Question

Given that IS is Y = 2500-50i, and the interest rate reaction function is ip = 2 + 0.5(P-P*), where ip is the central bank policy rate. Assume that i (interest rate) is 0.5 + ip (interest rate is a wedge over the policy rate). Determine the AD function. If AS function was Y = 0.25(P-P*) + 2000 determine Y* and P* and inflation rate. Assume P* = 105.

Answer 1

$i=0.5+2+0.5(P-P^*)=2.5+0.5(P-P^*)$

$Y=2500-50(2.5+0.5(P−P ^∗ ))=2500-125-25(P−P ^∗ )=2375-25(P−P^∗ )$

$AD = Y =2375-25(P−P^∗)$

Y*-equlibrium output

If P*=105

$AD=AS=Y^*$

$(P-105)=0.25(P-105)+2000$

$25.25(P-105)=375$

$P-105=14.85$

$P=119.85$

$Y^*=2375-25*14.85=2003.75$

ir-inflation rate. 

$ir=\frac{P-P^*}{P^*}*100=\frac{14.85}{105}*100=14.14$

ir=14.14%