L(i,Y) = Y/(5i1/3 ), i being the nominal interest
rate.
(a) What is the income velocity of money in Freedonia?
(b) Suppose output is growing at the annual rate of g. What is
the growth rate of real money demand?
(c) If the nominal interest rate is constant, what is the growth
rate of velocity?
(d) Suppose at time 1 there is a permanent increase in i. What...

1 Assume that the demand for real money balance (M/P) is M/P =
0.6Y – 100i, where Y is national income and i is the nominal
interest rate (in percent). The real interest rate r is fixed at 3
percent by the investment and saving functions. The expected
inflation rate equals the rate of nominal money growth.
a. If Y is 1,000, M is 100, and the growth rate of nominal money
is 1 percent, what must i and P...

Consider an economy in which the money demand function takes the
form:
(M/P) d = L (i, Y) = Y/(5i)
a. If output grows at rate g, at what rate will the demand for
real balances grow (assuming constant nominal interest rates)?
b. What is the velocity of money in this economy?
c. If inflation and nominal interest rates are constant, at what
rate, if any, will velocity grow?
d. How will a permanent (once-and-for-all) increase in the level
of...

Suppose that the real money demand function is
L(Y, r+πe)=0.01Yr+πe ,L(Y, r+πe)=0.01Yr+πe ,
where YY is real output, rr is the real interest rate, and πeπe
is the expected rate of inflation. Real output is constant over
time at Y=150Y=150. The real interest rate is fixed in the goods
market at r=0.05r=0.05 per year.
Suppose that the nominal money supply is growing at the rate of
10% per year and that this growth rate is expected to persist
forever. Currently,...

Assume that the demand for real money balance, (M/P) d = 0.5Y –
200i, where Y is national income and i is the nominal interest rate
(in percent). The real interest rate r is fixed at 2 percent by the
investment and saving functions. The expected inflation rate is 1
percent, real GDP is 5,000 and the money supply is 209,110.
a. What is the nominal interest rate?
b. What is the price level?
c. Now suppose Y is 2,000,...

For this question assume that the real money demand function is
L(R, Y) = kY - hR where k > 0 represents the sensitivity of the
money demand to income and h > 0 represents the sensitivity of
the money demand to the interest rate. Suppose that the economy of
Highland has high k and low h, while the economy of Lowland has low
k and high h. If the two countries are the same other than the
above difference,...

Assume that the real money balance (M/P) is M/P=0.6Y-100i, where
Y is the national income and I is the nominal interest rate. The
real interest rate "r" is fixed at 3 percent by the investment and
saving functions. The expected inflation rate equals the rate of
nominal money growth.
-If Y is 1,000, M is 100, and the growth rate of nominal money
is 2.5%, what must "i" and "P" be?
-If Y is 1,000, M is 100 and the...

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