Review of IS/LM Model (Chapters 10 & 11)
IS Curve LM Curve
Ceteris paribus, the Investment Saving or IS Ceteris paribus, the Liquidity Market or LM
Curve shows all of the (Y,r) pairs that Curve shows all of the (Y,r) pairs that
support (lead to) equilibrium in the Goods and support (lead to) equilibrium in the Money
Services market. (Asset) market.
S D S D D S
( i.e. Y = Y ↔ S = I ) ( i.e. M = M ↔ Asset = Asset )
Keynesian Cross Theory of Liquidity Preference
Short-Run (SR) Equilibrium output (Y* ) SR The real interest rate varies to determine
is determined by equating planned equilibrium in the money/assets market
expenditure (E = Y ) to actual expenditure GIVEN output (Y); the money supply (M ); S
(Y = Y SSR) GIVEN among other things fiscal the aggregate or average price level (P); and
policy (i.e. G & T) and the real interest rate the real money demand curve L(Y,r).
(thus I is fixed).
In essence, the IS Curve combines the Money market equilibrium implies all asset
interaction between r and I expressed by the markets are in equilibrium. Walras’ Law
investment function and the interaction states that if all but one market is in
between I and Y demonstrated by the equilibrium then the last market is also.
Keynesian cross. Therefore, consider assets as consisting of
two types monetary (money) and non-
monetary assets then M = M ↔ Asset = D
Having r rise (fall) shifts E down (up) thereby Having Y rise (fall) shifts the real money
decreasing (increasing) Y* SR.his traces out demand function ( L(Y,r) ) up (down) thereby
the IS Curve as downward sloping. increasing (decreasing) r*SR This traces out
the LM Curve as upward sloping.
1 IS Curve LM Curve
Algebraic Solution Algebraic Solution
NX = 0 Closed economy d
M = P∗( k*Y – h*r ) Nom money
C = C +0C ( 1 - T ) Consumption Function
M /P = k∗Y – h*r Real money
I = I0- I1∗r Investment Function
G = G 0 Exogenous FP M = M Exogenous MP (exog.
(spending policy) nominal money supply)
T = T Exogenous FP
0 P = P 0 Exogenous or fixed P level
S d S d
Y = C + I + G NII M = M or M /P = M /P
IS Curve LM Curve
Y = [ 1/(1-C )1]∗[ C +0I + 0 - C 0T ] 1 0 Y = (1/k)∗(M /P0) +0( h/k )∗r
- ( 1 /(1-C1) )∗r
IS is derived/drawn for: given, fixed or LM is derived/drawn for: given, fixed or
exogenous, levels of C , 0 , 0 , 0 , 0 & 1 1 exogenous, levels of M , P0, k 0 h
Y-axis intercept: Y-axis intercept:
Y = [ 1/(1-C )1]*[ C +0I + 0 - C0∗T ]1 0 Y = (1/k)∗(M /P0) 0
r-axis intercept: r-axis intercept:
r = [ C0+ I 0 G -0C ∗T1]/I0 1 r = ( -1/h )∗(M 0P 0
IS Slope: δr/δY = - (1-C )/1 < 1 LM Slope: δr/δY = k/h > 0
2 IS Curve LM Curve
IS shifts (parallel) up & right if: either C ; 0 LM shifts (parallel) down & right if: either
I0; or G0increases; or if T 0ecreases. M 0ncreases; or P de0reases.
i.e. if autonomous expenditures increases i.e. if (M /P) increases for some reason
(taxes represent negative autonomous
IS shifts and tilts (becomes steeper) if: LM shifts and tilts (becomes flatter) if:
C falls. h increases.
i.e. the marginal propensity to consume falls i.e. if (M /P) decreases due to an increase in
the sensitivity of real money demand to
(changes in) the real interest rate
3 IS Curve LM Curve
IS tilts up & right (becomes steeper) if: LM tilts down & right (becomes flatter) if:
I1decreases. k decreases.
i.e. the sensitivity of investment to the real i.e. if (M /P) decreases due to a decrease in
interest rate decreases (which also makes the the sensitivity of real money demand to
IS curve less interest rate sensitive, that is, (changes in) real income (GDP) [This is an
steeper) increase iS velocity (V) which acts the