Question

SCENARIO 5.Notation: C = currency; D = demand deposits; T = time deposits; & S= saving deposits. MB= monetary base. Suppose: money supply 1, M1= C + D. money supply 2, M2= C + D + T. money supply 3, M3= C + D + T + S. Suppose also that C= cD; T= tD; & S = sD. The Fed imposes the following reserve requirements: rd on demand deposits D; rt on time deposits T; and rs on saving deposits S. Banks keep the following excess reserve ratios: ed on demand deposits D; et on time deposits T; and es on saving deposits S.

28) Refer to Scenario 5. Using the generalized model where MS= MB.m, then for the money supply M1, the money multiplier m1 = ______.

29) Refer to Scenario 5. Using the generalized model where MS= MB.m, then for the money supply M2, the money multiplier m2 = ______.

30) Refer to Scenario 5. Using the generalized model where MS= MB.m, then for the money supply M3, the money multiplier m3 = ______. 

Answer 1

The “desired reserve ratio” is the sum of “required reserve ratio (r)” and the “excess reserve ratio (e)”. So, the “total reserve (R)” is the sum of “reserve coming from demand deposits”, “reserve coming from time deposits” and “reserve coming from saving deposits”.

=> R = (rD + eD)*D + (rT + eT)*T + (rS + eS)*S.

Now, the “monetary base (MB)” is the sum of “currency (C)” and “total reserve (R)”.

=> MB = C + R = C + (rD + eD)*D + (rT + eT)*T + (rS + eS)*S.

=> MB = C + (rD + eD)*D + (rT + eT)*T + (rS + eS)*S.

28).

For, money supply (M1), the money multiplier is given by.

=> M1/MB = m1 = [C+D] / [C + (rD + eD)*D + (rT + eT)*T + (rS + eS)*S].

=> M1/MB = m1 = D*[C/D + 1] / D*[C/D + (rD + eD) + (rT + eT)*T/D + (rS + eS)*S/D].

=> m1 = [C/D + 1] / [C/D + (rD + eD) + (rT + eT)*T/D + (rS + eS)*S/D].

=> m1 = [c + 1] / [c + (rD + eD) + (rT + eT)*t + (rS + eS)*s].

So, the money multiplier for money supply M1 is “m1= [c+1] / [c + (rD +eD) + (rT +eT)*t + (rS +eS)*s]”.

29).

For, money supply (M2), the money multiplier is given by.

=> M2/MB = m2 = [C+D+T] / [C + (rD + eD)*D + (rT + eT)*T + (rS + eS)*S].

=> M2/MB = m2 = D*[C/D + 1 + T/D] / D*[C/D + (rD + eD) + (rT + eT)*T/D + (rS + eS)*S/D].

=> m2 = [C/D + 1 + T/D] / [C/D + (rD + eD) + (rT + eT)*T/D + (rS + eS)*S/D].

=> m2 = [c + 1 + t] / [c + (rD + eD) + (rT + eT)*t + (rS + eS)*s].

So, the money multiplier for money supply M2 is “m2= [c+1+t] / [c + (rD +eD) + (rT +eT)*t + (rS +eS)*s]”.

30).

For, money supply (M3), the money multiplier is given by.

=> M3/MB = m3 = [C+D+T+S] / [C + (rD + eD)*D + (rT + eT)*T + (rS + eS)*S].

=> M3/MB = m3 = D*[C/D + 1 + T/D + S/D] / D*[C/D + (rD + eD) + (rT + eT)*T/D + (rS + eS)*S/D].

=> m3 = [C/D + 1 + T/D + S/D] / [C/D + (rD + eD) + (rT + eT)*T/D + (rS + eS)*S/D].

=> m3 = [c + 1 + t + s] / [c + (rD + eD) + (rT + eT)*t + (rS + eS)*s].

So, the money multiplier for money supply M3 is “m3= [c+1+t+s] / [c + (rD +eD) + (rT +eT)*t +(rS + eS)*s]”.