The liquidity trap

The liquidity trap. Consider the following model. The dynamics of inflation are given by the continuous-time version of λ > 0. The IS curve takes the traditional form,  The central bank sets the interest rate according to (6.26), but subject to the constraint that the nominal interest rate cannot be negative: i(t) = max[0,π(t) + For simplicity, normalizefor all t.

(a) Sketch the aggregate demand curve for this model—that is, the set of points in (y,π) space that satisfy the IS equation and the rule above for the interest rate

(b) Letdenote the point on the aggregate demand curve whereSketch the paths of y and π over time if