Econ 222 
Assignment 4
Solutions


Q1.  

i. With an expansionary fiscal polity G increases, which will cause
Sd = (Y-Cd-G) to decrease, and the IS curve will
shift up and right.  If there is a tax increase to finance the increase in
G, then Cd will decrease.  However, the decrease in C will be
less than the increase in G so Sd will fall.  (The fall in
government savings is larger than the fall in private savings.  
(see graph 1.1)

In the short run (at point e1), YFE increases to Y1,
r increases to re1, I d decreases and theh effects
on Cd are ambiguous (Y increasing causes Cd to
increase but r increasing causes Cd to decrease)

Because of excess demand, firms will have to pay workers a higher nominal
wage to work over time and producs above full employment output.  Excess
demand and higher nominal wages will cause prices to rise which will, in
turn cause the LM to shift up and left.  So that the new LM curve,
LM(P2) will pass through the FE-IS intersection at point e2.

In the long run P has increased, r has increased, Y is unchanged at
YFE, Cd has decreased (higher r, but same Y),
Id has decreased (higher r), W/P (real wages) are unchanged as
the increase in W was offset by an increase in P, and M/P is lower.

ii. A contractionary monetary policy implies that Ms decreases.
A decrease in nominal money supply, Ms results in an increase
in the real interest rate at which the asset market clears.  Thus, the LM
curve shifts up and to the left, to LM (M2/P).  (See graph 1.2) 

In the short run (at point B) r increases to rB, Y decreases to
Y1 (demand < supply) and Cd and Id both
decrease.

Because of the slack demand, frims may temporarily cut workers hours.
Prices will drop to bring the goods market into equilibrium.  The decrease
in the price level will cause the real money supply M/P to increase,
lowering the real interest rate which clears the asset market.  Thus LM
will shift down and right to LM(M2/P2)

In the long run (point A again) Y returns to YFE, r returns to
rA, prices  decrease to P2, real wages are unchanged
(nominal wages and price will offset eachother w=W/P).  Note that since r
and Y are back at original levels (unchanged in long run), all real
variables remain unchanged (so Cd and Id are also
unchanged along with N and w).
Thus, in the long run, Money is neutral (all it effects is price level)

iii. A temporary positive supply shock will increase the MPN causing
labour demand to increase (shift right) .  The increase in labour demand
will yeild a higher equilibrium N and w in the labour market.  Because
there is a higher level of equilibrium employment, there will be a higher
level of full employment output (Y is increasing in N), so the FE curve
will shift out and to the right.  Note that a temporary effect will not
effect future MPK.  Since MPKf is unchanged, IS will not shift.

In the short run, the IS and LM still intersect at e0.  The only things
that have changed are N, which has increased, and w which has increased.

Because demand is now less than full employment output, P drops to restore
equilibrium.  Because P has fallen, the LM curve will shift back to the
right and down again.  

The long run equilibrium is at e1.  Here Y has increased, r has
decreased, Cd and has increased (because Y has increased and r
has decreased), Id has increased (because r has decreased), w
and N have both increased and P has decreased.  Since Ms is
unchanged, real money balances are higher.


Q2.
a. To derive the IS and LM equations and solve for P, we can begin by
deriving an equation for savings:

S = Y - C -  G
  =  Y - 250 - 0.9Y + 0.9T + 430r - G
  =  0.1Y - 250 + 0.9(0.9G) - G + 430r
  =  0.1Y - 250 - 0.19G + 430r

Recall the IS curve is the locus of points where the goods market is in
equilibrium.  The equlibrium condition for the goods market is
Id=Sd, so the IS curve can be found as follows:

Sd =  0.1Y - 250 - 0.19G + 430r  = 400 - 410r = Id
so:

0.1Y = 650 + 0.19G - 840r

or

Y = 6500 + 1.9G - 8400r


Note that the IS curve gives you Y in terms of r, and that Y is decreasing
in r.  (Hence a negative sloping IS curve)


Recall the LM curve is the locus of points where the asset market is in
equilibrium.  The equlibrium condition for the asset market is
Ms/P = Md/P, so the LM curve can be found as
follows:

Md/P = 0.5Y - 200(r+0.1) = 2080/P  =  Ms/P   so:

0.5Y = 2080/p + 20 + 200r

or

Y = 4160/P + 40 + 400r

Note that the LM curve gives you Y in terms of r for a given P, and that Y
is increasing in r (Hence a positive sloping LM curve)


Since we know full employment output, determining the equilibrium values
of r and P is relatively simple.
Because we have full employment output, Y, already, we can find the
equlibrium r using the IS curve alone:

5000 = 6500 + 1.9G  8400r
5000 = 6500 + 1.9(100) - 8400r
5000 = 6690 - 8400r

so:   r = 1690/8400  = 0.201     = 20.1%

Now, with this r and the long run full employment output, we can solve for
P using the LM equation:


5000 = 4160/P + 40 + 400(0.2)
5000 = 4160/P + 40 + 80
4160/P = 4880      

so:  P =  4160/4880  =  0.85


b. If the tax rate is decreased to T = 0.5G we can calculate the short run
equilibrium value of r by equating the IS and LM curve given the initial
price level calculated above and the new tax rate. 
(see graph 2.b  => IS curve shifts up)

Recall previously:

IS: Y = 6500 + 10(1-0.81)G - 8400r

Now:

IS2: Y = 6500 + 10(1 - 0.45)G -  8400r   so Y = 7050 -  8400r 

and

LM: Y = 4160/P + 40 + 400r   so Y = 4880 + 40 + 400r    

Equating the two gives us:

7050 - 8400r = 4880 + 40 + 400r

8800r = 7050 - 4880 - 40   = 2130

r = 2130/8800   = 0.242  or 24.2%

Substitute this r back into the IS equation to get:

Y = 7050 - 8400(0.242) = 5017.2

The new general equlibrium values of Y and r are found by again using the
long run (general equlibrium) full employment output value that is given,
and solving for r in our new IS equasion, IS2.
(In the long run, we know that price has increased and the LM curve has
shifted up/left)

So we have:

IS2:  Y = 7050 - 8400r   which yields:

5000 = 7050 - 8400r

r = 2050/8400  = 0.244   or 24.4%

So we can solve for P in the LM again as follows:

Y = 4160/P + 40 + 400r
5000 = 4160/P + 40 + 400(0.244)
P = 4862.4/4160 = 1.17

c. Recall that the AD curve shows the relation between 
aggregate demand, Cd + Id + G, and price.  It shows
the amount of output demanded at any price level P which corresponds to
the intersection of the IS and LM curves.

We can solve for the AD curve by setting IS = LM from part A via r

Recall:

IS:  0.1Y = 669 - 840r
LM: 0.5Y = 200r + 20 + 2080/P

In terms of r:

IS: r =  -  0.1Y/840  + 669/840   
LM: r = 0.5Y/200 - 20/200 - 2080/(P*200)

Set the two equal to get:

- 0.1Y/840 + 669/840 = 0.5Y/200 - 20/200 - 2080/(P*200)

Y ( 0.1/840 - 0.5/200) =  669/840 + 20/200  + 2080/(P*200)

Y ( 20  + 420) =  133800 +  16800 + 1747200/P

440Y = 150600 + 1747200/P

Y =  3970.9/P + 342.27 


Now given Y = 6000, we can solve for P

P  = 3970.9/5657.73  = 0.7  

And the new equilibrium r would be:  r = 669/840 - 0.1(6000)/840  = 0.082


Q3.
a. Money Neutrality:  because prices adjust to changes in the money
supply, the effects on real variables is only temporary (as in Question 1
part ii)

Classical monetarists argue that monetary policy should be conducted by
rules.  They feel that monetary policy has powerful short run effects on
the real economy; however, in the long run, they feel that changes in the
money supply effect prices only (Money Neutrality)

Keynesians argue that the central bank should be able to use monetary
policy in any way that will lower and stabilize inflation, increase
economic growth, and decrease unemployment.  They believe in a highly
interventionary policy because they believe that prices and wages dont
adjust quickly; therefore money would not be neutral and policies can have
long term effects.

b. If the central bank lowers the overnight rate band, it will be easier
to borrow money (looser monetary policy).  Banks will be encouraged to
borrow which will increase the money base.  Therefore, the money supply
will increase.  (Since reserves are higher, banks expand their own loans
and deposits to restore their reserve-deposit ratios which is why money
supply increases)   When money supply increases, the equilibrium interest
rate which clears the asset market drops (see graph 3.b).  So
Ms increases and r decreases.

c.  enom = the number of units of British ponds that can be
                      purchased with one unit of canadian dollars.
Also enom = e(PGB/PCdn)

Purchasing Power Parity means that similar foreign and domestic goods or
baskets of goods should have the same price in terms of the same currency.
This implies:

enom = PGB/PCdn   (that is e=1)

So if Britain experiences domestic inflation (so PGB
increases), then the canadian exchange rate, enom, should
increase.

d.  If the exchange rate increases, then domestics will find it cheaper to
purchase abroad and foreigners will find it more expensive to purchase
domestic goods, so imports will increase and exports will decrease; thus
net exports will decrease.  

Similarly a decrease in e will cause domestics
to find it more expensive to purchase goods abroad and freigners will find
it cheaper to purchase domestic goods.  So imports will decrease and
exports will increase; thus net exports (exports-imports) will increase.

However, a decrease in the exchange rate may actually cause net exports to
drop in the short run.  for example, suppose a country that imports most
of its food faces a sharp increase in the price of food abroad.  In the
short run, the domestic country needs food (which takes a long time to
produce), so even though the price is high, they must purchase enough to
live by.  Given the higher price, the money spent on imports will actually
increase (even though the quantity imported may stay the same or decrease
a small amount).  So net exports would actually decrease in the short run.
In the long run, after a drop in the exchange rate, the domestic country
will produce more of its own food, imporst will drop and net exports will
increase.  This effect depicts the J curve (see graph 3.d)


GRAPHS

 Graph 1.1  now available HERE 
 Graph 1.2 now available HERE 
 Graph 1.3 now available HERE 
 Graph 2b now available HERE 
 Graph 2c now available HERE 
 AD curve now available HERE 
 Graph 3d now available HERE