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When I did my B.A. in economics, I never thought about extending $L(i)$ to negative y-axis.

A central bank like the US Federal Reserve is quantitative easing more. This means $\dfrac{M}{P}$ curve shifts to right. But what if $\dfrac{M}{P}$ shifts so much right to $\dfrac{M}{P}_3$ ? Won't $i_3 < 0$?

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  • $\begingroup$ Can you clarify (i.e put in words) what this question is actually asking, notations aside? I take it the context is the IS-LM model, about which you asked another question at the ZLB. (So I'm not sure how this question differs from that.) Also your title is basically missing a verb, making it even hard to figure out what is being asked here. $\endgroup$
    – Fizz
    Apr 12 '20 at 17:05
  • $\begingroup$ @fizz thanks. is my edit better? what happens if central bank shifts $M/P$ right so much that it causes negative interest rate? $\endgroup$
    – NNOX Apps
    Apr 12 '20 at 19:50
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In the IS-LM model the interest rate cannot become negative. In the model's world there are two types of assets available to the consumers for storing value - cash and bonds. The advantage of the cash is that it can be used for transactions. The advantage of the bonds is that they pay interest. The negative relationship between the real balances and the interest rate on bonds appears quite naturally. The higher the interest rate, the more worthwhile it becomes to invest in bonds instead of keeping the cash. If the interest rate is 0 this incentive disappears. The interest rate on bonds cannot be forced below zero due to arbitrage. If today's price of a bond that pays 100\$ in six months is 101\$, people will start selling to get an extra dollar for nothing until the price of the bond becomes 100\$ again. Thus the LM curve starts from the origin of the IS-LM graph and is identical to the x-axis until it lifts off for some positive value of Y and from there onward has the increasing shape you draw.

The observation of the model is true in the real world as well. In normal times the real world central banks target overnight deposit rates instead of bond rates. To be able to make the targeted interest rates negative the central banks (Fed, ECB) came up with a trick in 2008 - interest rates on excess reserves held at the central bank. The ECB started paying negative interest rates on reserves in June 2014, which has reliably pulled the overnight interest rate in the euro zone (EONIA) below zero. The ECB also removed the largest banknote - 500 EUR from circulation to make storing value in cash more expensive . The effect of negative interest rates has not been very textbook-like however .

The Fed has not made use of this option yet - its interest rate on reserves has never been below zero.

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