a. When the Treasury of the United States issues bonds and sells them to the public to finance the deficit, the money supply remains unchanged because every dollar of money taken in by the Treasury goes right back into circulation through government spending. This is not true when the Fed sells bonds to the public.
Budget deficit refers to the situation when the revenue of the government is less than the expenses of the government. To finance budget deficit, government can take various steps like borrowings, issuing bonds, raising taxes, etc.
Yes, this statement is true.
When the Treasury sells bonds to raise money to finance budget deficit, in this case firstly Treasury will raise money from the public and then it will use that money for the expenditures. In this way, money will go back to the public. Hence, level of money supply will remain unchanged. But this is not true for Fed because when Fed will sell bond it will take the money from the public but this money will not be spent by Fed because of this, money supply will reduce in this case.