## An alternative IS-LM look into the future

The IS-LM model is built upon two markets, the goods market (IS) and the money market (LM). The alternative view in this post will incorporate the effective demand limit into the IS-LM model.

### Money Market First

The money market is described by a plot of the interest rate (y-axis) and the quantity of money (x-axis). The line drawn is for money demand at a given level of nominal income, where nominal income (PY) is the real output multiplied by the price level (inflation). The money market model implies a corresponding and opposite bond market model. Graph #1: Source of graph, Department of Economics, University of Utah.

As the economy grows, nominal income (PY) shifts right. Graph #2: Source, Department of Economics, University of Utah.

In graph #2, money demand shifts right as nominal income grows from PY1 to PY2. If we hold the money supply constant, the interest rate will subsequently rise to the red dot. The excess money demand implies excess bond supply. Bond prices fall, thus raising the interest rate back up to the red dot equilibrium, where money supply is the same at a higher interest rate.

Remember that nominal income can grow by increasing real output or by increasing the price level. Normally as the economy grows after a recession, nominal income growth occurs with just increases in real output, not the price level. Therefore during this part of the business cycle where there is less tendency for inflation, the Fed will be accommodative, and through their open market operations of purchasing “bonds” and increasing the money supply, they will keep the interest rate at the blue dot.

The equilibrium points in this graph of the money market are plotted in the IS-LM model in order to give the LM curve. The LM curve gives the series of equilibrium points between the interest rate and real output. Graph#3: Source, Department of Economics, University of Utah.

Graph #3 assumes that the Fed is not going to be accommodative, which is an unreal assumption. Therefore the LM curve should actually be horizontal in graph #3. The constant rate of interest of the LM curve is an induced equilibrium path by the Fed. Graph #4: Source, Department of Economics, University of Utah. Adjusted by me.

So if the LM is horizontal when the Fed is being accommodative, when does the LM curve slope upwards? The answer… When real output reaches the effective demand limit. At this limit, real output will slow down and further increases in nominal income will show up as increases in the price level (inflation), not in real output. It is when the real output reaches the effective demand limit that the Fed stops being accommodative. Bond prices are allowed to fall raising interest rates. Graph #5: Source, Department of Economics, University of Utah. Adjusted by me.

Graph #5 shows that the Fed keeps the interest rate low by being accommodative until the effective demand limit. It is assumed that the Fed will start raising the interest rate as inflation appears at the effective demand limit. The equilibrium points of the LM are currently moving horizontally with a constant interest rate. However, there is a complication. The Fed is expecting real output to reach \$17 trillion (2009 dollars), while the effective demand limit is currently projected at \$16.1 trillion. Thus the problem that the Fed will be inclined to keep the interest rate low beyond the \$16.1 trillion effective demand limit. Graph #6: Source, Department of Economics, University of Utah. Adjusted by me.

Graph #6 shows a scenario that the Fed keeps the interest rate low beyond the effective demand limit while inflation pressures begin to appear. Maybe they see the inflation as temporary, and thus don’t react to it. Or maybe unemployment is still above 6.5%. Or maybe the Fed is still deep into QE, not expecting real output to slow down and inflation to rise, and would need time to unwind QE first before raising the interest rate. Unwinding QE by slowing down purchases of “bonds” may be enough to control inflation by raising the money market interest rate. People would be more willing to save their excess money income instead of using it to purchase goods and services. The result would be less pressure for inflation. However, a result could be an economic contraction from slowing down the momentum of the economic growth.

### Goods Market

The goods market is described by a graph with aggregate demand (y-axis) and national output (x-axis). Aggregate demand is given by the consumption function which is determined from aggregate autonomous spending  (A in graph) plus the marginal propensity to consume multiplied by national income (A + MPC * Y). Equilibrium (Y*) is found where aggregate demand (Z in graph) is equal to national output (Y). Thus a 45 degree line is drawn to determine equilibrium. Graph #7: Source, Department of Economics, University of Utah.

As the economy grows, the consumption function will shift upwards for various reasons. Equilibrium output will rise along the 45 degree line. In a standard goods market model, a lower interest rate will shift the aggregate consumption function upwards as equilibrium level of real output increases. Currently the Fed has lowered their overnight Fed rate as low as they can in order to shift aggregate demand upward. But they are working against a fallen labor share of income which shifted the aggregate demand function downward. Be that as it may, the aggregate consumption function continues upward.

What happens when the aggregate demand function reaches the effective demand limit? Graph #8: Source, Department of Economics, University of Utah. Adjusted by me.

Aggregate demand and output will grow to the effective demand limit. At that point, output supply (Y) will slow down. As aggregate demand then grows faster than supply, the equilibrium point between demand and supply slides upward vertically on the effective demand limit curve (see crossing point of thick green lines). The excess demand will not be able to express in increased output as it normally would below the effective demand limit. The excess aggregate demand over supply creates pressures for inflation.

Note: An excess aggregate demand over supply does not always lead to inflation, since there must be a mechanism to put that excess demand in the hands of consumers. If the excess demand ends up primarily in the hands of capital owners, there will be a bubble in assets prices instead of inflation for goods and services.

To transfer the information in graph#8 to the IS-LM curve, the result looks like this… Graph #9: Source, Department of Economics, University of Utah. Adjusted by me.

The IS curve of the goods market becomes interest rate inelastic at the effective demand limit, unless there exists a mechanism somewhere to shift the effective demand limit to the right. Otherwise full-employment is reached at the effective demand limit.

Note: As the IS curve goes inelastic at the effective demand limit, fiscal policy becomes ineffective. Thus, it is best to use fiscal policy for economic growth before the effective demand limit, like for instance, now….

Keynes sums up the above with a quote from his General Theory, chapter 21

“In this case we have constant returns and a rigid wage-unit, so long as there is any unemployment. It follows that an increase in the quantity of money will have no effect whatever on prices, so long as there is any unemployment, and that employment will increase in exact proportion to any increase in effective demand brought about by the increase in the quantity of money; whilst as soon as full employment is reached, it will thenceforward be the wage-unit and prices which will increase in exact proportion to the increase in effective demand. Thus if there is perfectly elastic supply so long as there is unemployment, and perfectly inelastic supply so soon as full employment is reached, and if effective demand changes in the same proportion as the quantity of money, the Quantity Theory of Money can be enunciated as follows: “So long as there is unemployment, employment will change in the same proportion as the quantity of money; and when there is full employment, prices will change in the same proportion as the quantity of money”.”

Note: I could have made the IS curve horizontal before the effective demand limit as Keynes states that supply is perfectly elastic. However, the main idea is that the goods market becomes interest rate inelastic with full-employment at the effective demand limit.

### To wrap it up…

There will be pressures for inflation or bubbles in asset prices when real GDP reaches the “currently projected” effective demand limit of \$16.1 trillion (2009 dollars). The Fed will be required to respond to control inflationary pressures. They will not be expecting real output to stall since they expect real output to continue up to \$17 trillion. The Fed will have to respond by unwinding QE. Otherwise they will have price level problems.

And the inflationary pressures depend on the momentum that real output growth carries into the effective demand limit. The momentum is economic, institutional, expected and generated. The greater the momentum, the greater the inflationary pressures. If the Fed was to slowly taper QE over the next year, they would control the momentum of real output going into the effective demand limit. The result in theory would be more manageable inflationary pressures.

Yet, we see that the Fed has not wanted to start tapering yet in order to maintain the momentum of real output growth. If the Fed were to allow QE to run full force into the effective demand limit, the future will be interesting to watch. I don’t expect that to happen though. QE will have to be tapered some over the next year.

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