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20 February, 11:28

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

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  1. 20 February, 12:47
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    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%
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