1. The Full Aggregate Expenditure Model Adding investment, taxes, government and the foreign sector

2. The Partial Model • Previous model put most of the emphasis on household consumption • Had autonomous and induced consumption • Especially ignored the effect of taxes on household consumption • Basic equilibrium conditions still hold • But want a richer understanding of how different sections interact

3. The Full AE Model • Fully specify all behavior actions • Richer induced behavior • Keep some elements exogenous • Government purchases • Exports • Investment (although will change this when we bring money into the economy) • Make taxes and imports endogenous

4. Mathematical Model • Starts with the same identity for AE AE = C + I + G + X – M • Add behavioral equations for components • Consumption C = c0 + c1*(Y-T) (Y-T) is called disposable income c0 is autonomous consumption, c1 is the MPC • Imports M = m*Y All imports are induced, m is the marginal propensity to import

5. Mathematical Model (cont) • Taxes are also endogenous T = t0 + t1*Y • Autonomous part (t0) are things like property taxes • Induced part (t1*Y) includes things like income taxes. Think of t1 as the marginal tax rate (a parameter) • Y is, of course, national product (which equals national income) • Keep government (G), exports (X) and investment (I) as exogenous

6. Mathematical Model (cont) • Final component is equilibrium condition • Y = AE • So substitute the component equations into the identity for AE

7. Mathematical Model (cont) Y = AE = c0+c1*[Y-(t0+t1*Y)] + I + G + X – mY collecting terms we get Y = [c0-c1*t0+I+G+X] + [c1*(1-t1)-m]*Y which we can write as Y = a0 + a1*Y where a0 =c0-c1*t0+I+G+X and a1 = [c1*(1-t1)-m]

8. Mathematical Model (cont) • We have autonomous and induced spending • a0 is autonomous • a1*Y is induced • a1 is the marginal propensity to spend • The portion of each additional dollar spent • It will be between 0 and 1 • An increase in the MPC increases a1 • Increases in the marginal tax rate (t1) or the marginal propensity to import (m) decreases a1

9. Mathematical Model (cont) • The equilibrium value of Y is Ye = a0/(1-a1) • Increases in autonomous spending, decreases in autonomous taxes will increase Ye

10. Changes in autonomous spending

11. Mathematical Model (cont) • Increases in MPC, decreases in t1 or m will increase Ye • Expenditure multiplier is 1/(1-a1) • It also increases as MPC goes up, or t1 or m go down

12. Changes in marginal propensity to spend

13. Policy Questions • Autonomous Taxes and Government Spending • Which has a bigger effect on the economy, cuts of autonomous taxes or spending increases • Hint, look at how each is affected by the multiplier • An increase in G is multiplied by 1/(1-a1) • A decrease is autonomous taxes increases C by c1*t0, so the cut in t0 is multiplied by c1/(1-a1) • Which is bigger?

14. Policy Questions (cont) • Marginal Tax Rates • Affects the expenditure multiplier • Thus, has a bigger effect by increasing (if t1 is cut) the multiplicative effect on all autonomous spending • How does this compare to cutting t0 • Trade Policy • Do changes in imports and exports have different effects?

15. Equilibrium in another context • Equilibrium requires that the circular economy is in equilibrium • That is, we assume leakages=injections • So I + X + G = S + M + T • Rearrange equilibrium of injections and leakages (T – G) + S = I + X - M • The left hand side is total economy savings • The right hand side is total economy investment

16. Equilibrium in another context (cont) • T-G is the total savings (or dissavings, if G>T) by the government • X-M tells us how much is gained (or lost if M>X) by foreign trade, which can be invested in the economy (but see below) • So still need (total) savings = (total) investment for equilibrium

17. Equilibrium in another context (cont) • Rearrange equilibrium of injections and leakages once more so we can where I comes from I = S + (M-X) + (T-G) • I is the amount available to invest in growth – for future consumption • Government deficits (when G>T) reduces investment (assuming S constant)

18. Equilibrium in another context (cont) • Trade deficits (when M>X) increases private investment because of more foreign investment in the US (assuming S constant) • Foreign owners gain US capital • So a trade surplus, (X>M) means private investment in US is lower (holding all else constant. • We’ll see that foreign exchange markets push that surplus into US investment in other countries • US gains ownership of foreign capital

19. Policy Questions • Kerry promises he has a funding source for all new programs he plans to institute • If taxes increase to cover new government spending, will DGP increase or decrease? • Will it matter if the funding is through autonomous or induced taxes? • HINT: think about changes in autonomous spending against changes in the multiplier.