Final answer:
To increase the money supply by $2 million using a required reserve ratio of 10% and assuming no excess reserves, the Fed must purchase $20 million in government securities.
Step-by-step explanation:
To determine the value of government securities the Fed must purchase to increase the money supply by $2 million, we need to use the required reserve ratio. The required reserve ratio is 10%, which means banks must keep 10% of their deposits as reserves. If the Fed wants to increase the money supply by $2 million, it needs to calculate the total increase in deposits that the banks can lend out. We can use the money multiplier formula to calculate this increase in the money supply.
The money multiplier formula is:
Money Multiplier = 1 / Reserve Ratio
We can plug the reserve ratio value of 10% into the formula:
Money Multiplier = 1 / 0.10 = 10
Now we can calculate the total increase in deposits:
Total Increase in Deposits = Money Multiplier x Increase in Reserves
In this case, the desired increase in reserves is $2 million. Plugging in the values:
Total Increase in Deposits = 10 x $2 million = $20 million
Therefore, the value of government securities the Fed must purchase to increase the money supply by $2 million is $20 million.