Chapter 5: Goods and Financial Markets: The IS-LM Model
The Goods Market and the IS Relation
The equilibrium condition in the goods market suggests that production Y be equal to
the demand for goods Z. Then total investment I equals the sum of private and public
savings, which represents the IS relation.
Y = Z = C ( Y- T ) + Ī + G
Suppose investment Ī is not an autonomous factor, but depends on production, Y,
positively and interest rate, i, negatively.
I = I(Y, i)
( +, -)
after substitution, Y = C ( Y- T ) + I ( Y, i ) + G, which suggests that production must be
equal to the demand for goods and it represent the IS relation. It also indicates that
Y↑→YD↑→C↑ and Y↑→I↑. The relation between demand and output for a given
interest rate is upward-sloping due to the positive relation between these two factors.
Given the demand function ZZ = C ( Y- T ) + I ( Y, i ) + G, an increase in interest rate,
which leads to a reduction in investment and production, tends to shift the demand
function downward and vice-versa. When demand drops, it meets a lower output level at
the new equilibrium. Then a higher interest rate corresponds to a lower investment level,
a lower demand level, then a lower output level. The IS function, which indicates the
relation between interest rate and output level, is downward sloping.
The IS Function
The IS curve implies equilibrium in the goods market at which production equals
demand. It gives the equilibrium level of output as a function of interest rate. Changes in
factors that decrease the demand for goods, such as an increase in taxes, T, or a drop in
government expenditure, G, or a reduction in consumption, C, or exports, X, given the
interest rate, shits the IS curve to the left and vice-versa.
Financial Market and the LM Relation
Recall the identity of M = $Y L(i), where M is the nominal money stock, $Y is nominal
income and i is interest rate. Equilibrium in the financial market requires the money
supply equals the money demand.
After dividing price level, P, from both side,