keynesian income determination. overview nkeynesian income determination models u private sector n...
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KeynesianIncome Determination
Overview 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
Private Sector
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 $
Consumption function = C = f(Y) [=c(y)in C&F]
where Y = income and dC/dY > 0, i.e., C rises as Y rises
Consumption
Household income
C = f(Y)
Consumption function = C = f(Y) [=c(y)in C&F]
where Y = income and dC/dY > 0, i.e., C rises as Y rises
Consumption
Household income
C = f(Y)
?
Linear Version
We will only deal with linear versions of the consumption function because it makes things simpler C = a + bY
Consumption
Aggregate Income = Y
C
Y
dC/dY = b
Manipulate Suppose the marginal propensity to consume rises. What
happens to the function? Under what circumstances would "a" rise? Or fall?
C = a + bYConsumption
Aggregate Income = Y
C
Y
dC/dY = b
Change in MPC Rise in MPC, b' > b would steepen curve
C = a + b' Y
Consumption
Aggregate Income = Y
dC/dY = b
C = a + bY
Change in "a" Under what circumstances would "a" rise? Or fall? Rise:
a' > a, fall: a' < a
C = a' + bYConsumption
Aggregate Income = Y
C = a + bY
Savings Function - derivation
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
45o Line
To facilitate derivation, and future work
Savings Function - derivationgraphical
C = a + bY
S = -a + (1-b)Y
Consumption
Savings
a
-a
Investment - I
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')
Investment - II
"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
Investment - III
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(Yt - Yt-1), investment a function of growth
I = I, investment assumed fixed for short run This last is C&F assumption, easiest to start with
Fixed Investment
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 Level of 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
Y C + I Equilibrium when planned expenditures = actual
expenditures, no unexpected accumulation or dis-accumulation of inventories.
I = I
C = a + bY
C+I = a + bY + I
Y
C, I
Ye
Y C + I
Suppose output greater than expected (A) or less than expected (B).
C+I = a + bY + I
Y
C, I
AB
excessinventories
Unplannedfall in
inventories
Ye
S I
Equilibrium also requires that planned I = planned S
I = I
S = -a + bY
Ye
S I ?
If planned I planned S, then the same mechanism of firms responding to unexpected changes in inventory will return Y to Ye
I = I
S = -a + (1-b)Y
Ye
S, I
Y
excessinventory
Unplannedfall in
inventories
I = f + gY
Let I = f(Y) and let f(Y) be linear, e.g., I = f + gY where f > 0, g > 0
I = f + gY
S = -a +(1-b)Y
Y
S, I
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"
Is this magic?
No! Multiplier - II
Assume I increases, clearly
S
I
I'
>but, by how much?
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
19291932
So What to Do?
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
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