Answers to Assignment Six

Determination of Equilibrium GDP

• Aggregate Expenditures-Domestic Output Approach

  • Equilibrium is established when C + Ig = Real GDP ($550 + $50 = $600).

  • Intersection of aggregate expenditures schedule and the 45-degree line shows the point where total output equals total spending (GDP).

    • Why the 45-Degree Line?

      • It represents points where aggregate expenditures equal GDP.

      • When AE > GDP, output expands.

      • When AE < GDP, output contracts.

      • Hence, the equilibrium level is identified where C + Ig = GDP.

Planned Equilibrium vs. Disequilibrium Investment

• Planned vs. Unplanned Investment

  • Planned investment relates to desired inventory levels.

  • If inventories exceed planned levels, producers cut output.

  • If inventories fall short, output is increased.

  • Equilibrium GDP occurs when inventories meet planned levels.

Closed Economy Data Analysis

• Equilibrium GDP and Exports/Imports

  • Given Data:

    Real GDP	Aggregate Expenditures	Exports	Imports	Net Exports
    $100	$120	$10	$15	-$5
    $125	$140	$10	$15	-$5
    $150	$160	$10	$15	-$5
    $175	$180	$10	$15	-$5
    $200	$200	$10	$15	-$5
    $225	$220	$10	$15	-$5
    $250	$240	$10	$15	-$5
    $275	$260	$10	$15	-$5

• Equilibrium GDP Questions

  • (a) For a closed economy, equilibrium GDP = $200 billion.

  • (b) For an open economy, equilibrium GDP = $175 billion.

  • (c) If exports increase by $5 billion, equilibrium GDP = $200 billion.

  • (d) If imports decrease to $5 billion, equilibrium GDP rises to $225 billion.

  • (e) Multiplier effect calculated at:

    • Aggregate expenditures change by $5, GDP changes by $25 → Multiplier = 5.

Impact of government spending and taxation

• Government Spending Influence

  • Government spending increases aggregate demand directly.

  • Increased spending creates successive rounds of income increases proportional to the marginal propensity to consume (MPC).

  • Tax increases lower disposable income but do not directly reduce aggregate demand.

  • Therefore, simultaneous increases in taxes and government spending lead to a net positive effect on equilibrium GDP.

Consumption Equation Analysis

• Consumption Model

  • Given Equation: C = 50 + 0.9Y with Y = $400

    • (a) Marginal Propensity to Consume (MPC) = 0.9

    • (b) Marginal Propensity to Save (MPS) = 0.1

    • (c) Consumption Level at Y = 400: C = $410

    • (d) Average Propensity to Consume (APC) = C/Y = 410/400 = 1.025

    • (e) Average Propensity to Save (APS) = -0.025

Equilibrium Income Calculation

• Equilibrium Level for Given Consumption Schedule

  • Consumption Schedule: C = 50 + 0.8Y

  • Autonomous Investment (Ig) = $40; Net Exports (Xn) = -$10

  • (a) Equilibrium Y:

    • Y = C + Ig + Xn → 400 = (50 + 0.8Y) + 40 + (-10)

  • (b) Impact of Changes to Investment:

    • If Ig falls to $20, GDP declines by $100 (Multiplier = 5, Change = 5 x $20).

    • New equilibrium GDP = $300.