General Theory: John Maynard Keynes's IS-LM Model

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Background: John Maynard Keynes published Keynes’s General Theory which is also known as The General Theory of Employment, Interest and Money in February 1936. Soon after the publication, J.R. Hicks published an article that attempted to integrate the insights he felt were useful in the General Theory and proposed his IS-LM curves model based on his studies on Keynes’s General Theory.
The IS-LM Model: IS stands for investment to savings and LM stands for the liquidity preference to money supply. The simplest version of the IS-LM model describes the macroeconomy using two relationships involving output and the interest rate. The model is presented as a graph of two intersecting lines. The IS and LM curves are the equilibrium relationships pertaining, respectively, to the product market and the money
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First, the demand for real money balances (L) is positively related to the level of income (Y), as people will hold more money to finance their increased expenditures but it is also negatively related to the interest rate (i), since the interest rate is the opportunity cost of holding money rather than bonds. The equation for real money demand can therefore be written as

L = kY - hi ( k > 0 and h > 0 )

Then real money supply, that is, nominal money supply (M) divided by the price level (P) is set equal to real money demand to achieve an equilibrium in the money sector. In other words, the equation of the LM-curve is derived in the following way.

(M/P) = L = kY – hi
Writing above equation in terms of i i = (1/h)[kY - (M/P)].

An increase in income will increase the demand for real money balances. Since real money supply is fixed, the interest rate will increase, reducing the quantity of real money balances demanded again until the money market clears. Therefore, the LM-curve is upward

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