1. Equilibrium in a Simple Model

2. Equilibrium Key concept in economics – illustrate with the simplest possible macro model Equilibrium is a point of balance or stability – Specifically in economics it is a point where economic agents plans are mutually consistently and therefore are realised Disequilibrium – plans are inconsistent – then someone’s plans are not realised – Somebody is disappointed – Behaviour will change – The economy will change – so not stable or balanced

3. MACROECONOMIC EQUILIBRIUM First, Output (which equals Income) is a function of inputs: for simplicity, Capital (K) and Labour (L) Y = f(K, L) – This is the amount firms plan to spend There will also be Aggregate Demand (Ep) – the amount of Expenditure which agents plan to make – Agents: Households, firms, the Government and foreigners In equilibrium plans are consistent Y = Ep Later we will see that sometimes Output or Income do not equal planned expenditure: this corresponds to a disequilibrium The general idea is that in equilibrium the forces acting on some variable (Y) are balanced and hence Y will not change.

4. AGGREGATE EXPENDITURE Conventionally we look at separate components of aggregate (planned) expenditure: C, I, G, NX. This is because they behave differently. Crucially C (Consumption) depends partly on Income: so part of Expenditure depends on Income: hence the term Induced (Consumption) Expenditure Other components of Expenditure are Autonomous: this should be understood as depending on something other than Income. We have – an Autonomous component of Consumption (Ca) – Investment (Ip) – Government purchases (G) – Foreign demand (NX)

5. THE CONSUMPTION FUNCTION (1) An equation that describes consumption plans Very Generally, Consumption depends on Disposable Income (Y minus net taxes, T). More specifically: C = Ca + c(Y – T) the “Autonomous” and “Induced” elements are on the right-hand side. The coefficient c (The Marginal Propensity to Consume) is > 0 and < 1, implying that for any given increase or decrease in disposable income C will change in the same direction, but by a lesser amount. i.e. 0 < dC/d(Y – T) = c < 1 This is a model of consumption insofar as it is a simplified representation of how people make their consumption plans – It doesn’t say that plans will be successful – It is very simple (even simplistic): no interest rates, future income, life cycle

6. THE CONSUMPTION FUNCTION (2) Note: Ca is “Autonomous” consumption; C/Y (APC) falls as Y increases; c (MPC) is < APC. 0(Y-T ) C Ca Ca + c(Y – T) 45  (C = Y) Slope = c

7. CONSUMPTION AND SAVINGS We have Y = C + S + T: hence S = Y – C – T Which gives: S = Y – Ca – cY + cT – T S = – Ca + Y(1 – c) – T(1– c) S = – Ca + (1 – c)(Y – T) And the MPS = dS/dY = (1 – c)d(Y – T) Suppose Y = 500, Ca = 50, c = 0.8, T = 150: Find C, S. C = 50 + 0.8(500 -150) = 50 + 0.8(350) = 330 S = – 50 + 0.2(350) = 20 Suppose Y increases to 600: (Y – T) increases to 450 dC/d(Y – T) = 0.8, so C increases to 410 dS/d(Y– T) = 0.2 so S increases to 40

8. EQUILIBRIUM As always equilibrium is plans are consistent Specifically in this case planned production is equal to planed demand Y = Ep, Sub in equation for planned expenditure (“Aggregate Demand”) Ep = C + Ip + G + NX To get Y = C + Ip + G + NX Sub in consumption function To get: Y = Ca + cY – cT + Ip + G + NX Note – cY is the one part of Expenditure which depends on Income – The other components (Ca –cT + Ip + G + NX) may be termed autonomous planned spending, in that they do not depend in Income (at least for now…) Alternatively we might term them the Endogenous and Exogenous components of planned spending.

9. Eqm vs Identity We have an accounting identity: Y = C + I + G + NX This different from the equilibrium condition The equilibrium condition describes planned magnitudes – These plans may or may not be realised The identity describes what actually happens – This may or may not have been what was planned Thus the equilibrium condition is true only for certain values of the variables The identity is true always – Best thought of as an account rule

10. DISEQUILIBRIUM To illustrate the concept of equilibrium consider a numerical example – Suppose we have Ca = 50, c = 0.8, T = 150, Ip = 40, G = 150, NX = 60 Suppose we have Y = 600 Is Income at equilibrium? Calculate Planned expenditure (Aggregate Demand) – Ep = Ca + c(Y – T) + Ip + G + NX – = 50 + 0.8(450) + 40 + 150 + 60 – 300 + 360 = 660 So Planned Production (Y) < Planned Expenditure (Ep) – Somebody’s plans will not be realised – Production is not sufficient to meet demand Plans must be updated – How? – We will assume that production will be increased to meet demand – Note we assume prices don’t change – Will provide empirical evidence later

11. EQUILIBRIUM What is Equilibrium Y in this case? We could try by trial and error Or we could solve the equations By definition equilibrium is where planned production equals planned expenditure: Y = Ep Y = Ca + c(Y – T) + Ip + G + NX Y – cY = Ca – cT + Ip + G + NX Y(1-c) = Ca – cT + Ip + G + NX Y(1 – c) = Ap Where Ap = Autonomous planned spending = Ca – cT + Ip + G + NX Plug in numbers – Y = Ap/(1 –c) = (50-120+40+150+60)/(0.2) = 180/0.2 = 900 One can re-check by plugging in all the components of Ep when Y = 900 and getting Ep = 900, i.e. equilibrium

12. EQUILIBRIUM This can all be illustrated graphically When Ep > Y, Y < Ye hence Y rises: similarly when Ep < Y….. 0Y Ep Ap Ep = Ap + c(Y – T) 45  (Èp = Y) Ye

13. Comment The process is self sustaining – If we are not at equilibrium there is an automatic adjustment process that will bring us into equilibrium – If this were not the case no point in studying eqm If not at eqm we are heading there We assume for the moment that the adjustment process works by producers changing out put to meet demand We also assume that prices don't change – Seems counter intuitive – This model effectively assumes that prices are fixed Will provide empirical evidence alter that this is approximately true in the short run

14. A CHANGE IN AGGREGATE SPENDING (1) Suppose Ip and therefore Ap fall by 40, Ye1 falls to Ye2 by a multiple of 40 (  Ye >  Ap) 0Y Ep Ap1 Ep1 = Ap1 + c(Y – T) 45  (Èp = Y) Ye1 Ep2 = Ap2 + c(Y – T) Ap2 Ye2

15. A CHANGE IN AGGREGATE SPENDING (2) Initial Equilibrium is: Y 1 = Ap 1 + c(Y 1 – T) Following Shock to Ap: Y 2 = Ap 2 + c(Y 2 – T) Subtracting: Y 2 – Y 1 = Ap 2 – Ap 1 + c(Y 2 – Y 1 ) i.e.  Y =  Ap + c  Y so  Y(1 – c) =  Ap And thus:  Y/  Ap = 1/(1 – c) or 1/s So if c = 0.8, s = 0.2, multiplier = 5: etc…. Intuitively: an increase in Ap (say G) is spent: it becomes income to someone who re-spends c times the increase, etc…  Y =  G(1 + c + c 2 + c 3 + ….. + c n )  c  Y =  G(  c  c 2  c 3 + ….. + c n+1 ) then adding And  Y(1  c) =  G(1) (the other terms cancel) So  Y/  G = 1/(1-c) or 1/s

16. CHANGES IN SAVINGS, TAXES In the previous example, an increase in G of 100 produced an increase of 500 in Y. As T is given this means that (Y – T) increased by 500, and C increased by c.  Y so savings increased by s.  Y = 100 Financing the increased G by selling Bonds to Savers?? Now what happens if T were reduced by 100 instead of increasing G? Initial Equilibrium is: Y 1 = Ap + c(Y 1 – T 1 ) Following cut in T: Y 2 = Ap + c(Y 2 – T 2 ) i.e.  Y = c.  Y – c.  T So  Y(1 – c) = – c.  T   Y/  T = – c/(1 – c) Thus if c = 0.2, –c/(1 – c) = – 0.8/0.2 = – 4. Note sign, magnitude (intuition of this)