Ec. 132 Harold Petersen
Principles of Economics-Macro January 28, 2014
Lecture 5: Theory of Output Determination .
Last time we worked with the AS-AD framework and talked about
business cycles. We are working with the Keynesian model of output
determination. We illustrate this with an AS-AD diagram in which AS slopes
gently up to potential output Q* and then steeply thereafter. If spending falls
off, firms cut back output but we find that prices and wages change very little.
They are inflexible on the downside. But if spending increases beyond AD, so
that people want to buy more than Q*, then output increases by very little but
prices rise a great deal. This is the so-called Mainstream Keynesian Model. Now
consider an extreme case of this. Assume that in the short run if spending falls
off, prices and wages do not fall at all. Only output and employment fall. And if
spending increases beyond AD, only prices rise.Q* is an upper limit which
cannot be exceeded even in the short run. Thus we draw AS as a horizontal line
up to Q* and a vertical line thereafter.
P Q* AS
Qo Q1 Q*
Mainstream Keynesian Model Extreme Keynesian Model
You will see the diagram on the right on p. 140 of your text, or p. 442 of the
hardcover version. We take this approach in order to develop the Keynesian
multiplier principle, focusing on how a change in spending will impact output by
several times over, initially with an assumption that there is no impact on prices
and no change in interest rates or availability of credit. This is the sort of
situation we might expect at the present time, with a great deal of slack in the
Consider now a formal model. The Keynesian Multiplier Model:
Model I. Assume: No government spending or taxes.
No corporate retained earnings
No imports or exports. 2
Thus GDP = DI = Q.
We have just two components of spending, C and I. We assume
consumption to be solely dependent on DI, with an MPC less than one. We take
I as given (invariant to income but dependent on profit expectations.) As an
C = 100 + 2/3 DI = 100 + 2/3 Q
I = 200
where C and I are understood to be components of AD, or the amount
households wish to spend on consumption and firms wish to spend on new
plant, equipment, and inventories.
We now state as an equilibrium condition: total desired spending equals
C + I = Q subject to Q ≤ Q*
We can solve for Q algebraically or alternatively with a table.
C + I = Q
100 + 2/3 Q + 200 = Q
100 + 200 = Q - 2/3 Q Check: At Q = 900
C = 100 + 600 = 700
300 = 1/3 Q I = 200
3(300) = 3(1/3)Q C + I = 900
Q = 3(300) = 900
Using a table, list alternative values of Q, along with C and I
Q DI C I C+I I' C+I'
300 300 300 200 500 300 600
600 600 500 200 700 300 800
900 900 700 200 900 300 1000
1200 1200 900 200 1100 300 1200
1500 1500 1100 200 1300 300 1400
At what output does C + I = Q? At Q = 900Suppose that actual output
were 600. At Q = 600, consumers want to buy 500 of goods and firms want to
buy 200 of machines. People want to buy more than is being produced. What 3
happens? Firms sell more than they are producing, inventories decline, and
firms see they could sell more. They increase output, in response to orders.
The Keynesian model says that firms will always respond to orders, that
spending calls the tune. Suppose Q were 1200, with AD as given. Firms are
producing 1200 but people are buying just 1100 (C + I). The extra output piles
up on the shelves or in the lots, as excess inventory. Firms cut back output and
in doing so lay off workers.
We can illustrate C+I and the equilibrium Q graphically as follows:
900 Q (Real GDP)
We use a 45-degree line (or Q line) to help us plot and to help us locate the
equilibrium. We plot C+I against Q. Where C+I = Q, we note the equilibrium,
indicated as point E. We drop a line to the Q axis and label it Qo, for equilibrium
Now suppose I rises by 100, from 200 to 300 (perhaps because of an
increase in business confidence). What happens to Q? Look at this first on the
chart. We see that Q rises by 300, from 900 to 1200. Investment spending
has increased by 100, but Q has gone up by 300. Why? Because of the
multiplier effect. As I spending increases by 100, firms raise output by 100 to
meet the new demand. But in doing so they add workers and pay out additional
DI of 100. Now households spend more on consumption. How much more?
This depends on the MPC. With an MPC of 2/3, as DI goes up by 100, C goes
up by 66 2/3. But now firms respond to the new C spending by producing
more goods. They hire more workers and pay out more in wages, interest, or
profits. DI income goes up and C goes up some more. C spending continues to
rise, and Q continues to rise, in successive stages, but each time by a lesser and
lesser amount. We find eventually that Q is up by several times the initial
increase in spending--in this case by exactly three times the initial increase.
We can trace this through as a series of stages of additional spending. 4
Initial C I Q DI
Equil. 700 200 900 900