In our case, the increased proceeds from taxes will have to amount to $30 million, in order to set-off the increase in government spending and to maintain the same GDP. The increase in government expenditures will fully offset the negative impact of taxes.

If only $100 million are spent by the government, the rest of $50 million will have to come from tax cuts. The effect will be the total elimination of the $1.5 trillion aggregate demand.

Question 6.

1. Deposit Expansion Multiplier

While a single bank can only lend its excess reserves, the banking system can increase the money supply by a multiple of initial excess reserves.

Deposit expansion multiplier = 1/(reserve requirement)

The initial assumption is that banks hold no excess reserves and that there is no currency drain from the banking system. If the exceeds reserves are zero, a theoretical infinite increase of the money supply is achievable.

2. If the reserve requirement ratio is 0.08 and all banks lend out all their excess reserves, the effect on the money supply is as follows:

Increase in money supply = Deposit * Deposit expansion multiplier = $10,000 * 1/0.08 = $10,000 * 12.5 = $125.000

3. If the banks have to hold an additional 4% of the total deposits on reserve, than they will lend only $9,600 instead of $10.000. The Deposit expansion multiplier is the same, since the reserve requirement ratio hasn't changed, so the Increase in money supply = Deposit * Deposit expansion multiplier = $9,600 * 1/0.08 = $9,600 * 12.5 = $120.000

4. The Federal Reserve is in control of reserves by lending money to banks and changing the "Federal Reserve discount rate" on these loans and by "open-market operations." The Federal Reserve uses open-market operations to either increase or decrease reserves.

The Federal Reserve controlled the amount of reserves and of borrowing by member banks mainly by changing the discount rate. It did so based on the theory that borrowed reserves made member banks reluctant to extend loans, because their...

Then, the Federal Reserve found out that open-market operations also created reserves, changing non-borrowed reserves offered a more effective way to offset undesired changes in borrowing by member banks. The Federal Reserve then tried to control what are called free reserves, or excess reserves minus member bank borrowing.
A. Schwartz also points out that "To increase reserves, the Federal Reserve buys U.S. Treasury securities by writing a check drawn on itself. The seller of the Treasury security deposits the check in a bank, increasing the seller's deposit. The bank, in turn, deposits the Federal Reserve check at its district Federal Reserve bank, thus increasing its reserves. The opposite sequence occurs when the Federal Reserve sells Treasury securities: the purchaser's deposits fall and, in turn, the bank's reserves fall."

The interest rate of government bonds heavily influences interest rates. If the Fed sells these bonds, the banks which buy them modify their interest rate accordingly, in conjunction with the one of the bonds. This rate is the one expected by the Federal Reserve in the future, so the banks have to act on it. One other factor is that government bonds are actually without risk, so banks gain money by simply collecting the difference between rates.