Suppose consumers only hold checkable deposits. The demand for money for transactions by consumers is equal to Y * (0.3 - i), where i is in decimals. Income is 800, and the reserve ratio of banks is 0.4. The supply of currency by the central bank is 40. What is the equilibrium interest rate

Answer: 17.5%

Explanation:

The equilibrium will occur where the money demanded equals to the money supplied i. e Ms = Md

From the question, the supply of currency by the Central Bank = 40

Money Supply (Ms) = m * B

where m = Money multiplier = 2.5

Note that the money multiplier can also be equal to 1/rr in situations wherebt the consumers do not hold any currency.

rr = reserve ratio, = 0.4

B = monetary base = 40

Note that the monetary base here is 40.

Since reserve ratio = 0.4, therefore

m = 1/0.4 = 2.5

Therefore, Ms = m * B

= 2.5 * 40

= 100

Thus Money supply Ms = 100.

Money demand (Md) = Y (0.3 - i),

Y = income = 800

i = interest rate

Since (Md) = Y (0.3 - i),

Md = 800 (0.3 - i)

Equate the equation for the money demand and money supply together.

Ms = Md

100 = 800 (0.3 - i)

100 = 240 - 800i

800i = 240 - 100

800i = 140

i = 140/800

i = 0.175

= 17.5%

Therefore, the interest rate is 17.5%