Suppose In Fantasia, A Bank Initially Has 10,000 Deposits

2suppose In Fantasia A Bank Initially Has 10000 Of Deposits Out

Suppose in Fantasia, a bank initially has $10,000 of deposits; out of this deposit, it keeps reserves of $2,000, and had already created loans of $8,000. All monetary transactions are made by check, no one uses currency. Furthermore, Fantasia’s central bank has a required reserve of 10% of deposits.

a) Suppose the bank lends out all of the excess reserves (keeps only the required reserve), and people do not keep cash, how much does the money supply change due to the new loan?

b) Due to the upcoming New Year holiday, people in Fantasia increased their cash holding from zero to 20% of total deposits (while the bank still keeps zero excess reserve); what is the money multiplier now?

c) And then, following b); at the same time, suppose the bank anticipated a withdrawal from a client, so it decided to hold more excess reserves, about 15% of total deposits to anticipate some cash withdrawals, what is the multiplier now?

Paper For Above instruction

The scenario of banking operations and monetary policy in Fantasia presents a comprehensive case for understanding the mechanics of the money supply, reserve requirements, and the effects of varying reserve holdings on the money multiplier. This analysis explores how changes in bank reserves, hoarding behavior, and central bank activities influence the broader money supply within the economy.

Firstly, when examining how the money supply is affected by reserve management, it is essential to understand the initial conditions. The bank starts with $10,000 in deposits, of which $2,000 is held as reserves, and $8,000 has been lent out. The reserve requirement mandated by the central bank is 10%, which means the bank must hold reserves equal to 10% of total deposits. In this initial state, the bank retains $2,000 in reserves, matching the required reserve of 10%, and an additional $0 in excess reserves (since total reserves equal the required reserve).

The central question in part (a) is: if the bank lends out all its excess reserves (which initially are zero, since reserves exactly equal the required reserve), how much does the money supply change? Given that the bank is already holding reserves equal to the requirement ($2,000) and has lent out $8,000, the excess reserves at this stage are zero. Therefore, if the bank lends out all of its excess reserves, the potential increase in the money supply depends on the available excess reserves. However, initially, there are no excess reserves; thus, the loan expansion remains limited by this fact. If, hypothetically, the bank had excess reserves, say an amount above the required, lending out these could generate a multiple increase in deposits based on the reserve ratio.

In this specific case, because the bank's reserves are exactly at the required level, the excess reserves are zero. Therefore, in the initial scenario, the banks cannot lend more unless reserves increase or the bank adjusts its reserve holdings.

Second, in part (b), when consumers increase their cash holdings to 20% of total deposits, the effective money multiplier decreases. Traditionally, the money multiplier is calculated as the reciprocal of the reserve requirement (1/0.10 = 10) under the assumption that all other factors are constant, and there is no cash hoarding. However, with consumers holding cash outside the banking system, fewer funds are available to circulate through bank loans, effectively reducing the multiplier. The new multiplier can be expressed as the reciprocal of the sum of reserve ratio and cash holding ratio: 1 / (reserve ratio + cash holding ratio). With a cash holding of 20%, the multiplier becomes 1 / (0.10 + 0.20) = 1 / 0.30 ≈ 3.33. This indicates that for every dollar in reserves, the total money supply expands roughly 3.33 times, rather than 10 with no cash hoarding.

Finally, in part (c), if the bank anticipates withdrawals and increases its excess reserves to 15% of deposits, the effective reserve ratio increases. This scenario further diminishes the money multiplier, because more reserves are kept in anticipation of cash withdrawals, and fewer funds are available for lending. The new effective reserve ratio becomes the sum of the required reserve ratio plus the excess reserves held as a percentage of deposits. Given that excess reserves are 15%, the total reserve ratio is 10% (required) + 15% (excess) = 25%. The adjusted money multiplier becomes 1 / (reserve ratio + cash holding ratio). If we assume cash holdings remain at 20%, the new total reserve ratio becomes 0.10 + 0.15 = 0.25, and the multiplier again is 1 / 0.25 = 4.

In conclusion, the dynamics of the money supply in Fantasia are sensitive to reserve policies, consumer cash holdings, and anticipated withdrawals. These factors directly influence the money multiplier and the extent of deposit expansion within the banking system, illustrating the importance of central bank policies and banking management in stabilizing and controlling the money supply.

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