1. A bank has $120 million in total assets, which are composed of reserves,
loans, and securities. Its only liabilities are $120 million in transactions
deposits. The banks exactly satisfies its reserve requirement, and its total
reserves equal $6 million. What is the required reserve ratio?
2. Suppose that the value of the potential money multiplier is equal to 4. What
is the required reserve ratio?
3. Suppose that the quantity of money in circulation is fixed but the income
velocity of money doules. If real GDP remains at its long-run potential
level, what happens to the equilibrium price level?
was just wondering if thers a formula for these prblems. how would i set up number 1??
1. To find the required reserve ratio, we need to determine the ratio of required reserves to transaction deposits.
Given that the bank's total reserves equal $6 million and its total transaction deposits equal $120 million, we can set up the following equation:
Required Reserve Ratio (RR) = Required Reserves / Transaction Deposits
Since the bank exactly satisfies its reserve requirement, the required reserves will be equal to the total reserves. Thus, we have:
RR = $6 million / $120 million
Simplifying this expression, we find that the required reserve ratio is 0.05 or 5%.
2. The potential money multiplier is calculated as the reciprocal of the required reserve ratio. So, if the value of the potential money multiplier is 4, we can find the required reserve ratio as follows:
Required Reserve Ratio (RR) = 1 / Potential Money Multiplier
Substituting the given value, we have:
RR = 1 / 4
Therefore, the required reserve ratio in this case is 0.25 or 25%.
3. In this scenario, if the quantity of money in circulation remains fixed and the income velocity of money doubles, we can expect some effects on the equilibrium price level.
The equation of exchange, which relates the quantity of money (M), velocity of money (V), price level (P), and real output (Y), is given by:
M × V = P × Y
Since the quantity of money (M) is fixed, if the income velocity of money (V) doubles, we can write the equation as:
Fixed M × (2V) = P × Y
If real GDP (Y) remains at its long-run potential level, the increased velocity of money (2V) should result in a proportional increase in the price level (P) to maintain the equation of exchange. Therefore, the equilibrium price level would also double.
1. To find the required reserve ratio, you need to know the total reserves and the transactions deposits of the bank. The formula to calculate the required reserve ratio is:
Required Reserve Ratio = Total Reserves / Transactions Deposits
In this case, the total reserves are given as $6 million, and the transactions deposits are given as $120 million. By substituting these values into the formula, you can solve for the required reserve ratio:
Required Reserve Ratio = $6 million / $120 million
Required Reserve Ratio = 0.05 or 5%
Therefore, the required reserve ratio for the bank is 5%.
2. The potential money multiplier is the reciprocal of the required reserve ratio. So, if the value of the potential money multiplier is given as 4, you can find the required reserve ratio by taking the reciprocal of 4:
Required Reserve Ratio = 1 / Potential Money Multiplier
Required Reserve Ratio = 1 / 4
Required Reserve Ratio = 0.25 or 25%
Hence, the required reserve ratio is 25% if the potential money multiplier is 4.
3. The equilibrium price level is determined by the equation of exchange:
MV = PQ
Where M represents the quantity of money, V represents the income velocity of money, P represents the price level, and Q represents the real GDP.
In this scenario, the quantity of money in circulation is fixed, which means M remains constant. However, the income velocity of money doubles, so V increases. If the real GDP remains at its long-run potential level, Q remains constant.
The equation of exchange can then be rewritten as:
MV = PQ
Since M, Q, and V are constant, we can say that M/V is also constant. Therefore, any changes in V will result in an equal proportional change in P.
In this case, if the income velocity of money doubles, it means that V increases by a factor of 2. Consequently, the equilibrium price level, P, will also double.
So, in summary, if the quantity of money in circulation is fixed, the income velocity of money doubles, and real GDP remains constant, the equilibrium price level will double.