In Westlandia, the public holds 50% of M1 in the form of currency, and the requi

Question

In Westlandia, the public holds 50% of M1 in the form of

currency, and the required reserve ratio is 20%. Estimate how

much the money supply will increase in response to a new

cash deposit of $500 by completing the accompanying table.

(Hint: The first row shows that the bank must hold $100 in

minimum reserves—20% of the $500 deposit—against this deposit,

leaving $400 in excess reserves that can be loaned out.

However, since the public wants to hold 50% of the loan in

currency, only $400 × 0.5 = $200 of the loan will be deposited

in round 2 from the loan granted in round 1.) How does your

answer compare to an economy in which the total amount of

the loan is deposited in the banking system and the public

doesn’t hold any of the loan in currency? What does this

imply about the relationship between the public’s desire for

holding currency and the money multiplier?

Explanation / Answer

Part 1: Customer Initial Amount Customer Holds Deposit Amount Bank Holds Bank Loans A $500.00 $250.00 $250.00 $50.00 $200.00 B $200.00 $100.00 $100.00 $20.00 $80.00 C $80.00 $40.00 $40.00 $8.00 $32.00 D $32.00 $16.00 $16.00 $3.20 $12.80 E $12.80 $6.40 $6.40 $1.28 $5.12 F $5.12 $2.56 $2.56 $0.51 $2.05 G $2.05 $1.02 $1.02 $0.20 $0.82 H $0.82 $0.41 $0.41 $0.08 $0.33 I $0.33 $0.16 $0.16 $0.03 $0.13 J $0.13 $0.07 $0.07 $0.01 $0.05 K $0.05 $0.03 $0.03 $0.01 $0.02 L $0.02 $0.01 $0.01 $0.00 $0.01 M $0.01 $0.00 $0.00 $0.00 $0.00 $833.33 $416.66 $416.66 $83.33 $333.33 So, the initial $500 becomes $833.33 Part 2: The easy way to find this is to use this formula: Final Amount=Initial Amount*(1/Reserve Ratio) Final Amount=500*(1/.2)=$2500 The long way is this: Customer Initial Deposit Bank Holds Bank Loans A $500.00 $100.00 $400.00 B $400.00 $80.00 $320.00 C $320.00 $64.00 $256.00 D $256.00 $51.20 $204.80 E $204.80 $40.96 $163.84 F $163.84 $32.77 $131.07 G $131.07 $26.21 $104.86 H $104.86 $20.97 $83.89 I $83.89 $16.78 $67.11 J $67.11 $13.42 $53.69 K $53.69 $10.74 $42.95 L $42.95 $8.59 $34.36 M $34.36 $6.87 $27.49 N $27.49 $5.50 $21.99 O $21.99 $4.40 $17.59 P $17.59 $3.52 $14.07 Q $14.07 $2.81 $11.26 R $11.26 $2.25 $9.01 S $9.01 $1.80 $7.21 T $7.21 $1.44 $5.76 U $5.76 $1.15 $4.61 V $4.61 $0.92 $3.69 W $3.69 $0.74 $2.95 X $2.95 $0.59 $2.36 Y $2.36 $0.47 $1.89 Z $1.89 $0.38 $1.51 AA $1.51 $0.30 $1.21 AB $1.21 $0.24 $0.97 AC $0.97 $0.19 $0.77 AD $0.77 $0.15 $0.62 AE $0.62 $0.12 $0.50 AF $0.50 $0.10 $0.40 AG $0.40 $0.08 $0.32 AH $0.32 $0.06 $0.25 AI $0.25 $0.05 $0.20 AJ $0.20 $0.04 $0.16 AK $0.16 $0.03 $0.13 AL $0.13 $0.03 $0.10 AM $0.10 $0.02 $0.08 AN $0.08 $0.02 $0.07 AO $0.07 $0.01 $0.05 AP $0.05 $0.01 $0.04 AQ $0.04 $0.01 $0.03 AR $0.03 $0.01 $0.03 AS $0.03 $0.01 $0.02 AT $0.02 $0.00 $0.02 AU $0.02 $0.00 $0.01 AV $0.01 $0.00 $0.01 AW $0.01 $0.00 $0.01 AX $0.01 $0.00 $0.01 AY $0.01 $0.00 $0.01 AZ $0.01 $0.00 $0.00 BA $0.00 $0.00 $0.00 BB $0.00 $0.00 $0.00 BC $0.00 $0.00 $0.00 $2,499.99 $500.00 $1,999.99 The same $500 dollars is much larger when the public does not hold currency. Overall, the smaller the public's desire to hold money is, the more the money will multiply.

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