## About the IS and LM Curves (Economics 100b; Spring 1996)

Professor of Economics J. Bradford DeLong
601 Evans, University of California at Berkeley
Berkeley, CA 94720
(510) 643-4027 phone (510) 642-6615 fax
delong@econ.berkeley.edu

February 14, 1996

Happy Valentine's Day
Where Is the IS Curve?
Why Is the IS Curve Where It Is?
The Keynesian Cross
Where Is the LM Curve?
Why Is the LM Curve Where It Is?
IS-LM Since 1971

Happy Valentine's Day

Where Is the IS Curve?

Where is the IS curve?

• In real interest rate, output space; the U.S. IS Curve in 1995 was at (\$6.7 trillion; 4%)
• In real interest rate, unemployment space; the U.S. IS Curve in 1995 was at (5.5%, 4%)

What is Y*?

• Somewhere between 5 and 7 percent of unemployment...
• Somewhere between \$6.6 trillion and \$6.9 trillion of output...

What is the slope of the IS curve?

• Alan Greenspan: 1% is to \$150 billion
• Other model estimates: 1% is to \$75 billion

So it runs from (\$6.7, 4%) to (\$6.4, 8%) to (\$7.0, 0%)
Uncertainty about location of the IS curve...
Uncertain about the value of Y*...

Why Is the IS Curve Where It Is?

Y = C + I + G

--with planned expenditure equals production equals income, which as we know is the same as:

Sp = DEF + I(r)

equilibrium in the loanable-funds market, or the equalization of savings with planned investment.

We have the consumption function:

C(Y-T) = c0 + c'(Y-T)

And let's think of an investment function:

I(r) = I0 - Ar

Substitute back into the national income identity:

Y = c0 + c'(Y-T) + I0 - Ar + G

Rearrange terms:

(1 - c')Y = c0 + G - c'T + I0 - Ar

Y = (c0 + I0)/(1-c') + DEF/(1-c') + T - Ar/(1-c')

We see here:

• A term involving the "intercepts" of the consumption and investment functions: the higher up are the consumption and investment functions--the higher are the"exogenous" components of consumption and investment--the higher is output going to be for any given level of Y.
• A term involving the deficit--the higher the deficit, the higher is output.
• A term (that I wish would go away) corresponding to the size of government (the "T" term). An expansion of the size of government (keeping the deficit fixed) will tend to push C down by less than it pushes G up, and tend to make a higher level of total output and employment consistent with Sp = DEF + I(r), consistent with equilibrium in the loanable funds market
• A term showing the effect of higher interest rates on depressing investment and "cooling off" the economy.
• A fraction 1/(1-c') -- the inverse of 1 - MPC -- that appears just about everywhere. This fraction is called the multiplier

The Keynesian Cross

Where does this multiplier come from?

We can see where it comes from in the math. It comes from the fact that consumption--on the right hand side of equation #?--is a function of income, so that when we substitute the consumption function into the equation we get a Y on the left-hand side and a -c'Y on the right hand side, and collecting terms gives us a (1-c')Y on the left-hand side, so we have to divide everything by (1-c').

But you may find this explanation less than fully helpful; less than fully intuitive. So let me give another--the so-called Keynesian Cross.

Plot expenditure--what people, firms, and governments will spend, on the vertical axis, and income on the horizontal axis. Hold the interest rate fixed. Start with government--spending invariant to the level of income. Add investment--also not affected by changing levels of income.

Add consumption--upward sloping--marginal propensity to consume.

Equilibrium where expenditure equals income. Circular flow.

Suppose we boost investment. Shift the C+I+G line as a function of Y upwards by an amount DI.

At current Y, expenditure greater than income. So move up--then over. But the first increment to income, the DI, is not sufficient to restore equilibrium. Why? Because the boost to income has also increased planned consumption, because of the upward-slope imparted to C+I+G from the consumption function, the fact that households do not save everything out of income but spend some on consumption goods.

So we have:

DI + (DI)(c') + (DI)(c')^2 + (DI)(c')^3 + (DI)(c')^4 + (DI)(c')^5+ ... a lot more similar terms which together add up to:

DI/(1-c')

Where Is the LM Curve?

Why Is the LM Curve Where It Is?

Details of money demand...
These days money demand pretty elastic...
Lots of substitute ways to spend purchasing power...
Hence surprisingly big moves in quantity of liquidity needed to have a material effect on output or interest rates...

• Does this play a role in the Federal Reserve's preference for interest-rate targetting? Not sure...

Conversely, surprisingly large moves in IS curve produce relatively little interest rate action...

IS and LM Since 1971

A potted history of where the IS-LM model says that we have been since the early 1970s. Long and variable lags. Differences between short-term and long-term interest rates; between real and nominal; trend growth of the economy; shifting trend growth.

Flatten all these out by looking at unemployment rates and at last-year's short-term real interest rate...

What do we see?

• 1971-1973: An economy with a 5.9% unemployment rate with which we would be happy, but they then were not (thinking that structural plus cyclical unemployment amounted to 4%); inflation a bit high; bipartisan agreement to impose various price-control and -restraint programs while easing monetary policy; riding down the IS curve to 1973, with what we would now see as high output and very low real interest rates.
• 1973-1975: First oil shock. In the wake of the 1973 Arab-Israeli War OPEC tripled the world price of oil. Effects twofold (a) burst of inflation, and (b) collapse in investment--strong shift of IS curve to the left; Federal Reserve responds to burst of inflation and fears of a truly deep recession by raising interest rates, but roughly only as much as inflation rose.
• 1975-1978: IS curve moves back to the right as more businesses are willing to invest at new relative prices once it becomes clear that the recession is not going to be deep or prolonged. Falls in inflation lead the Federal Reserve to lower nominal interest rates by about as much as inflation falls (thus shifting the LM curve out to the right as well). But well before the economy had reached what people then saw as full employment, inflation began to accelerate.
• 1978-1982: The Volcker deflation. Faced with what he feared would become unstable accelerating double-digit inflation, the Federal Reserve under chairman Paul Volcker contracts monetary policy. The economy rides up the IS curve to 1982, where real interest rates are at levels unseen since the Great Depression--and unemployment is at levels unseen since the Great Depression as well. Inflation falls rapidly.
• 1982-1989: The expanded federal deficits created by Reagan-era tax cuts shift the IS curve out to the right; the Federal Reserve responds to falling inflation by easing monetary policy as well; the shift in monetary policy dominates--for most of the 1980s unemployment and real interest rates drift downward as repeated policy stimulations fail to re-start inflation.
• 1989-1992: Fears of another Iraqi-driven oil shock and other factors pull the IS curve back to the left. The Federal Reserve responds too slowly--or so we now see in retrospect--and the economy enters a recession.
• 1992-1994: Repeated monetary easing pushes the economy down and to the right as it rides down the IS curve once again, heading for full employment.
• 1994-1995: As the economy reaches what the Federal Reserve guesses to be "full employment," monetary policy is tightened slightly to keep strong investment demand from pushing the economy back into the inflationary-spiral region; the Federal Reserve pursues the elusive concept of a "soft landing."

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# Econ 100b

Created 4/30/1996
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