$2$ . Assume a given economy has an equilibrium GDP of $\$ 325$ billion. ( $18$ points) $\newline$ a. If government spending and taxes both increase by $\$ 25$ billion, determine the new equilibrium GDP. $\newline$ b. If both $\mathbf{G}$ and taxes increase by $\$ 25$ billion, what impact will these two changes happening at the same time have on the budget? In other words, will these two changes alone cause a surplus, a deficit, or a balanced budget? $\newline$ c. Solve for the numerical value of the balanced budget multiplier.

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Grade 8

Interpreting Linear Expressions

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2

. Assume a given economy has an equilibrium GDP of

\$ 325

billion. (

18

points)

\newline

a. If government spending and taxes both increase by

\$ 25

billion, determine the new equilibrium GDP.

\newline

b. If both

\mathbf{G}

and taxes increase by

\$ 25

billion, what impact will these two changes happening at the same time have on the budget? In other words, will these two changes alone cause a surplus, a deficit, or a balanced budget?

\newline

c. Solve for the numerical value of the balanced budget multiplier.

Analyze Scenario: Step $1$ : Analyze the initial scenario. $\newline$ The initial equilibrium GDP is $\$325$ billion. If government spending (G) and taxes (T) both increase by $\$25$ billion, we need to calculate the new equilibrium GDP.
Calculate New GDP: Step $2$ : Calculate the new equilibrium GDP. $\newline$ The formula for GDP considering government spending and taxes is $\text{GDP} = C + I + G + (X - M) + (T - G)$ , where $C$ is consumption, $I$ is investment, $X$ is exports, $M$ is imports, and $T$ is taxes. Since $G$ and $T$ both increase by the same amount, the net effect on GDP is zero, assuming other factors remain constant. $\newline$ New GDP = \$($325$ \text{ billion}) + (\$($25$ \text{ billion}) - \$($25$ \text{ billion})) = \$($325$ \text{ billion}).
Impact on Budget: Step $3$: Determine the impact on the budget.$\newline$Since both government spending and taxes increase by $\$25$ billion, the increase in taxes offsets the increase in spending. This results in a balanced budget.
Calculate Multiplier: Step $4$: Calculate the balanced budget multiplier.$\newline$The balanced budget multiplier is calculated as the change in GDP divided by the change in government spending when taxes are adjusted to maintain a balanced budget. Since the change in GDP is $\$0$ (from Step $2$), the balanced budget multiplier is:$\newline$Balanced Budget Multiplier = Change in GDP / Change in G = $\$0 / \$25$ billion = $0$.