Download - IS LM, AD AS (closed economy)
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.