
Keynesian Income Determination Models
 Private sector
 Consumption demand
 Investment Demand
 Supply & demand for money
 Public Sector
 Government expenditure
 Government taxes
 Monetary policy manipulation of money supply
 International
 imports, exports, net exports


Simple model
 Consumption & Aggregate Demand
 Savings & Investment

Consumption is consumption of "household"

Savings
 in C&F, savings = savings of consumers out of unspent income
 but most savings = retained business profits

Investment: by business thru profits & borrowed $

 where Y = income
 and dC/dY > 0, i.e., C rises as Y rises
Consumption
C = f(Y)
Household income

 where Y = income
 and dC/dY > 0, i.e., C rises as Y rises
Consumption
C = f(Y)
Household income
?


We will only deal with linear versions of the consumption function because it makes things simpler
C = a + bY
Consumption dC/dY = b 
C

Y
Aggregate Income = Y

 Suppose the marginal propensity to consume rises. What happens to the function? Under what circumstances would
"a" rise? Or fall?
Consumption
C = a + bY dC/dY = b 
C

Y
Aggregate Income = Y

 Rise in MPC, b' > b would steepen curve
C = a + b' Y
Consumption dC/dY = b
C = a + bY
Aggregate Income = Y

 Under what circumstances would "a" rise? Or fall? Rise: a' > a, fall: a' < a
C = a' + bY
Consumption
C = a + bY
Aggregate Income = Y


Savings function = flip side of consumption function, what you don't spend you save

C = a +bY

Y = C + S

Y = a + bY + S

Y - a - bY = S

-a + (1 - b)Y = S

S = -a + (1-b)Y

o

To facilitate derivation, and future work

C = a + bY
Consumption a
Savings
S = -a + (1-b)Y
-a


Investment = "real" investment, i.e., the expenditure of money to buy and employ labor and raw materials and machines to produce commodities, i.e., M - C(MP,L) ... P... C'

Buying, employing and accumulating "capital stock"
 machines (MP)
 inventories of raw materials (MP)
 inventories of produced goods (C')

 
"Planned" investment
 Planned purchases of inputs & inventory accumulation
 
"Actual" investment
 Actual purchase & accumulation

Actual can be different than Planned I
 difference is usually unexpected changes in inventories
 if actual > planned, firms have excess inventory
 if actual < planned, firms have less inventory


We can make various assumptions about determinants of Investment
 I = f(

), investment a function of profits,dI/dp >0
 I = f(Y), investment a function of level of economic activity,dI/dY >0
 I = f(Y t
- Y t-1
), investment a function of growth
 I = I, investment assumed fixed for short run
 This last is C&F assumption, easiest to start with


To assume I is fixed, or given, at all levels of Y means we have an investment function like this:
I
I = I
Y


"Equilibrium" means same as with supply & demand
 any move away will set forces in motion that will return you to equilibrium

Given expenditures C and I, the equilibrium level of Y will = C + , or total aggregate demand.

Given investment I and savings S, the equilibrium level of Y will be given by S = I


 Equilibrium when planned expenditures = actual expenditures, no unexpected accumulation or disaccumulation of inventories.
C, I C+I = a + bY + I
C = a + bY
Y e
I = I
Y

Y

C + I
 Suppose output greater than expected (A) or less than expected (B).
C, I C+I = a + bY + I
Unplanned fall in inventories excess inventories
B Y e
A
Y

S

I

Equilibrium also requires that planned I = planned S
S = -a + bY
I = I
Y e

S

I ?

If planned I
 planned S, then the same mechanism of firms responding to unexpected changes in inventory will return Y to Y e
S, I
S = -a + (1-b)Y
Unplanned fall in inventories excess inventory
I = I
Y
Y e

I = f + gY

Let I = f(Y) and let f(Y) be linear,
 e.g., I = f + gY
 where f > 0, g > 0
S, I
S = -a +(1-b)Y
I = f + gY
Y

Algebraic Solutions

Y = C + I
 where C = a + bY
 where I = I, or I = f + gY
 Solve for equilibrium Y

S = I
 where S = -a + (1-b)Y
 where I = I, or I = f + gY
 Solve for equilibrium Y

Problems

Most of problems in C&F ask you to solve for equilibrium Y given values of variables

You can also experiment to see what will happen when various kinds of events occur in the private sector
 e.g., business goes on strike, cuts back on I
 e.g., a burst of optimism (or demoralization) raises (or lowers) b or a such that the consumption function shifts

Take real numbers and calculate parameters

Multiplier - I

Contemplation of the previous phenomena, using these tools, especially with numerical examples will lead you to notice that changes in a or I will produce larger changes in Y, the effects will be
"multiplied"

No! Multiplier - II

Assume I increases, clearly but, by how much?
>
S
I
I'

Multiplier - III

Y = C + I

C = a + bY

I = I

Y = a + bY + I, so now substract bY from ea. side

Y - bY = a + I, regrouping

(1 - b)Y = a + I, divide both sides by (1-b)

Y = a/(1-b) + I/(1-b), take derivative
 dY/dI = 1/(1-b), so if b = .75, then dY/dI = 4

Multiplier - IV

S = I

S = -a + (1-b)Y

I = I

You solve for dY/dI

You solve for dY/da

Why?

Keynes developed this conceptual approach to looking at the whole economy because he didn't like the kinds of results generated by the private sector and wanted tools that could help figure out how to intervene

For example, in Great Depression, faced with stock market crash and industrial unions, business cut way back on investment, results could be analyzed with these tools.

Great Depression

Business strike =

I
C + I
C + I'
I' < I
1932 1929


Partly answer will come from widening analysis to include government

Partly answer will come from widening analysis to include financial sector

Both will provide tools to help government decide how to intervene to restore the earlier (and higher) levels of national output