MACROECONOMICS – IS/LM, AD/AS (CLOSED ECONOMY)

THE IS CURVE

IS curve: Locus of points of equilibrium in the goods market.

Requires that Planned Real expenditure on goods (Yd) is equal to output (Y). Yd=Y

Yd = C (consumption) + I (investment) + G (Government Expenditure)

Next logical step is to find functions for C and I (and assume G is an exogenous constant, for now)

THE IS CURVE

C = Co + Cy (Y – T); Co = Autonomous expenditure, Cy = Marginal Propensity to Consume (MPC), T = Tax

T = Ty.Y, Ty = Marginal Propensity to Tax. C = Co + Y.Cy(1 – Ty) I = A – ar A = Autonomous level of investment, a =

investment sensitivity to (real) interest rates, r = real interest rate.

THE IS CURVE

Thus: Yd = Co + Y.Cy(1-Ty) + A – ar +G Yd = Y Y – Y.Cy(1-Ty) = Co + A – ar + G Y= [Co + A – ar + G]/[1 – Cy(1-Ty)] 1-Cy = Sy (Marginal Propensity to Save) Y=[Co + A – ar + G]/[Sy + Cy.Ty]: The IS

curve. However, re-arrange such that r = f(Y)

(because of the axis of the IS/LM diagram). r = [Co+A+G]/a – [Sy + Cy.Ty].Y/a

THE IS CURVE

1/[Sy + Cy.Ty] is the MULTIPLIER. Sy + CyTy are the sources of the leakages from the economy.

Thus, we can see how to SHIFT and SKEW the IS curve:

SHIFT: Any change in the autonomous constants (Co, A, G).

SKEW: Any change in the interest sensitivity of investment or the multiplier.

THE LM CURVE

The LM Curve: A locus of equilibrium in the money markets.

Terminology: We will often be referring to the real Money Supply/Demand. This is where we take into account the Price level (P).

Equilibrium occurs when Ms/P = Md/P (real money supply = real money demand).

THE LM CURVE

Md/P is a Liquidity preference function (the preference for you to hold your stock of wealth in Liquid assets – Money).

Liquidity preference functions have two main variables; Y = income, and i = nominal Interest rate.

As the interest rate rises, the opportunity cost of holding your wealth in cash (with a 0% rate of return) rises.

Thus, Md/P rises with Y (greater income, greater need for cash to carry out transactions) and will fall as i rises.

Md/P = L(y, i) = ky - li

THE LM CURVE Since Md/P = Ms/P in equilibrium, and that

we want an equation that has interest rates as the dependent variable (remember the axis on the IS/LM diagram) and income as the independent variable, re-arrange:

Ms/P = ky – li i = (k/l)y – [(Ms/P)/l] : The LM curve

equation Hence, a change in the Money Supply or the

Price level will SHIFT. A change in the interest sensitivity of the

asset demand for money (l) or a change in the income sensitivity of the asset demand for money (k) will SKEW.

IS + LM = AD

The Aggregate Demand (AD) Curve can be derived from the IS/LM curves.

But first, it is important to note that the IS curve used the REAL exchange rate (r) and the LM curve used the NOMINAL exchange rate (i).

This can be reconciled via use of the FISHER equation: (1+i)=(1+πe)(1+r), where πe is the expected rate of inflation. Hence, r ≈ i – πe as r. πe is negligible. We will assume that πe is zero.

AD The AD curve can be

shown by considering the effects of price changes. If there is a Price rise (P P’), then the LM curve will shift to the left (Ms/P).

There will therefore be a corresponding fall in output.

Hence, the AD can be derived as seen to the side.

IS

LM (P)

LM (P’)

Price

P

P’

AD

Y

Y

AS – PERFECTLY COMPETITIVE

The LRAS curve can be derived from the labour market.

First consider the perfectly competitive market.

On the supply side: W.N = Pe.C; Wages x Number of Labour Hours = Expected Prices x Consumption of goods

Hence, W = Pe.g(N); Wages = Price expectations x function of N.

AS – PERFECTLY COMPETITIVE

On the Demand Side, firms must be profit maximising:

Π = P.f(N) – W.N; Profit = {Price x Output (=function of N)} – {Wages x N}.

Πmax = dΠ/dN = P.f’(N) – W = 0 W/P = Real wage = f’(N) = Marginal product

of Labour (MPL). Before plotting these curves, let us consider

the imperfect case.

AS – IMPERFECTLY COMPETITIVE

The implications for the supply side is that Unions have been introduced and there are additional reasons for labour immobility (Hysteresis, insider-outsider theory, loss of skills over time).

This means that that at any level of wages, LESS people will be willing to supply labour.

AS – IMPERFECTLY COMPETITIVE The change on the demand side is that prices are

now also a function of output (the firm is a price maker, not a price taker and faces a downward sloping, not horizontal, demand curve). Hence:

Π = P[y].f(N) – W.N; But because output is a function of N;

Π = P[f(N)].f(N) – W.N dΠ/dN = P[f(N)].f’(N) + f(N)[dP/d{f(N)} . f’(N)] = 0 W/P = [1 + (dP/dy)(y/P[y])].f’(N) (dP/dy)(y/P[y]) is the elasticity of demand (which

is always negative (or 0)). Hence, the demand side is: W/P = a.f’(N), where a is a constant less than 1.

Hence, W/P in an imperfect market are always lower than in a perfect market at a given N.

AS: BLUE = IMPERFECT, ORANGE = PERFECT

Maximum ‘N’

N

W/P SS

DD

LRAS LRAS

YY’Voluntary unemployment

Involuntary unemployment

AS CONCLUSION Thus, we can see that by modelling the

imperfect labour market we can allow for involuntary unemployment (which isn’t allocated for in the perfectly competitive model).

The LRAS curve can be derived as it is the level of output (Y) that corresponds with the level of N at equilibrium. The level of N will be constant because the supply curve responds to Pe and the demand curve responds to P. A shift in P will always be matched by an equal shift in Pe (hence the curves will shift by the same amount horizontally).

It allows for a short-run AS curve as well, as the shift in P might not be immediately matched by a shift in Pe.