Aggregate Expenditures The four expenditure components of national income accounting were developed around the multiplier model. AE = C + I + G + (X - IM)

Expenditures Function AE = C + I + G + (X - IM) AEo = autonomous expenditures that don’t change as income changes.  AE/  Y = those expenditures that change as income changes We simplify the model for Econ 100: we pretend that only consumption changes when income changes.

The Marginal Propensity to Consume The mpc is the fraction spent from an additional dollar of income.

Consumption and Income Consumption depends on income. When income rises, consumption increases. The marginal propensity to consume is the change in c divided by the change in y. YD = C + S MPC = C/YD MPS = S/YD

Consumption and Saving The MPC plus the MPS equals one. To see why, note that, if you receive an additional $100 in disposable income, you will spend part of the income or not spend part of the income, that is save it. In algebra: C + S = YD.

Consumption Function

Aggregate Expenditure Diagram

Aggregate Expenditure Diagram

The Marginal Propensity to Consume and AE Since only consumption expenditures depend on income, in our simple model:

Expenditures Function The expenditures function is expressed as a mathematical function: AE = AEo + mpcY AE = aggregate expenditures AEo = autonomous expenditures mpc = marginal propensity to consume Y = income

The Multiplier Equation The multiplier is a number that reveals how much income will change in response to a change in autonomous expenditures. Multiplier = 1/(1 – mpc)

Alternative Equation mpc + mps = 1 mps = 1 - mpc multiplier = 1/mps By definition: mpc + mps = 1 Alternatively expressed: mps = 1 - mpc multiplier = 1/mps

What you don’t consume is what you save. The two equations Multiplier = 1/(1 – mpc) multiplier = 1/mps Because 1-mpc = mps What you don’t consume is what you save.

An Upward Shift of AE, Fig. 10-8a, p 248 Real expenditures Real income 1,052.5 AE1 $4,210 30 1,022.5 AE0 4,090 $4,090 $120

An Downward Shift of AE, Fig. 10-8b, p 248 Real expenditures Aggregate production AE0 1,412 $4,152 AE1 1,382 30 $4,062 4,062 $90 Real income

An Example of the Multiplier Suppose Investment rises by $ 100 million the mpc is .8 so the mps is .2 Multiplier = 1/(1 – mpc) = 1/(1-.8) = 1/.2 = 5 multiplier = 1/mps = 1/.2 = 10/2 = 5 Rise in Equilibrium Income 5 * $100 = $500

Realistic Multipliers Our simple model pretends that no one pays taxes and no one buys imports We also assume that Investment and government spending don’t change when income changes. The real multiplier is closer to 2 than to 5.

Realistic Multipliers Observe that the multiplier is calculated assuming prices are not changing. The multiplier tells us how much the AD curve shifts to the right. When AD shifts, prices change so the change in equilibrium income is even less than an accurate multiplier predicts.