Question

1. aggregate expenditures and income

the following table shows consumption (c), investment (i), government spending (g), and net exports (x - m) in a hypothetical economy for various levels of real gdp (y). assume that the price level remains unchanged at all levels of income. all figures are in billions of dollars.
compute aggregate expenditures for each income level and fill in the last column in the following table.

the following graph shows real gdp on the horizontal axis and aggregate expenditures (ae) on the vertical axis. the orange line (square symbols) represents a 45 - degree (y = ae) line.
use the blue points (circle symbol) to plot the aggregate expenditures line for this economy. line segments will automatically connect the points.

place the black point (cross symbol) where the aggregate expenditures line intersects the 45 - degree line. dashed drop lines will automatically extend to both axes.
the equilibrium output at this price level is equal to
suppose real gdp is currently $500 billion. assuming the price level remains constant, this would mean that, which would send a signal to firms to
the marginal propensity to consume (mpc) for this economy is and the spending multiplier for this economy is equal to

Explanation:

Step1: Calculate aggregate expenditures

The formula for aggregate expenditures \(AE = C+I + G+(X - M)\)

• For \(Y = 500\): \(AE=400 + 100+100+( - 50)=550\)
• For \(Y = 600\): \(AE=475 + 100+100+( - 50)=625\)
• For \(Y = 700\): \(AE=550 + 100+100+( - 50)=700\)
• For \(Y = 800\): \(AE=625 + 100+100+( - 50)=775\)
• For \(Y = 900\): \(AE=700 + 100+100+( - 50)=850\)

Step2: Find equilibrium output

Equilibrium occurs where \(Y = AE\). From the calculations above, when \(Y = 700\), \(AE=700\)

Step3: Analyze when \(Y = 500\)

When \(Y=500\), \(AE = 550\). Since \(AE>Y\), inventories decrease. Firms will increase production.

Step4: Calculate MPC

\(MPC=\frac{\Delta C}{\Delta Y}\). \(\Delta C=475 - 400 = 75\), \(\Delta Y=600 - 500=100\), so \(MPC = 0.75\)

Step5: Calculate spending multiplier

The formula for the spending multiplier \(k=\frac{1}{1 - MPC}\). Substituting \(MPC = 0.75\), we get \(k=\frac{1}{1 - 0.75}=4\)

Answer:

• Aggregate expenditures: 550, 625, 700, 775, 850 (for \(Y = 500,600,700,800,900\) respectively)
• Equilibrium output: 700
• When \(Y = 500\): Aggregate expenditures exceed real GDP; increase production
• MPC: 0.75
• Spending multiplier: 4