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Deriving the Multiplier Algebraically quiz

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  • What is the formula for the multiplier in a simple aggregate expenditures model?
    The multiplier is 1 divided by (1 minus the marginal propensity to consume), or 1/(1-MPC).
  • In the simplified model, what components make up aggregate expenditures in a private closed economy?
    Aggregate expenditures consist of consumption (C) and investment (I).
  • How is consumption (C) modeled in the aggregate expenditures equation?
    Consumption is modeled as autonomous consumption plus MPC times disposable income.
  • Why is all income considered disposable income in this model?
    Because there are no taxes or government transfers in the private closed economy model.
  • At equilibrium, what is the relationship between aggregate expenditures and GDP?
    Aggregate expenditures equal GDP at equilibrium.
  • What equation represents equilibrium in the aggregate expenditures model?
    Y = A + MPC × Y + I, where Y is GDP, A is autonomous consumption, and I is investment.
  • How do you rearrange the equilibrium equation to solve for GDP (Y)?
    You factor out Y and rearrange to get Y = (A + I) / (1 - MPC).
  • What does the multiplier effect imply about changes in investment or autonomous spending?
    It implies that any increase in investment or autonomous spending leads to a multiplied increase in GDP.
  • How does an increase in investment affect GDP according to the multiplier?
    An increase in investment increases GDP by the amount of the increase times the multiplier.
  • What is autonomous consumption?
    Autonomous consumption is the level of consumption that occurs even if income is zero.
  • Why is the multiplier important during a recession?
    Because increasing investment or spending can have a multiplied effect on boosting GDP.
  • What does MPC stand for and what does it represent?
    MPC stands for marginal propensity to consume and represents the fraction of additional income that is spent on consumption.
  • How do you factor Y out of the equation Y - MPC × Y = A + I?
    You factor Y to get Y × (1 - MPC) = A + I.
  • What happens to the multiplier as MPC increases?
    As MPC increases, the multiplier becomes larger.
  • What is the general effect of the multiplier on equilibrium GDP?
    The multiplier amplifies the effect of changes in autonomous spending or investment on equilibrium GDP.