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The real interest rate ($$r$$) at the zero lower bound (ZLB) is derived from the Fisher equation ($$r = i - \pi^E$$) by setting the nominal interest rate ($$i$$) to its floor of 0%. This results in the real interest rate at the ZLB ($$r_{\text{ZLB}}$$) being equal to the negative of the expected inflation rate ($$\pi^E$$). The formal derivation is: $$ \begin{align*} r &= i - \pi^E \\ i_{\text{ZLB}} &= 0\% \\ r_{\text{ZLB}} &= i_{\text{ZLB}} - \pi^E = -\pi^E \end{align*} $$

Formula for the Real Interest Rate at the Zero Lower Bound

In an economy where the policy nominal interest rate is fixed at its lowest possible value of 0%, an increase in the public's expectation of future inflation will lead to a decrease in the real interest rate.

Given the following economic scenario, calculate the effective real interest rate and explain why the central bank's policy may be ineffective at stimulating the economy.

Economic Stimulus Challenge at the Interest Rate Floor

Imagine an economy where the central bank's main policy interest rate is already at its absolute minimum of 0%. If the central bank wants to further stimulate the economy by making borrowing even cheaper (i.e., lowering the real cost of borrowing), what must happen to the public's expectations about future price levels? Explain your reasoning using the relationship between nominal rates, real rates, and expected price level changes.

Policy Limitations at the Interest Rate Floor

A central bank has set its policy nominal interest rate to its absolute minimum of 0% in an attempt to stimulate a struggling economy. If the public's expectation for inflation over the next year is 2.5%, what is the resulting real interest rate?

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