Consider the A$($S$)/($A$)$D model covered in class, but where the AS curve $($ie$,$ the Phillips curve$)$ depends

on unemployment, not current output. The implicit assumption is that the demand for firm product

and services is determined by the strength of the labor market, not total income.

In addition, let$$s add a third equation $($Okun$$s law$),$ which relates the unemployment rate with

current output. The parameter $\backslash$phi $>0$ governs the strength of that relationship.

eYt $=$ a $-$ bm$(\backslash$pi t $-\backslash$pi $)($AD$)$

$\backslash$pi t $=\backslash$pi t$-1-$ v$($ut $-$ u$)($AS$)$

ut $=$ u $-\backslash$phi eYt $($Okun$$s law$)$

$1$

$($a$)$ Suppose that the economy is in steady$-$state at t $=0,$ then there is a demand shock a $>0$ at time

t $=1.$ Compute the effect on output eY$1.$ What happens when $\backslash$phi is very small? Interpret.