$(2)(12$ points$)$ A country called Technalia experienced rapid development of computing and information technology that led to a big increase in potential real GDP$.$ The central bank wanted to stimulate aggregate demand to ensure the economy fully utilizes the increased potential but wanted to keep inflation from increasing as well.

$($a$)(3$ points$)$ Starting from the initial long$-$run equilibrium, describe the short$-$run effects of the technological boom without intervention by Techlandia's central bank in terms of price and output. Use the AD$/$AS model to assist your reasoning. $[$Note that potential output does not stay constant in this example$]$

$($b$)(3$ points$)$ Describe the long$-$run effects of the technological boom without intervention by Techlandia's central bank. Use the AD$/$AS model to assist your reasoning.

$($c$)(3$ points$)$ Now assume that Techlandia's central bank used a moderate expansion policy during this period. How did this influence the economy $($price and output$)$ in the short run? Use the $\backslash (\backslash$mathrm$\{$AD$\}/\backslash$mathrm$\{$AS$\}\backslash )$ model to assist your reasoning.

$($d$)(3$ points$)$ Describe the new long$-$run equilibrium. Was the central bank's job of keeping inflation low $($stable price level$)$ hard given the general economic conditions? Explain.

$(3)(5$ points$)$ An economy is producing output $\backslash (\backslash$$ $400\backslash )$ billion less than the natural level of output, and fiscal policymakers want to close this recessionary gap. The central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. The marginal propensity to consume is $\backslash (4/5\backslash ),$ and the price level is completely fixed in the short run. In what direction and by how much must government spending change to close the recessionary gap?