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Can someone explain how to do these problems? i get the money multiplier, but im lost on the rest?

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1. current money supply is $4000. for each of the following state the money multiplier, monetary base, and by how much the fed must change the reserve requirement to achieve the desired change in the money supply. assume banks hold on excess reserves and individuals hold no money:

a. reserve requirement is currently 0.2, the fed wants to decrease the money supply by $800

b. reserve requirement is .5, the fed wants to increase money supply by $1000

c. reserve requirement is currently .25, the fed wants to increase money supply by $1000

2. current money supply is $10,000. state the money multiplier monetary base, and what open market operation the fed would have to take to achieve the desired change in the money supply. assume banks hold no excess reserves and individuals hold no money

a. reserve requirement is .1, feds want to decrease money supply by $800

b. reserve requirement is .5, fed wants to increase money supply by $1000

c. reserve requirement is .4, fed wants to increase money supply by $1000

3. current money supply is 8000. state money multiplier, monetary base, and how the fed would have to change the discount rate to achieve the desired change in the money supply. assume that for every percentage point decline in the discount rate banks borrow an additional $50. assume banks hold no excess reserves and individuals hold no money

a. reserve requirement is .1, fed wants to increase money supply by $600

b. reserve requirement is .5, fed wants to increase money supply by $400

c. reserve requirement is .4, fed wants to decrease money supply by $250

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  1. .#1.

    MS - money supply

    MB - monetary base

    M - multiplier

    R - reserve requirement

    r - discount rate

    M=1/R

    R=MB/MS

    MS=MB/R

    MS=4000

    MB=MS*R

    MB= constant

    R=var

    MS=var

    a)

    ΔMS% = -800/4000 = -20%

    ΔMS% = 1/ΔR%

    (1 -20%) = 1/ΔR%

    0.8=1/ΔR%

    ΔR%=1/0.8 = 1.25 = +25%

    R= 0.2 + 25% = 0.2 * 1.25 = 0.25

    MB=MS*R = 4000*0.2 = 800

    M = 1/0.2 = 5

    b)

    MB=4000*0.5 = 2000

    M=1/0.5 = 2

    MS=(4000+1000) =5000

    R=MB/MS= 2000/5000 = 0.4

    c)

    MS=4000+1000= 5000

    MB=4000*0.25=1000

    R=1000/5000 = 0.2

    .#2.

    R=const

    MB=var

    MS=var

    a)

    MB1=10000*0.1 = 1000

    MS=10000-800 = 9200

    R=0.1

    M=1/0.1=10

    MB2=9200*0.1=920

    ΔMB = 920-1000 = -80

    Openmarket sell.

    b)

    R=0.5

    M=1/0.5=2

    MS=10000 + 1000 = 11000

    MB1 = 10000 * 0.5 = 5000

    MB2 = 11000*0.5 = 5500

    ΔMB = 5500 - 5000 = +500

    Openmarket purchase

    c)

    R=0.4

    M=1/0.4=2.5

    MS=10000 + 1000 = 11000

    MB1 = 10000 * 0.4 = 4000

    MB2 = 11000 * 0.4 = 4400

    ΔMB = 4400 - 4000 = +400

    Openmarket purchase

    .#3.

    R=constant

    MS=var

    MB=var

    a)

    R=0.1

    M=1/0.1=10

    MB=8000*0.1=800

    ΔMS= + 600

    ΔMB= 600*0.1 = +60

    Δr = - (60/50) = -1.2 percentage points

    b)

    R=0.5

    M=1/0.5=2

    MB=8000*0.5=4000

    ΔMS= + 400

    ΔMB= 400*0.5 = +200

    Δr = - (200/50) = - 4.0 percentage points

    c)

    R=0.4

    M=1/0.4=2.5

    MB=8000*0.4=3200

    ΔMS= - 250

    ΔMB= -250*0.4 = -100

    Δr = - ( - 100/50) = +2.0 percentage points

    (but discount rate shouldn't approach/fall below zero - liquidity trap).

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