**ANSWERS TO ECON 2030 STUDY PROBLEM: KEYNESIAN MACROECONOMICS**
**plus a graphical exposition
of the solution (in PowerPoint)**

1. *What is the MPC?* The Marginal Propensity to Consume is the
slope of the consumption function. It's the coefficient of Y, or 0.8. We
call it "b." *What is the MPS? * The Marginal Propensity
to Save is the slope of the saving function. It's always equal to1-b.
Here, it's 0.2. The 0.8 and the 0.2 add to 1.0. When we earn
an extra (i.e., marginal) dollar, we spend an extra $0.80 and save the
$0.20. *What is the significance of the "100"? * It's the
level of consumption spending that corresponds to an income of zero. With
no income, this spending would also represent "dissaving." (The fact that
a > 0 reminds us that the Keynesian consumption equation applies to the
short run.)

2. *What are the spending multipliers?* The investment multiplier
is 1/(1-b) = 1/(1-0.8) = 1/0.2 = 5. The government-spending multiplier
is also 5. The leverage that an increase in spending entails is independent
of who (the investment community or the government) is actually doing the
spending.

3. *Write the specific savings equation that corresponds to the consumption
equation.* S = -100 + 0.2Y

4. *At what level of income does savings equal zero?* Write:
0 = -100 + 0.2Y; and solve: Y = 500. You can confirm this answer
by plugging Y = 500 into the consumption equation: C = 100 + 0.8Y = 100
+ 0.8(500) = 100 + 400 = 500. If you earn 500 and spend 500, you save nothing.

5. *How much is aggregate demand, or total spending, when income (Y)
is 1100?* Aggregate demand, or total spending, is simply C + I
+ G. Evaluate C by plugging Y = 1100 into the consumption equation:
C = 100 + 0.8Y = 100 + 0.8(1100) = 100 + 880 = 980. Then add I and
G to get C + I + G = 980 + 50 + 60 = 1090. * Is the economy in equilibrium
at this level of income?* No. Y doesn't equal C + I + G. Rather, 1090
= C + I + G < Y = 1100.

6. *Sketch the aggregate demand curve and locate the different income
magnitudes relative to one another.* The key here is recognizing that
C + I + G < Y. Thus, starting from Y = 1100 on the horizontal axis,
the distance up to the C + I + G curve (1090) is less than the distance
up to the 45-degree line (1100). So, an income of 1100 is located beyond
the income where aggregate demand drops below the 45-degree line. What
you notice, here, is that the (given) *full-employment* income ( Y_{fe
}=
1300) lies above the current income of 1100, while the *equilibrium*
level of income (Y_{eq}) lies below it. The income level needs
to *rise* if prosperity is to be achieved, but the market process
(as envisioned by Keynes) will instead cause income to *fall*--until
the level of savings is just enough to finance the current level of investment
and government spending. This sort of perversity is characteristic of the
market system according to John Maynard Keynes's 1936 book, *The General
Theory of Employment, Interest, and Money*.

7. *What is the equilibrium level of income?* Y_{eq}
= 1050. You get this value by setting income equal to expenditures (Y =
C + I + G), substituting 100 + 0.8Y for C, plugging in the given values
for I and G, and solving for Y. * Describe the economic process
that brings about this Keynesian equilibrium.* The shortfall of expenditures
below income (i.e., 1090 < 1100) means that inventories are accumulating.
The excess inventories, which are amount to 1100 - 1090 = 10, cause businesses
to cut back on production--and to lay of workers. The workers' loss of
income means reduced spending, but spending isn't reduced as much as the
reduction in income (This is the key implication of Keynes's consumer-spending
theory: b < 1.) Income and expenditures spiral downwards until the excess
inventories are dissipated--at which point income equals expenditures,
and the economy is in macroeconomic equilibrium with Y = E = C + I + G
= 1050.

8. *Suppose that the government raises the level of government spending
by 30. What does this do to the equilibrium level of income?*
We've already calculated the government-spending multiplier: 1/(1-b) =5.
The increase in the equilibrium level of income, then, is 5 times 30, or
150. That is DY = 1/(1-b) DG.
The government's extra spending of 30 raises equilibrium income from 1050
to 1200.

9. *How much *more* government spending is required to achieve
full employment?* With income now at 1200, the economy is still 100
short of the (given) full-employment income (of 1300). Using, once again,
the multiplier of 5, we see that the government can raise income by 100
by spending an additional 20. That is, write DY
= 1/(1-b) DG, plug in DY
= 100 and 1/(1-b) = 5, and solve for DG.

10. *What assumptions about wage rates and prices do your calculations
presuppose.* Wage rates and prices are "sticky downwards"--and
for simplicity, we assume that they do not change at all. If they did actually
change quickly enough to clear the markets for goods and for labor, then
there would be no lapses from full employment to theorize about. (We do
assume that prices and wages adjust upward when aggregate demand is greater
than full-employment income. Trying to push the economy beyond its full-employment
level causes inflation and results in no sustainable increases in real
output and real income.)