Consider an exogenous increase in real money demand $($e$.$g$.,$ a substantial decrease in credit card usage$)$ in a closed economy. Assume that prices are fixed in the short run. Also assume that there are no changes in long$-$run aggregate supply.

$($a$)$ Will the interest rate increase in the short run?

$($b$)$ Will income increase in the short run?

$($c$)$ Will the price level increase in the transition from the short run to the long run $($absent any policy response$)?$ For future reference, denote the resulting long$-$run price level by $\backslash (\backslash$mathrm$\{$P$\}^\{*\}\backslash ).$

$($d$)$ Now, assume that there was a policy response. In particular, the government intervened in order to stabilize OUTPUT in the short run.

$($i$)$ Assuming no change in government spending, did the government intervention involve an increase or a decrease in tax revenue?

$($ii$)$ Did the intervention also stabilize the interest rate in the short run?

$($iii$)$ Will the long$-$run price level $($following the government's intervention$)$ end up greater, smaller, or equal to $\backslash (\backslash$mathrm$\{$P$\}*\backslash )?$