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Econ 100b

Created 4/30/1996
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Lecture Eleven

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
http://www.j-bradford-delong.net

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?

What is Y*?

What is the slope of the IS curve?

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?

Start with:

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:



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...

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?


>

Econ 100b

Created 4/30/1996
Go to
Brad De Long's Home Page


Professor of Economics J. Bradford DeLong, 601 Evans
University of California at Berkeley
Berkeley, CA 94720-3880
(510) 643-4027 phone (510) 642-6615 fax
delong@econ.berkeley.edu
http://www.j-bradford-delong.net/