The Demand for Goods Total Demand

The Demand for Goods C = c 0 + c 1 Y D Consumption (C)

The Demand for Goods Investment is (largely) an exogenous variable Exogenous/autonomous/independent variables are not explained in our model Endogenous/dependent variables depend on other variables in our model C is endogenous because it responds to production: C = c 0 + c 1 (Y – T) I, G & T are (largely) exogenous I = b 0 + b 1 Y – b 2 i ≈ b 0 + b 1 Y for now b 1 = marginal propensity to invest G = G T = t 0 + t 1 Y t 1 = marginal tax rate

The Determination of Equilibrium Output Demand for Goods (Z) Z = c 0 + c 1 Y D + b 0 + b 1 Y + G = c 0 + c 1 (Y – T) + b 0 + b 1 Y + G = c 0 + c 1 (Y – (t 0 + t 1 Y)) + b 0 + b 1 Y + G = [c 0 - c 1 t 0 + b 0 + G] + [c 1 – c 1 t 1 + b 1 ]Y = [c 0 + b 0 + G - c 1 t 0 ] + [(1 - t 1 ) c 1 + b 1 ]Y = Autonomous spending + Spending induced by Y

Y = Supply Z = Demand = [c 0 + b 0 + G - c 1 t 0 ] + [(1 - t 1 ) c 1 + b 1 ]Y Y = equilibrium Y = [c 0 + b 0 + G - c 1 t 0 ] + [(1 - t 1 ) c 1 + b 1 ]Y or {1 – [(1 - t 1 ) c 1 + b 1 ]} Y = [c 0 + b 0 + G - c 1 t 0 ] Solving for equilibrium Y Y = {1/[1 - (1 - t 1 ) c 1 - b 1 ]} x [c 0 + b 0 + G - c 1 t 0 ] Y = Autonomous spending multiplier x Autonomous spending When b 1 = 0 and t 1 = 0, Autonomous spending multiplier = 1/(1 - c 1 ) Determination of Equilibrium Output

The Determination of Equilibrium Output When b 1 = 0, t 1 = 0, and b 0 = I

Demand-Side Equilibrium and the Multiplier At equilibrium: Y = C + I + G = Z Increase in Y = Spending Multiplier x {Increase in Autonomous Spending} Multiplier = 1/[1 - (1 - t 1 ) c 1 - b 1 ]

1) Algebra to confirm the logic 2) Graphs to build the intuition 3) Words to explain the results The Determination of Equilibrium Output Three Steps to Solving a Model

–The larger the marginal propensity to consume, c 1, the larger the spending multiplier The larger the propensity save (1 – c 1 ), the less is respent, the smaller is the multiplier –A high marginal tax rate, t 1, reduces the multiplier Income leaks off into taxes and is not respent –The higher the propensity to invest as output expands, b 1, the greater is the multiplier –A change in autonomous spending changes output, income and spending more than the direct change in autonomous spending Determination of Equilibrium Output