Question $1$:$[50$ pts $]$

The government has announced a plan to restore budgetary balance by significantly cutting public expenditures over the next three years. Using the AS$/$AD model, analyse the potential short$-$term and long$-$term effects of this policy on the economy.

a$)($Year One$)$ What kind of shock does this represent, and which variable in the AS$/$AD model is affected? Illustrate the shock on an AS$/$AD diagram, labeling the economy's initial equilibrium as A and the new position after the initial impact as $B.$ Explain the changes in output and price levels resulting from the initial impact of this shock.

b$)($Year Two$)$ Let the parameter $\frac{?}{\text{b}\text{a}\text{r}}(o)$ to be zero. Write down the equation of the AS curve in Year $1$ and Year $2$ separately. Compare these twd equations. If output is zero in Period $2,$ what is the corresponding level of inflation? Identify this point on the AS$/$AD diagram and draw the Period $2$ AS curve. Label the economy in Period $2$ as $C_1.$ Explain the changes in inflation and output between Period $1$ and Period $2,$ and discuss the underlying reasons driving these changes.

c$)($Year Three$)$ Similar to part b$),$ write down the equation of the AS curve in Year $3.$ What is the corresponding level of inflation if output is zero in Period $3?$ Identify this point on the AS$/$AD diagram and draw the Period $3$ AS curve. Label the economy in Period $3$ as C$.$ Compare the points $C_1($from Year $2)$ and $C($from Year $3),$ explain the changes in inflation and output between Period $2$ and Period $3.$

d$)($Year Four$)$ In year four, the budget cuts come to an end, and the government restores spending to its normal level. Which variable in the AS$/$AD model is affected? Illustrate this change on the AS$/$AD diagram, and label the new economic position as $D.$ How do they differ, and why? Note: economy moves from $C($from Part c$)$ to $D.$ Ensure the diagram reflects the location of C from Part c$)$ when drawing the new location. Compare the output and inflation levels at $D$ with those of the original economy $($from Part a$).$