Basic IS-LM Model  (closed economy, no foreign trade)

 

The Keynesian Cross Model shows how an increase in investments spending (i.e., firms buying captal goods) leads to higher income or output.  That is, higher investment spending vertically boosts the aggregate expenditure line, leading to higher equilibrium GDP.   We also know that lower interest rates promote greater investment spending.  All of that is taken for granted here.

The IS-LM Model brings in the interest rate into the macroeconomic analysis as an "endogenous" variable.  This basic version ignores foreign trade.

 

If we set up a graph with interest rates on the vertical axis, and GDP or income (Y) on the lower axis, a downsloping line (upper left to lower right) would reveal the relationship between interest rates and the level of GDP.  The lower the interest rate, the higher the GDP, because the investment spending which corresponds to low interest rates stimulates the economy.  This is the I-S curve.

 

The I-S curve, then,  shows the locus of points for which there is equilibrium in the goods market.  It is named that because equilibrium requires Saving to equal Investment (more broadly, leakages equal injections).   More simply put, equilibrium requires the demand for goods to be equal to the supply of goods.  Given any particular interest rate,  there is a unique amount of investment (as could be shown with an investment demand curve).  So for each interest rate there is a unique GDP (assuming a given consumption pattern, given government spending).

 

The L-M curve is drawn using the same type of graph.  Interest rate on vertical axis, GDP or income on horizontal.  The L-M curve is an uphill line running from lower left to upper right.  It is built on the idea that, considering the workings of the "money market" (supply and demand for money), the greater the GDP, the higher will be the interest rate, other things equal.  Here's why that is expected.  Given a money supply, as set by the Fed, the demand for money determines the interest rate.  The demand for money curve shifts right or left with changes in GDP (the transactions demand for money, covered elsewhere in these writings).  So as GDP increases, so does the interest rate.

 

The L-M curve, then, is the locus of points for which there is equilibrium in the money market.  For every level of GDP there is a corresponding interest rate.

 

Putting both IS and LM on the same graph, we get a uniquely determined GDP and interest rate.  This point is given by the intersection of the two lines.  At that point there is equilibrium in both markets at once  That is, based on the demand for goods, especially due to investment spending, and based on conditions in the money market, the economy will settle at some level of GDP, with some particular interest rate in effect for borrowing and lending.

 

As usual, the idea of equilibrium here implies a balance among the forces at work. The equilibrium point will not unleash forces which would change the GDP or interest rate.  Any other point in the space defined by the axes would not be a stable outcome.  For example consider a point "due east" of the intersection.  Here, the interest rate is not low enough to support the level of investment spending needed for that GDP to exist.