Suppose the money demand function is Md Y05 5i where nomin

Suppose the money demand function is Md = $Y(0.5 – 5i) where nominal GDP ($Y) is $1,000 billion, Md is the quantity demanded of money and i is the interest rate. The quantity supplied of central bank money is $100 billion. Half of the money is held as currencies. The reserve ratio is 0.1.

a. The money multiplier is _________

b. quantity supplied of overall money is _________

c.  The money market equilibrium interest rate is _________

Solution

a. The money multiplier is= 1/reserve ratio = 1/0.1 = 10

b. Qs-overall economy = money multiplier*Qs of central bank money = 10*100= $1000 billion

c. The money market equilibrium interest rate is where quantity of money demanded is equal to money supplied
Qs=Qd
1000= 1000*(0.5-5i) =500-5000i
5000i = -500
i = -500/5000 = -0.1, ignoring negative sign it is 10 percent