EC 313 Intermediate Macroeconomics

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Oct 28, 2013 (3 years and 10 months ago)

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EC 313 Intermediate
Macroeconomics

Lecture 3

Thursday 10/8/2013


Go to the board to explain the multiplier
intuitively with the circular flow diagram



To the board…



Process takes time to unfold in the real world,
probably in the 6
-
18 months range, perhaps
longer for, say, infrastructure spending by the
government

An alternative way to look at equilibrium


Recall that equilibrium is where Y = Z, or
where Y = C + I + G


But note that we can write Y, income, as

Y = C + S +T (income goes to taxes or
consumption, whatever is left over is saving).


Then, at equilibrium


C + S + T = C + I + G


Cancel the C terms to get


S + T = I + G


Rearrange terms to get


I = S + (T
-
G)


This says that
investment = saving
, i.e. S =
private saving and (T
-
G) is public saving (which
can be negative)


Now, note that S = Y


C


T. Sub in to get


S = Y


(
c
0

+ c
1
(Y
-
T
))


T


Or, combining terms


S =
-
c
0

+
(1
-
c
1
)(Y
-
T
)


This is the
saving function
, and
(1
-
c
1
) is the
marginal propensity to save
.


Now use this to find the equilibrium (recalling
that I = I
0
)


I
0

=
S + (T
-
G
)


Sub for S


I
0

=
-
c
0

+ (1
-
c
1
)(Y
-
T
)
+ (T
-
G
)


Solve for Y


Y
= [1/(1
-

c
1
)][c
0

+ I
0

+ G


c
1
T
]


This is the same equilibrium. It has to be, it
was derived from Y=Z.



Show graphically on the board…

How easy is this in the real world?


Changing G or T


getting this through
Congress


is not easy


We held all else equal, e.g. investment and net
exports, but when these change and it’s not
fully predictable, hitting a policy target is
much harder


Expectations of the future also matter, we
have abstracted from this (for now)


There may be side effects, e.g. deficits or
inflation

Practice Problems


Example 1


C = 200 + .8(Y
-
T)


I = 160


G = 300


T = 200


Find equilibrium income, disposable income, and
consumption. How large is the deficit?


Let autonomous consumption increase to 300. Use
the multiplier to find the new equilibrium for output


If full employment is when output = 4000, how much
should G change to reach full employment?


Example 2 (Balanced Budget Multiplier)


C = 300 + .75(Y
-
T)


I = 200


G = 400


T = 400


Find equilibrium income


Notice that the budget is in balance, i.e. G=T. Let
both G and T increase by 50 so that the budget
stays in balance. What happens to output?


If the government spends a dollar more, and takes
a dollar back in taxes at the same time, how can
output go up? Why does this increase demand?



Example 3 (paradox of thrift)


C = 800 + .75(Y
-
T)


I = 600


G = 500


T = 400


Find equilibrium income. Find saving.


Let autonomous consumption, c
0
, decrease from 800
to 700. That is, let people be “virtuous” and try to
save more and consume less.


Find the new values for output and saving.


Why doesn’t saving change (this is the paradox, that
people try to save more, but this reduces output and
they end up with the same savings as before)



Chapter 4 Financial Markets

The Demand for Money


What determines the demand for money? (Note
the distinction between income, money, and
wealth)


Will assume financial wealth (the accumulation
of past saving and dis
-
saving) can be held as
either:


Money (which pays no interest)


Bonds (pay interest


this is a placeholder for all
assets that offer a return)


Money = currency plus checkable deposits (i.e.
M1, will cover M2, etc. later). It can
beused

for
transactions


Bonds pay interest I, but cannot be used for
transactions (again, this is a placeholder


and
aggregate


capturing all interest bearing
financial assets, in real world many types of
assets each with its own interest rate)


Question for us: How much wealth should be
held as money, and how much as bonds?


Wealth = Money + Bonds


You could leave as much as possible in bonds, and
when you need money transfer over the exact
amount by a phone call to a broker, cell phone
standing in checkout line, etc. That would
maximize interest income.


But if there is a cost of doing this


and there is


and if each additional time you do make a
transfer it gets more irksome and the benefit falls


there is a limit to how many transfers you will
make (could be zero, i.e. hold all wealth as
money)


To the board to illustrate…


Money demand will depend upon two variables


The volume of transactions, which we will capture as
income (not perfectly related, but close enough)


The interest rate which captures the opportunity cost of
holding money


Do people really behave like this? When interest rates
are high, people do tend to put as much money as they
can in things like money market accounts (the money is
used to buy bonds)


we see money move from
checking to these types of accounts (and businesses
manage their money carefully as well)


Presently, the benefit is so low (since interest rates are
so low) that most people are simply holding money


So we can write
M
d

= PYL(
i
) , where PY is nominal
income (book uses $Y) and L(
i
) is a function that
is negative in the interest rate. That is, when
i

increases, L(
i
) (and hence
M
d
) fall.


Graphically (show on board)


Negatively related to the interest rate (when
i

goes up, move wealth from money to bonds)


Shifts out when P or Y increases (need more for
transactions). If PY doubles, need twice as much
money to buy the same amount of stuff (since y
held constant)

Determining the Interest Rate


We have a money demand curve, but to get to
an equilibrium (a particular M and
i
), need to
add the money supply


For now, assume that all cash is in currency,
there are no banks and no checking accounts


Will add banks and demand deposits soon,
simplifies things for now.


Assume monetary authority sets the money
supply at whatever level is desired, i.e.
M
s

= M


Show
M
d

=
M
s

on board …


Equilibrium


A change in Y


A change in P


A change in
M
s

Figure 4
-
2
The Determination of the Interest Rate

Figure 4
-
3
The Effects of an Increase in Nominal Income on the Interest Rate

Figure 4
-
4
The Effects of an Increase in the Money Supply on the Interest Rate

Monetary Policy and Open Market Operations


Look at how central banks actually change the
money supply (and reintroduce the banking
sector)


In particular, look at “open market operations”
which can be expansionary (money supply rises)
or
contractionary

(money supply falls)


It does this by buying and selling bonds (buying


trading new money for bonds


increases the
money supply, and selling


giving people bonds
in return for money


reduces it

Bond Prices and Bond Yields


Won’t go into as much detail as the text, but
the point of this section is that the prices of
bonds and the interest rate are inversely
related


Explain with an example


Let the price of a bond today be P
B
, and value
a year today be $100 (what you get when you
cash it in a year from today).


Then


i

= ($100
-
P
B
)/P
B


With a bit of algebra this becomes:


P
B

= $100/(1+i)


Thus, when
i

increases, P
B

declines. They are inversely
related.


Now think about open market operations. Let the Fed
buy bonds (increase the
M
s
). This reduces the supply of
bonds on private markets, so it must be that PB
incfreased
, And since I and P
B

are inversely related,
i

must have gone down. Thus, the purchase of bonds
increases the money supply and reduces the interest
rate.


When the Fed sells bonds, the opposite happens, the
supply goes up, P
B

goes down, and
i

goes up.


Explain by referencing the
M
d
-
M
s

diagram


Should the Fed choose money or the interest
rate? Presently, the Fed targets an interest
rate, and lets the money supply adjust as
necessary to hit the interest rate target.


Show graphically on board with
M
d
-
M
s

diagram