demand for goods (Z)  

• Z = C+I+G+X-IM
• demand = sum of consumption, investment, gov't spending, exports, minus imports
• closed economy >> X = IM = 0 >> Z = C+I+G

equilibrium output - where production (Y) equal to demand (Z)  

• Y = Z = C+I+G
  • Y = (c₀+c₁(Y-T)) + (I+G)
  • Y = [I+G+c₀-c₁T] / (1-c₁)
• note that changes to I and G impact output Y more than equivalent changes to T, which is decreased by c₁(<1)
• multiplier = 1 / (1-c₁), always greater than 1
  • propensity to consume (c₁) increases >> multiplier effect increases
  • augments the effect of G,I,T >> more bang for your buck
  • autonomous spending = (I+G+c₀-c₁T), doesn't depend on output

• production Y=Y
  • production line always has slope 1 (income is consumer's production)
• demand Z
• equilibrium Y=Z

• note that a shift in the demand produces a greater shift in the equilibrium points
• demand shift = change in autonomous spending (c₀-c₁T+I+G)
• slope again depends on c₁

Calculate the multiplier and equilibrium if G = g₀-g₁Y instead of being exogenous.  

• Z = Y = C+I+G = (c₀+c₁(Y-T)) + I + (g₀-g₁Y)
• Y(1-c₁+g₁) = c₀ - c₁T + I + g₀
• Y = 1 / (1-c₁+g₁) * (c₀-c₁T+I+g₀) = equilibrium
  • multiplier = 1 / (1-c₁+g₁), smaller than original