Keynes & Neoclassical Synthesis: IS-LL (Hicks’ IS-LM)

John R. Hicks, in his article “Mr. Keynes and the Classical; a Suggested Interpretation”, published in 1937 in the journal Econometrica, developed a model known as IS-LL, which will later become IS-LM. The purpose of the article was to compare classical economists’ view on the goods and money market, with Keynes’ views.
In a few words, Hicks would assume Keynes’ innovations (possibility of frictional unemployment, the impact of animal spirits on investment, as well as money illusion effects) to take place in the short run, while classical views (such as full employment, perfect competition and the ability of the economy to re-equilibrate itself without government intervention) to be valid on the long run.
Hicks starts with the following assumptions, which we will maintain:

-he considers the short period;

-the quantity of physical equipment is fixed;

-homogeneous labor;

-depreciation can be neglected;

-rate of money wages (w) can be taken as given;

-quantity of money (M) is given;

-price level of goods equals their marginal cost.

(For the sake of simplicity, we will not consider differences between investment and consumption goods, nor the differences on the distribution of income.)

He also defines the following variables, which we will reformulate according to the level of simplicity we are aiming at:

-Y: total income;

-M: money quantity (which is given);

-I: investment;

-S: savings;

-i: rate of interest.

By uniting both classical and Keynesian views, Hicks writes the following three equations:

-M(Y,i) : we see that money quantity depends on both total income and the rate of interest;

-I(i) : investment depends on the rate of interest;

-I=S(Y) : investment must equal savings, which depend on total income.

From these three equations, we can see the relation between total income and the rate of interest in both markets:

-money market: since the money quantity is given, the LL curve (blue) will slope upwards, because an increase in income usually raise the demand for money (people need cash to consume goods) and an increasing rate of interest tend to lower money demand (the explanation of this can be made from two different angles: people will rather save more money since the interest rate is higher, therefore will spend less and demand less cash; or people are less willing to borrow money from banks, to spend it or invest it, because of the higher rate of interest);

-goods market: the IS curve (green) shows the relation between income and interest needed to make savings equal to investment. It slopes downwards because the lower the interest, the more people will invest, and therefore the higher will the total income be.

Income and the rate of interest are therefore determined where the IS and LL curves intersect (point P).

This model (more precisely, the IS-LM) is used nowadays to show the effect of diverse economic policies on a closed economy, and served as a starting point for the later Mundell-Fleming model, which helps understand their effects on an open economy.