Income Determination
The Monetary Dimension - II
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
Money Demand
$ In Classical economics we saw an
analysis of the supply and demand for
"loanable funds"


supply = deposits in banks of money being saved
demand = borrowing from banks deposits, mostly for
investment
$ In Keynesian analysis focus shifts to
demand for money, to those who want to
hold money, as opposed to interest
bearing assets and their reasons
Keynes gave three motives
$ Transactions demand
$ Precautionary demand
$ Speculative demand
Cost of holding money
$ Money vs C&F's "bond"
$ If you hold cash, you earn no interest
income
$ If you hold an interest bearing account
you do earn interest
$ So, assuming profit maximizing behavior,
you would expect people to deposit all
their money into interest bearing assets
unless they had reasons to do otherwise
Transaction Demand
$ Main reason to hold money: to have it on
hand to finance various transactions



you keep money in your pocket to by a coke
you keep money in your checking acct to pay rent
businesses keep money for regular purchases
$ Income and transaction demand



income and spending are not synchronized
e.g., income comes in once a month
e.g., money needs to be spent more frequently
Optimal Balance
$ On the one hand you want to earn interest
$ On the other you need money in hand
$ How much?
Transactions Demand Graph
$ One way to think about the transactions
demand is in relation to income: md = kY,
the more income, the more cash needed
md
mdt = kY
Y
But you can also earn i
$ So there is a trade-off
$ Amount to be held for transactions
determined by interest rates vs
transactions costs, i.e, how much it costs
you to convert interest bearing assets to
money
$ Given costs, the higher the interest rate,
the less money you would want to hold
Transactions Demand for Money
$ Lower the interest rate, greater the
demand for money
interest rate
i
Mdt
Money, M
Precautionary Demand
$ People hold money because they can't
anticipate every need, there is uncertainty,
so they hold more
$ With uncertainty independent of the
interest rate then you might expect the Md
curve to be a little more to the right than
otherwise.
$ "IF" the interest rate measures risk, then
the Md curve might be steeper
Precautionary Demand Graph
$ One way to think about the precautionary
demand is in relation to income: mdp = jY,
the more income, the more cash might be
needed
md
mdp = jY
Y
Speculative Demand
$ Speculation = buying an asset in the
hopes that its price will rise, e.g, a bond
$ bond prices vary inversely with interest
rates, i.e., if interest rates rise, bond prices
fall and visa versa
$ So, the lower interest rates, the more you
might expect them to rise and bond prices
to fall, so you would hold fewer bonds and
more money, so shape is same
Speculative Demand
$ Speculative Demand, a lot like transactions
demand
i
Mds
M
Total Demand for Money
$ Transactions (Mdt) + Precautionary (Mdp) +
Speculative (Mds)
i
Liquidity Preference Curve
Md, LPC
M
Quantitative Considerations
$ The demand will vary according to


income, Keynes was concerned with this
prices, Keynes largely ignored this (we will too)
$ A rise in income will shift curve to right
$ A rise in the price level will shift curve to
right
$ So Md = f(i, Y, P)
$ With dMd/di < 0, dMd/dY > 0, dMd/p > 0)
Equilibrium Interest Rate
$ Combine demand with supply of money
I
N
T
E
R
E
S
T
Ms controlled by Fed
Md, LPC
M
Fed Policy - I
$ Expand supply of money to decrease i
i
Ms controlled by Fed
Msi
Md, LPC
M
Fed Policy - II
$ Contract supply of money to increase i
Ms controlled by Fed
 Msi
Md, LPC
Link Money w/Income
Determination Model
$
$
$
$
$
Y = C + I + G + (X - M)
C = a + bY
I = e + fY
Md = f(i, Y, P)
Ms = Ms
$ Where is link? Between i & I, i & C (Keynes
only concerned with link btwn i & I)
Marginal Efficiency of Capital
$ Amount of investment is determined by
comparing expected rate of return to i
i
Investment
Marginal Efficiency of Capital
$ Amount of investment is determined by
comparing expected rate of return to i
i
higher the interest rate, the less the
investment forthcoming
MEC
Investment
Fed Policy & Investment
$ Keynes focused on Fed influence on I thru
manipulation of i
MEC
LPC
I
Money Policy & Income
$
$
$
$
If Ms iI
then with Y = C + I + G + (X - M),
an I Y
which we can see in the following 3 part
diagram
I
N
T
E
R
E
S
T
MEC
LPC
Investment, Savings
I
N
C
O
M
E
Y
Feedback Effect
$ However, remembering that
$ Md = f(i, Y, P), dMd/dY > 0
$ We know that an increase in Y will result in
a right shift in Md, offsetting the increase
in Ms somewhat so i won't be quite as low,
and thus also I & Y won't increase as
much
$ Two solutions:


algebraic
change models
IS - LM Model
$ Alternative formulation of Keynesian
model which moves consumption to
background and highlights interest rate.
$ IS = locus of equilibrium points between
investment and supply (I & S, IS)
$ LM = locus of equilibrium points in supply
& demand for money.
IS - LM Graph
I
N
T
E
R
E
S ie
T
LM
IS
Ye
Y
 Ms
I
N
T
E
R
E
S ie
T
LM
IS
Ye Y'e
Y
Derivation of IS
$ We begin with the MEC shedule which we
will assume is linear, I = e + fY + gi
MEC
Derivation of IS
$ From this we know what I will be
generated by any given level of I
i
i1
MEC
I1
Investment
Algebraic
$ If our linear MEC curve is given by the
equation I = e +gi, [or i = e + gI] w/g<0

NB: given our past discussion of investment we would
be more likely to use I = e + fY +gi. This would cause no
problem in solving the model for equilibrium Y, but in
this simple graphic derivation we leave Y out because it
is Y we are looking for.)
$ Then for any given i we can calculate the
level of investment, I that we would expect
to be forthcoming at that I.
I=S
$ We also know that in equilibrium I = S, so
if we know I1 we also know what S1 will be
Savings
S1
I1
Investment
S = -a + (1 - b) Y
$ But from the savings function, we know
the level of Y necessary to generate S1
Savings
S1
Y
Y1
Algebraic
$ Given a rate of interest (i), we found the
resulting level of investment (I)
$ We know that in equilibrium, I = S
$ Therefore, we know S
$ The only question that remains is what
level of Y will generate that level of S
$ We can find this from the Savings function
(S = -a + (1-b)Y)
Equilibrium Point
$ So, beginning with a given interest rate,
we have found the level of Y at which I = S.
$ We can repeat this procedure to obtain the
locus of points that forms the IS curve.
$ We can also put these four diagrams
together to see their interaction
i
Savings
S
S1
Investment
i
i
i1
MEC
Income
Y1
I1
Investment
i
Savings
S
S1
S2
Investment
i
i
i2
i1
MEC
Income
Y2
Y1
I2
I1
Investment
i
Savings
S
S1
S2
Investment
i
i
IS
i2
i1
MEC
Income
Y2
Y1
I2
I1
Investment
Algebraic
$
$
$
$
$
$
If Y = C + I
and if C = a + bY, I = e + fY + gi
then, Y = a + bY + e + fY + gi
Y - by - fY = a + e + gi
Y(1-b-f) = a + e + gi
Y = a/(1-b-f) + e/ (1-b-f) + [g/ (1-b-f)]i

-- an equation in Y and i of the sort Y = f(i) [or we could
find i = f(Y)] which is what we are looking for.
Derivation of LM
$ We begin with the speculative demand for money,
assuming some i, we know the level of Mds that
will be desired
i
Speculative demand
ms = L(i)
i1
Mds
Md1
M
Algebraic
$ In linear form, the relation between the
interest rate and the speculative demand
of money is of the sort:
$ i = m + nMds where n<0, e.g.,:
$ i = 5.1 - 0.05Mds
Total M = Mdt + Mdp + Mds
$ So, total M can be divided btwn Mds and
Mdt + Mdp (which we will lump together)
Mdt + Mdp
and derive how much money will be
held for transactions and precautionary
motives
Mds
Md1
Algebraic
$ The total demand for money,
$ M = Mdt + Mdp + Mds
$ in equilibrium, will be equal to the supply
and therefore given (M)
$ so if we have found Mds, then Mdt + Mdp
will = M - Mds
$ and both Mdt and Mdp are determined by
Y, therefore we can find the level of Y that
will generate Mdt + Mdp
Mdt + Mdp
$ We can combine the Mdt and Mdp curves
as both are a function of Y and ask what
level of Y will generate Mdt + Mdp
Mdt + Mdp
Y
One Point on LM
$ We now have a level of Y that will be
compatible with the originally posited
level of interest. That level of Y will
generate a level of transactions and
precautionary demand compatible with the
desired level of speculative demand.
$ We can see the relationships in the
following diagram.
Mdt
+
Mdp
Mdt
+
Mdp
Y
Mds
i
i
Mds
Y
M
Mdt
+
Mdp
Mdt
+
Mdp
Mds
i
i
Mds
Y
M
Mdt
+
Mdp
Mdt
+
Mdp
Mds
LM
i
i
Mds
Y
M
Algebraic - I
$
$
$
$
$
$
i = m + nMds where n<0
Mds = i/n - m/n
M = Mds + [Mdt + Mdp]
[Mdt + Mdp] = Mdy = f(Y), say
Mdy = p + qY
M = i/n - m/n + p + qY, but Md = Ms, so for
every Ms,
$ we can find an equation in Y and i
Algebraic - II
$ In problems all this is sometimes
simplified into a single demand for money
function, e.g.,
$ i = 5.1 - 0.05Md
$ ignoring the dependence of Mdt and Mdp
on Y, e.g., sample test #2 on web-forum
Thus, the IS - LM Graph
I
N
T
E
R
E
S ie
T
LM
IS
Ye
Y
Algebraic
$ Each of these two curves are represented
mathematically as equations of the sort:
i = r + sY
$ Therefore, an equilibrium solution can be
found by solving the two equations
simultaneously for i and Y.
$ You now have two ways of solving these
models


simply combine all the equations and givens
find the equations for IS and LM curves and solve
Fiscal Policy & IS Curve
I
N
T
E
R
E
S ie
T
LM
IS'
IS
Ye
Y'e
Y
Monetary Policy &LM
I
N
T
E
R
E
S ie
T
LM
LM'
IS
Ye
Y'e
Y
Homework
$ Now, factor in G and T and re-derive the IS
and LM curves. How does their inclusion
change the graphs?
$ Finally, factor in net exports (X - M) and do
the same.
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