Derivation of the Change in Output from an Investment Shock
The change in equilibrium output () resulting from a change in investment () is derived by calculating the difference between the new and original equilibrium output levels. Starting with the equilibrium equation , the change is expressed as . By simplifying this expression, the terms cancel out, leaving the final relationship: .
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Ch.3 Aggregate demand and the multiplier model - The Economy 2.0 Macroeconomics @ CORE Econ
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Derivation of the Change in Output from an Investment Shock
In a simplified economic model, the equilibrium output (Y) is determined by the equation Y = k(c₀ + I), where 'k' is a multiplier with a value greater than 1, 'c₀' represents spending that does not depend on income, and 'I' represents investment spending. If businesses suddenly become more pessimistic about the future and reduce their investment spending (I), while 'k' and 'c₀' remain unchanged, what will be the resulting effect on the equilibrium output (Y)?
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In the macroeconomic model where equilibrium output is represented by the equation
Y = k(c₀ + I), match each component of the equation to its correct economic description.In a closed economy with no government, a sudden wave of business optimism leads to a $50 billion increase in planned investment spending. If the marginal propensity to consume is 0.8, what will be the total change in the economy's equilibrium output?
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In a closed economy with no government, a sudden wave of business optimism leads to a $50 billion increase in planned investment spending. If the marginal propensity to consume is 0.8, what will be the total change in the economy's equilibrium output?
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In a simple, closed economy with no government, a technological breakthrough causes a wave of optimism among firms, leading to a total increase in equilibrium output of $500 billion. If the marginal propensity to consume in this economy is 0.8, what was the initial autonomous increase in investment spending that sparked this economic expansion?
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Derivation of the Change in Output from an Investment Shock
In a simple, closed economy with no government, a technological breakthrough causes a wave of optimism among firms, leading to a total increase in equilibrium output of $500 billion. If the marginal propensity to consume in this economy is 0.8, what was the initial autonomous increase in investment spending that sparked this economic expansion?
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Formula for Change in Output from an Autonomous Spending Shock
An economy's equilibrium output is initially described by the equation
Y₁ = k(c₀ + I). After an increase in investment (ΔI), the new equilibrium isY₂ = k(c₀ + I + ΔI). To find the total change in output (ΔY), we calculateΔY = Y₂ - Y₁. Which algebraic step is the most direct and crucial for simplifying the resulting expression,ΔY = k(c₀ + I + ΔI) - k(c₀ + I), to its final, most concise form?Arrange the following algebraic expressions in the correct logical sequence to derive the relationship between a change in investment (ΔI) and the resulting change in equilibrium output (ΔY).
Analysis of the Output Change Derivation
In the process of determining the total change in equilibrium output (ΔY) following a change in investment (ΔI), the algebraic derivation starts with ΔY = k(c₀ + I + ΔI) - k(c₀ + I) and simplifies to ΔY = k * ΔI. What is the key economic insight revealed by the fact that the
k(c₀ + I)terms cancel out during this simplification?