3.8 The multiplier model: including government and net exports

new aggregate demand function

AD = consumption + planned investment + government spending + net exports

consumption in the new model

everything apart from changes based on changes in income is considered exogenous and just shifts the function up or down.

aggregate investment function

I = a₀ - a₁r
a₀ = autonomous investment

a₁ = how sensitive investment is to the interest rate

r = interest rate

**al influences on investment besides interest rate are included in autonomous investment

**gov investment is included in a₀

government spending

part of the y-intercept, just leads to shifts up and down

net exports equation

net exports = X - mY
m = marginal propensity to income which is the fraction of each additionl unit of income spent on imports (between 0 and 1)

**assume this is only dependent on spending

new aggregate demand curve and changes in different values

AD = C₀ + C₁(1-t)Y + a₀ - a₁r + G + X - mY

change in c₀, G, X, a₀ —> parallel shift up or down

increase in r reduces investment —> parallel shift downward

decrease in r increases investment —> parallel shift upward

change in c1 or t are the only things that change the slope

**t = tax rate

when we include taxation and imports in the model, what should happen to the multiplier?

the effect of a given rise in spending on GDP is smaller bc some increase in income go to taxes and some are used to buy G+S abroad

things affecting size of multiplier

only components that also affect slope:
higher marginal propensity to import —> smaller multiplier = flatter curve

increase in tax rate —> reduces size of multiplier = flatter curve

increase in exports or gov spending shifts AD curve up in multiplier diagram

new multiplier equation

k = 1 / (1 - c₁(1-t) + m)

do you expect the multiplier in an economy to vary over its business cycle

yes because during recessions more households become credit constrained so MPC increases —> multiplier increases

and during booms, fewer households are credit-constrained so MPC decreases —> multiplier decreases