Question

Derive the IS and LM curve in Keynes’s model. Using the IS-LM and AD-AS frameworks, explain the working of Keynes’ model.

Answer 1

The LM curve shows the different levels of output and interest rates when the Financial market is in equilibrium. We can derive the LM curve as follows.

In the above graph the supply of money (MS) is determined by the Federal Bank and the demand for money (MD) is determined by the income level (Y1). The point at which the Supply and demand curve meet the line from the x-axis which measures the interest rate shows that the financial market is in equilibrium. In our given graph it is in equilibrium at the rate of interest of 15% at income level Y1.

Now as we move to the other graph which shows the LM curve, we can see that the financial market is at equilibrium at an output level of Y1 and an interest rate of 15 %. This can be observed at the point where interest rate line meets the Y1(output level) line. Now as the output level increases to Y2 on the second graph the demand for goods and services will also increase. This in turn leads to an increase in demand for money, which is seen in the curve Md(Y2). The increase for money supply means more bonds will be sold at lower prices meaning the interest rates on bonds will increase. This gives a new equilibrium at 20% interest rate. Therefore we can see that the increase in output level of Y2 in graph 2 will correspond to the increased interest rate of 20% and they meet at a point on graph 2 where they satisfy equilibrium conditions. The LM curve is the derived by joining the two points of equilibrium on graph 2 which show different output levels at different interest rates.

IS Curve:

In Graph -I : We measure interest rate on the Y-axis and Investment on the x-axis. Let us assume at 15% interest rate we have an investment of 150 and at an interest rate of 10 % we have an investment of 200. The increase in investment is due the decrease in interest rate which encourages more investment. The investment function is hence a downward sloping line(I).

In Graph II-- We take a look at the goods market. We have the demand for goods and services including consumption spending, government spending and investment spending. Hence we take the investment at the rate of 10% at which we assume the vertical intercept at x axis is 250. Using the multiplier which is taken as 5 we can calculate the equilibrium level of income which is equal to Multiplier * vertical intercept= 5* 250= 1250. Point (a) shows us the equiliibrium level in the goods market at 15% interest rate.

In graph III- At an interest rate of 15% the goods market in graph II is in equilibrium at 1250. We measure interest rate in the Y-axis and mark 15% interest rate which meets the point of equilibrium level of output at 1250 carried down to the x-axis. They are in equilibrium at point A on the graph.

In graph I- We see that the intersest rate has decreased from 15% to 10% this leads to a corresponding increase in investment from 150 to 200. Since investment is a part of Demand in the goods market the demand for goods and services after the decrease in interest rate will increase to 300 at DD2 curve at 10% interest rate.(shown in graph-II)

In graph II: Since the investment in graph one increased by 50 so in graph II we increase autonomous investment in the vertiacl intercept by 50. This gives us a new investment level of 300 at 10% interest rate and an increased demand of DD2. Again we calculate the equilibrium level of income which is Multiplier * corresponding vertical intercept = 5*300 = 1500. This shows us that there has been an increase in the equilibrium level in the economy at 1500.

In Graph III: The interest rate of 10 % is corresponding to the equilibrium level of production at 1500. So point B represents equilibrium level in the goods market. A line drawn through points A and B gives us the IS curve which gives the various combinations of interest rate, income, demand and investment in the goods market.

Keynesian model explained using AS-AD:

The Keynes model uses Aggregate supply and Aggregate demand to explain the relationship between price level and output.The aggregate demand curve or the AD curve is derived from the IS-LM equilibrium income at different price levels.

According to the Keynes model unlike the classical theories, economy will not correct itself. Keynes also proposed that in a modern sector the fall in wages is very rare and this prevents the economy from reaching a state of equilibrium as the Aggregate supply may exceed the Aggregate demand.

Recessionary Gap:

When there is surplus resources and less demand the production is affected and hence leads to unemployment. According to Keynes this can be handled by laying off the workers and keeping the prices at the same level. The short run aggregate supply is to be maintained at the same level.

Recessionary gaps leading to shift in aggregate demand--- As mentioned above the short run aggregate supply remaining the same leads to workers losing their jobs. This in turn leads to an increase in savings and cut in expenditure. So by that logic, consumption and investment takes a hit and the real GDP falls back. Hence the aggregate demand falls and makes the recession really bad.

This proves that a modern sector can be in a recessionary period for a long time.

For this situation Keynes suggests an increase in government spending and a cut in taxes which encourages households to spend more. This way the aggregate demand can be raised again and, thus, closing the recessionary gap.

Incase of an inflationary gap, Keynes recommends cutting government spending and increasing taxes in order to discourage consumption. This closes the inflationary gap due to a fall in aggregate demand.