Question

include correctly labeled diagrams, if useful or required, in explaining your answers. a correctly labeled diagram must have all axes and curves clearly labeled and must show directional changes. if the question prompts you to \calculate,\ you must show how you arrived at your final answer. the table below provides data on the spending on final goods, in billions of dollars, by consumers, businesses, and the government in equilibrium in a country with no international trade.

aggregate variables	value (in billions of dollars) in the base year
investment spending	$400
government spending	$200
transfer payments	$60

the marginal propensity to save is equal to 0.4 and there are no exports or imports. (a) calculate the real gdp in this country. show your work. (b) calculate the marginal propensity to consume. show your work. (c) suppose that the government increases spending from $200 billion to $300 billion. (i) calculate the maximum change in real gdp. show your work. (ii) given the change in real gdp in part (c)(i), calculate the maximum level of the new equilibrium real gdp. show your work. (d) suppose that taxes decrease by $100 billion. will the maximum change in real gdp be larger than, smaller than, or equal to the change in real gdp identified in part (c)(i)? explain.

Explanation:

Step1: Calculate real GDP

In a closed - economy (no international trade), real GDP (Y) is calculated using the expenditure approach: $Y = C+I + G$, where $C$ is consumption, $I$ is investment, and $G$ is government spending. Given $C = 900$, $I = 400$, and $G=200$.
$Y=900 + 400+200=\$1500$ billion.

Step2: Calculate marginal propensity to consume

The marginal propensity to save (MPS) and the marginal propensity to consume (MPC) are related by the equation $MPC + MPS=1$. Given $MPS = 0.4$.
$MPC=1 - MPS=1 - 0.4 = 0.6$.

Step3: Calculate the government - spending multiplier

The government - spending multiplier ($k_G$) is given by the formula $k_G=\frac{1}{MPS}$. Since $MPS = 0.4$, $k_G=\frac{1}{0.4}=2.5$.

Step4: Calculate the maximum change in real GDP due to government - spending increase

The change in government spending ($\Delta G$) is $300 - 200=\$100$ billion. The change in real GDP ($\Delta Y$) is given by $\Delta Y=k_G\times\Delta G$.
$\Delta Y = 2.5\times100=\$250$ billion.

Step5: Calculate the new equilibrium real GDP

The initial real GDP is $Y_1 = 1500$ billion. The new equilibrium real GDP ($Y_2$) is $Y_2=Y_1+\Delta Y$.
$Y_2=1500 + 250=\$1750$ billion.

Step6: Analyze the tax - change effect

The tax multiplier ($k_T$) is given by $k_T=-\frac{MPC}{MPS}$. Since $MPC = 0.6$ and $MPS = 0.4$, $k_T=-\frac{0.6}{0.4}=- 1.5$. A decrease in taxes ($\Delta T=-100$ billion) leads to a change in real GDP of $\Delta Y_T=k_T\times(-\Delta T)$.
$\Delta Y_T=1.5\times100 = 150$ billion. The maximum change in real GDP due to a $100$ - billion decrease in taxes is smaller than the change in real GDP due to a $100$ - billion increase in government spending ($250$ billion) because the absolute value of the tax multiplier ($|k_T| = 1.5$) is less than the government - spending multiplier ($k_G = 2.5$).

Answer:

(a) Real GDP = $1500$ billion
(b) MPC = $0.6$
(c)(i) $\Delta Y = 250$ billion
(c)(ii) New equilibrium real GDP = $1750$ billion
(d) The maximum change in real GDP due to a $100$ - billion decrease in taxes is smaller than the change in real GDP in part (c)(i) because the absolute value of the tax multiplier ($1.5$) is less than the government - spending multiplier ($2.5$).