Question #209535

1 Given the Liquidity Function:

and the real interest rate as 4%, the expected rate of inflation as 2.4%, the price level as 4 and the nominal money supply as 50 answer the followings:

a) What is the equilibrium level of real output in the economy (5 Points).

b) What is the level of velocity in the economy? (5 Points).

Expert's answer

(a) The quantity theory of money gives the relation the relation between money supply and price level, (MV equals PY) where M is money supply, V is velocity of money, P is price level and Y is real output.

We are given that real interest rate (r) is 4% and expected rate of inflation is 2.4%

So, real interest rate plus expected rate of inflation is equal to nominal interest rate.

Real interest rate + inflation rate = nominal interest rate

"4\\%+2.4\\%=i\\\\i.6.4\\%\\\\MV=PY"

Real money demand

"=[\\frac{M}{P}]^d\\\\=\\frac{Y^{0.5}}{(10i)^{0.5}}"

So real money demand

"=\\frac{Y^{0.5}}{(10\u00d76.4)^{0.5}}\\\\=\\frac{Y^{0.5}}{(64)^{0.5}}\\\\=\\frac{Y^{0.5}}{8}"

We are given that price level (P) is 4 and nominal money supply (M) is 50, so that the real money supply is 50÷4 or 12.5.

At money market equilibrium, the real money supply is equal to the real money demanded.

So,

"\\frac{M}{P}^s=\\frac{M}{P}^d\\\\12.5=\\frac{Y^{0.5}}{8}\\\\Y=10000"

"\\frac{Y}{P}=\\frac{10000}{4},\\\\\\frac{Y}{P}=2500"

So, nominal income (Y) is 10,000 and real income is 2500.

(b) The value of real money is the nominal money divided by the price level. So, value of real money is 50÷4 or 12.5.

The velocity is found according to the equation MV equals to PY.

"MV=PY\\\\50\u00d7V=4\u00d72500\\\\V=200"

Thus, velocity of money is 200.

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