Consider the following economy:

Aggregate Expenditure=Et=Ct+It+Gt+XtMt

Consumption =Ct=ac+bcYt

Investment=It=aibiRt

Inflation=t=te+vYt+ot

Policy Rule=Rtr=m(t)

Government Expenditure and Trade=Gt=G,Mt=M,Xt=X

Use the previous equations to answer the following questions:

(a) (5 points) Derive the AD curve.

(b) (10 points) Assume thatte=t1. Suppose the economy is at its potential output equilibrium with a constantinflation rate. Using the AS-AD model, carefully explain what happens to the economyover timeif there is a one-period positive demand shock.