Introduction: The IS–LM Model in Two-Sector Economy
It's interesting that Keynes had developed his product market theories in isolation of the product market, and money market theories in isolation of the product market, whereas the activities and variables of the two sectors are interrelated, interdependent and interactive.
Therefore, changes in the variables of one sector affect the activities of the other sector. In simple words, changes in product market affect the money market equilibrium and vice versa.
The Keynesian theory ignores the effect of changes in the money market on the product market and the effect of changes in the product market on the money market.
Therefore, his theories related to the product and money markets are considered to be partial and incomplete. It was J.R. Hicks who highlighted this fact and developed his own model in 1937—just one year after the publication of Keynes’s The General Theory. Opens in new window
He integrated Keynesian theories of product and money markets to show how equilibrium of both the sectors coincide at the same level of income and interest rate. His model is widely known as the IS–LM model.
In this model, the term IS represents the product sector equilibrium condition (I = S) and the term LM represents the money market equilibrium condition (L = M), where L stands for liquidity preference or money demand (MD) and M stands for money supply (MS).
It is important to note here that Hicks has developed his IS–LM model in the framework of a simple, two-sector economy. The economists have, however, extended his model to three-sector and four-sector models also.
For our purpose, we elaborate on the Hicksian IS–LM model in a simple, two-sector economy, including household and firm sectors only. The three-sector and four-sector IS–LM models are subsequent entries.
We begin by showing the interdependence of the product and the money markets.
The Interdependence of Product and Money Markets
As mentioned above, working of the product and the money markets is interlinked and interdependent. The two most important variables that interlink the working of the two sectors are investment and interest rate.
The investment (I ) is a money-market variable determined by the demand for and supply of money.
Let us now look at the interdependence of the product and money markets in a simple economy model.
Dependence of Product Market on Money Market
The product market attains its equilibrium at the level where Y = C + I. Referring back to the Keynesian analysis of the product-market equilibrium, I was assumed to be a constant factor or an autonomously or exogenously determined variable.
In reality, however, I is not only autonomously or exogenously determined: it is determined within the system also by the level of income and the interest rate. More importantly, given the income, investment (I ) depends on the rate of interest.There is an inverse relationship between the interest rate and investment.
Assuming a constant ∆I/∆i, the inverse relationship between the investment (I) and the interest rate (i) is stated by a linear investment function2 of the following form.
I = Ī – hi, (h > 0) --- (eqn. 1)
where, Ī = ‘autonomous investment,’ i = interest rate and h = ∆I/∆i.
The implication of the investment function in the interdependence of the product and money markets can be shown as follows.
Recall that the product market is in equilibrium where Y = C + I
Here, C (consumption) is the function of income, and I (investment) is the function of interest.
For the sake of brevity, let us denote consumption function as C(Y) and investment function as I(i ). By substitution, the product market equilibrium condition can be rewritten as Y = C (Y ) + I(i ) --- (eqn. 2)
Eqn. 2 implies that unless i (interest) is determined, I cannot be determined and unless I is determined Y cannot be determined. It means, unless i is determined, the equilibrium level of Y cannot be determined.
Also, the interest rate (i) is determined in the money market and equilibrium rate of interest is determined where Md = Ms. For interest rate to remain stable, money market must be in a stable equilibrium. It may thus be concluded that
Unless money market reaches its equilibrium and interest rate (i) is determined, product market cannot attain its equilibrium.
This shows the dependence of the product market on the money market.
Dependence of Money Market on Product Market
Let us now look at the dependence of the money market on the product market.
In the Keynesian system, money market reaches its equilibrium where
Ms = Md
and interest rate (i) is determined where MS = MD.
Md = Mt + Msp, where Mt = kY and Msp = ƒ(i ).
Therefore, Md = kY + ƒ(i ) --- (eqn. 3)
Eqn. 3 implies that unless Y is determined, kY cannot be determined and, therefore, Md cannot be determined.
And, unless Md is determines, money market equilibrium cannot be determined and interest rate (i ) would not be determined. It may thus be concluded that
Unless product market reaches its equilibrium and Y is known, money market cannot reach its equilibrium.
This shows the dependence of the money market on the product market.
It needs to be emphasized here that unless both product and money markets reach equilibrium simultaneously, the economy Opens in new window cannot attain its general equilibrium nor can any of the two sectors be in equilibrium.
The IS–LM Model: An Elementary Exposition
After having shown theoretically the interdependence of the product and money markets, we move on to the to present Hick’s IS–LM model and show how product and money markets interact to reach their equilibrium simultaneously and also the same level of income and interest rate.
The IS–LM model combines the equilibrium conditions of the product and money markets to arrive at the general equilibrium. In order to show general equilibrium, Hicks had derived two curves, namely IS and LM curves.
Note that the term ‘general equilibrium’ is used to denote the simultaneous equilibrium of all elements of the economy including individual products, individual decision-makers (households, firms, labor, etc.), money market, at both micro and macro levels.
However, here the term ‘general equilibrium’ has been used to denote the simultaneous equilibrium of the product and money markets.
The IS curve (meaning I = S) represents the money market equilibrium, both at different rates of interest and level of the aggregate product or national income.
In deriving his IS curve, Hicks made an important deviation from the Keynesian approach.
- While Keynes assumed investment (I ) to be autonomous and determined exogenously, Hicks assumes that I is determined endogenously and is the function of the rate of interest i.e., I = ƒ(i ).
- Likewise, his LM-schedule shows the equilibrium path of the money market at different rates of interest and levels of income.
He has then combined the two schedules to show the general equilibrium of the economy. This has come to be widely known as the IS-LM model.
The Basic Model
In his IS-LM model, in its simplest form, Hicks integrates the equilibrium conditions of the product and money markets and produces conditions for the general equilibrium.
He incorporates a money market variable, interest (i), into the income determination model by replacing Keynes’ constant I with the investment function.
With these modifications in the Keynesian model Opens in new window, Hicks defines the equilibrium level of income as:
Y = C (Y ) + I (i )
This function yields the IS-curve. It shows the relationship between Y and i at different equilibrium levels of saving and investment (I = S ) and the product market equilibrium at different levels of Y and i.
Similarly, the IS-LM model incorporates income, Y, the main product-market variable, in the money market model by linking total demand for money to Y.
This is done by using an Mt-function of the form Mt = kY, and an Msp-function as Msp = L (i ) into the money market model. The money-market equilibrium condition is then written as
Ms = Md = kY + L (i ) --- (eqn. 4)
Eqn. 4 yields the LM-schedule which shows the relationship between Y and i at different equilibrium levels of Md and Ms. It shows also the money market equilibrium at different levels of Y and i.
Finally, the IS-LM model brings the IS and LM functions together and lays down the condition for the general equilibrium as:
IS = LM
or C (Y ) + I (i ) = kY + L (i ) ---- (eqn. 5)
If C (Y ), I (i ) functions are known, the equilibrium values of Y and i can be easily obtained.