Exercise: federal funds market

Assume that you have the following information about the federal funds market:

$\\D_f:\rho=10- \$ \\\ S_f: \$= 8.5 \\\ DR: \rho= 5$

Note that the discount rate must be above the federal funds rate in order for the latter to be effective. In other words, the supply curve becomes perfectly elastic at the DR.

Another important point is that the demand for federal funds also becomes perfectly elastic when the interest rate is at or below zero percent. At this rate, commercial banks demand federal funds as much as they can.

You are tasked with conducting the optimal open market operation given that the economy just started to experience a downturn. Given available data you conclude that the optimal rate must be at 0.5%.

Solve for the new supply curve, find how many government bonds (in terms of dollars) should the Fed buy or sell. Then, explain what will happen to the aggregate demand on the AD/AS model.

solve for the original rho (FFR):

$D_f=S_f\rightarrow \rho_1=1.5\%$

Set the FFR equal to 0.5%, and solve for the dollar amount:

$0.5=10-\$\rightarrow \$=9.5$

Assuming that in our case $=1 is worth one million dollars, the Fed must increase the amount of liquidity by one million dollars in the banking system for excess reserves. Thus, they central bank must buy one million dollars worth of bonds from commercial banks.

Buying bonds from commercial banks shifts the money supply curve to the right, lowering the nominal interest rate, which will ultimately shift the aggregate demand to the right. This is an expansionary policy.

Let's graph that:

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