# A Liquidity Trap in an AS/AD Framework (Part III of IV)

It’s been a while. In my previous two posts on this topic, we saw first how the AS/AD worked, and then how it was modified to include the possibility of the zero lower bound (ZLB). Recall that the ZLB means that central banks cannot reduce the nominal interest rate below 0%.

Recall that the AS curve is given as:

AS: $\pi_t = \pi_{t-1} + \bar{v}\tilde{Y}_t + \bar{o}$

Back in November, we saw the following result for the AD curve:
AD: $\tilde{Y}_t = \bar{a} - \bar{b} \bar{m} (\pi_t - \bar{\pi})$  if  $\pi_t \ge \frac{\bar{m}\bar{\pi}-\bar{r}}{1+\bar{m}}$

$\tilde{Y}_t = \bar{a} + \bar{b} \bar{r} + \bar{b} \pi_t$  otherwise.

Plotting the AS and AD equations, we have:

Now, let’s see what would happen in the AS/AD model if we had a small negative demand shock, and we had started at the equilibrium depicted above:

We see that since the AD curve has shifted left, it causes disinflation.  Since inflation has fallen, the intercept of the AS curve, which includes  $\pi_{t-1}$ , is now smaller.  In other words, the AS curve shifts down.  The downward shift of the AS curve causes another decrease in inflation, and this process will repeat until the output gap is closed (i.e. output returns to potential, at the point short-run output = 0% in the above graph).  We can see that the the economy above is self stabilizing for small demand shocks – that is, a small demand shock does not cause any explosive behavior, such as sending inflation to infinity or to negative 100%.

But what would happen if a bigger demand shock hit?  If the shock is large enough so that the kink in the AD curve falls to the left of 0%, and if this shock is long lasting, it will eventually result in a deflationary spiral:

From the graph, it’s easy to see that the output gap can never be closed, it will always be negative, no matter how the AS curve shifts.  Due to the zero lower bound, the Fed cannot stabilize the economy, and the economy explodes towards both an output gap and inflation of -100%. In other words, the economy continuing shrinking until there is 100% unemployment, and no currency.  This is obviously an extreme scenario; we are basically pushing this model to its breaking point.  However, it illustrates how deflation and the zero lower bound can cause severe economic problems in real life, such as prolonged depressions or secular stagnation.

What happens when the shock ends? Will the deflationary spiral end?  How could we avoid this episode in the first place? I’ll try to answer these questions, at least in this simple model, in my next post.