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 is Y₂ = k(c₀ + I + ΔI). To find the total change in output (ΔY), we calculate ΔY = 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?

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?