1. ©2019 Jennifer P. Wissink, all rights reserved.
Finding Y* Lecture 12
Dr. Jennifer P. Wissink
©2019 Jennifer P. Wissink, all rights reserved.
March 6, 2019 1

2. Pay-Day!
Aggregate output (income) (Y) is a combined term used to remind you of the exact equality between aggregate output and aggregate income.
Aggregate income is the total income received by all factors of production in a given period.
Aggregate output is the total quantity of goods and services produced in an economy in a given period. 2

3. The Frugal Economy: Determining Aggregate Desired Expenditures=AEd
Pay-Day!
What HHs spend out of Y = Consumption (C)
How much Firms desire for investment = desired Investment (Id)
AEd = C + Id (for now)
Note: AEd depends on Y! 4

4. HHs: Consumption (and Saving) out of Y
Assume (for now): A household can do two, and only two, things with its income:
Consume (C)
a.k.a. consumption
Save (S)
a.k.a. saving and not savings
NOTE the following identities (for now):

5. HHs:The Consumption Function
Determinants of HH consumption include:
Aggregate Output (Income)
Household wealth
Interest rates
Households’ expectations about the future
Other stuff, too.
In The General Theory, Keynes argued that household consumption is directly related to its income. (Lots of other work by others, too.)
So...C = f(Y), where Y = Aggregate Output (Income) holding constant...
Other stuff, too, liked lagged Y, etc.

6. HHs: Consumption Function Concepts
the subsistence level of consumption
the breakeven level of income
dis-saving and saving
the marginal propensity to consume (MPC)
the average propensity to consume (APC) 7

7. HHs: Saving Function From consumption to saving
Recall: C + S = Y, so… S = Y - C
Like a see-saw
the marginal propensity to save (MPS)
the average propensity to save (APS)
Note it will always be the case that:
MPC + MPS=1
APC + APS=1

8. A LINEAR Aggregate Consumption Function Derived from the Equation C = 100 + .75Y
AGGREGATE INCOME, Y (BILLIONS OF DOLLARS)
AGGREGATE CONSUMPTION, C (BILLIONS OF DOLLARS)
100 80
160
175
200
250
400
600
550
800
700
1,000
850

9. Deriving a Saving Function from a Consumption FunctionY - C = S
AGGREGATE INCOME (Billions of Dollars)
AGGREGATE CONSUMPTION (Billions of Dollars)
AGGREGATE SAVING (Billions of Dollars)
100
-100 80
160
-80
175
-75
200
250
-50
400
600
550 50
800
700
1,000
850
150 Y S Y

10. Firms: Actual versus Desired/Planned Investment
Desired or planned investment refers to the additions to capital stock and inventory that are desired or planned by firms.
Actual investment is the actual amount of investment that takes place; it includes items such as unplanned changes in inventories.
Could be additions
Could be depletions

11. Firms: The Desired Investment Function
Desired Investment might depend on:
Aggregate Output(Income): Y
expected rate of return
interest rates
technological state of world
business expectations
animal spirits?
attitudes?
We will make this part of our model very simplistic for a while...
Note: Keynes’ understanding/modeling of investment was so-so

12. Firms: The Desired/Planned Investment Function
For now, we assume that desired/planned investment does not change when income (Y) changes.
It is said to be an autonomous variable.
a.k.a. exogenous
NOTE:
Define MPI
So..., marginal propensity to invest = 0

13. Aggregate Desired Expenditure (AEd) for our Simple Linear Frugal Economy

14. Equilibrium Y* Equilibrium Y* is when: Y* = AEd(Y*)
Recall: Aggregate output/income ≡ Y
Recall: Aggregate desired expenditure =AEd(Y) = C(Y) + Id
Equilibrium Y* is when: Y* = AEd(Y*)
Suppose: Y > [C(Y) + Id]
So actual aggregate output/income > aggregate desired expenditure
So inventory investment is greater than planned/desired
So actual investment is greater than planned/desired investment
So something will change! Firms will produce less!
Suppose: [C(Y) + Id] > Y
So aggregate desired expenditure > actual aggregate output/income
So inventory investment is smaller than planned/desired
So actual investment is less than planned/desired investment
So something will change! Firms will produce more!

15. Equilibrium Y* - Graphically
AEd
45° helping line where AEd=Y Y

16. Equilibrium Y* - Algebraically
There is only one value of Y* for which this statement is true. We can find it by rearranging terms:
By substituting (C) and (Id) into (AEd) we get:
Now impose the equilibrium condition that Y* = AEd(Y*).

17. Equilibrium Y*- Using A Chart
(1)
(2)
(3)
(4)
(5)
(6)
AGGREGATE OUTPUT (INCOME) (Y)
AGGREGATE CONSUMPTION (C)
DESIRED INVESTMENT (Id)
AGGREGATE DESIRED EXPENDITURE (AEd) C + Id
UNPLANNED INVENTORY CHANGE Y - (C + Id)
EQUILIBRIUM? (Y = AE?)
100
175 25
200
- 100 No
250
275
- 75
400
425
- 25
500
475
Yes
600
550
575
+ 25
800
700
725
+ 75
1,000
850
875
+ 125

18. 20