Assignment 3 Solutions
Q1.    

a)
Recall: The asset market is a set of markets.  Demand for each asset
depends on its expected return, rist, and liquidity relative to all other
assets.  At any given time, the supply of assets is usually fixed.

The asset market is in equilibrium when quantity demanded of each asset
equals the fixed quantity supplied of each asset.  There is a need to
aggregate the market.  To simplify, we assume that we can group assets
into two categories: 1. Monetary, 2. Non-Monetary

Money is assumed to have same risk and pay the same nominal interest rate
i^m  ;fixed supply of money = M; All non-monetary assets are
assumed to have the same risk and liquidity and to pay the same nominal
interest rate i=r+pi^e  ; fixed supply = NM.

Now the asset market equilibrium can be reduced to M^d = M^s (aggregate) because of the following:
Consider:  M^d  = aggregate money demand   NM^d =agregate demand for non-monetary assets.

M^d  + NM^d  =aggregate nominal wealth   (via demand) (1)

Because money and non-money assets are the only assets in the economy, we
also know that: 

M + NM =aggregate nominal wealth   (via supply)  (2)

Subtract (2) from (1) to get:


(M^d - M) +   (NM^d - NM) = 0  
   
this is excess demand for money plus excess demand for non-money assets
must sum to 0

If  M^d= M then  NM^d - NM = 0, thus NM^d = NM.

By definition, if quantity demanded equals quantity supplied for
each asset, then the asset market is in equilibrium, therefore, if
M^d = M the asset market is in equilibrium.


b)

Quantity Theory:  M/P = Y/V  =  15,000/3  =  5,000

At equilibrium  M^d  = M       

=> M^d/P = 5,000 		 

=> M^d   =  5,000 x P

So real money demand = nominal money demand = 5,000 since P=1


c)  note /pi is the code for the lower case greek letter pi, if your
browser does not support this code, you will see forward slash pi rather
than the character.

/pi^e= (P_t+1-P_t )/P_t  

		=[(M_t+1-M_t)/M_t] - [(L_t+1-L_t )/L_t]  
     		= 10 - 15 
     		= -5


d)

because (Y_t+1-Y_t)/Y_t    = 0,  we know
that /pi^e = (M_t+1-M_t)/M_t 
So  /pi^e  = 0.15

L(Y,i) = 0.2(500) / (0.07 + 0.15)
            = 100/0.22    = 454.5

In equilibrium PxL(Y,i) = M   nominal money supply

So  Px454.5 = 250       => P = 250/454.5 = 0.55


Q2.

a) An increase in the liquidity of non-monetary assets will result in a
decrease in demand for money.  Since the supply of money remains fixed,
price level will have to increase in order to restore asset market
equilibrium.  The rise in P will cause interest rates to fall.  Since Y is
unchanged, ad fall in r will increase I and reduce C.   Final result: Y is
unchanged, r has decreased and P has increased.
(the diagram for this question is simply showing a decrease in the money
demand curve, reversion back to equilibrium M^d=M^s
and a drop in r.)


   
b) An increase in wealth has two paths in which it effects the asset
market:  1. An increase in wealth causes labour supply to be reduced,
which implies real wages rise, and a fall in total employment.  Because
employment is reduced, total future output is reduced which causes as
decrease in the demand for money.  Prices will rise to restore asset
market equilibrium.  This will generate an increase in the interest rate
which in turn will cause a decrease in the demand for money. 2. An
increase in wealth will also reduce savings which will cause an increase
in r.  The ultimate result is an increase in r, an increase in P and a
decrease in future output. (note: wealth may also have a direct impact on
money demand, causeing it to fall as richer people have access to better
payment techniques and have less need to hold on to money)


Q3.

a) Recall CA = S-I
So if foreign country has decreased willingness to save, then their
savings demand curve will shift left and up.  This will cause the world
equilibrium interest rate to rise.  If r^w rises, then demand
for savings in home will rise, and invesment demand in home will fall.
This implies that CA in home will rise.  See graph 3a (link at bottom)


b) Recall S = Y-C-G
So if there is a decrease in government purchases for the home country
(i.e. fall in G) then S will rise in the home country.  That is, the
savings curve for home country will shift right and down.  This shift will
induce a fall in the equilibrium world interest rate.  Home will have an
increased CA, while the foreign country will have a decreased CA.  See
graph 3b.


c) If Ricardian equivalence holds, a change in the foreign countrys taxes
will have no effect on their savings and no effect on their investment.
Therefore, this change will not effect the foreign countrys CA, nor will
it effect the world interest rate.  Because the change wont effect the
world interest rate, it also will not affect the home countrys savings,
investment or current account.   If Ricardian equivalence doesnt hold,
however, an increase in the foreign countrys tazes will cause an increase
in their savings (so the savings curve for foreign will shift down and to
the right).  Given this shift, there will be a downward pressure on the
world interest rate (supply of funds, internationally, will exceed
demand).  The new equilibrium world interest rate will be lower.  As the
equilibrium real interest rate is lower, savings at home will be decreased
and investment at home will be increased.  Therefore, since CA=S-I, the
current account at home will be decreased.  So in the end: real world
interest rate has decreased, savings at home has decreased, investment at
home has increased and CA at home has decreased.  See graph 3c.

d) A decrease in the foreign countrys future MPK will cause an decrease in
the capital demand in the foreign country.  This means that investment
demand in the foreign country decreases (the I curve shifts right and up)
The equilibrium world interest rate will be decreased.  This decreased
real world interest rate will cause an decrease in savings at home and an
increase in investment at home.  Since CA=S-I, this implies that the CA at
home will increase.  See graph 3d.



Q4.
a)
S^d = Y - C^d
   = Y - 300 - 0.3Y + 175r
   = 0.7(1000) - 300 + 175r
   = 400 + 175r

in Equlibrium:   S^d=I^d

so         400 + 175r = 500 - 250r
                    r=100/425 = 0.24


b)
S^d =   Y - C^d - G
   = 300 + 175 r

using equilibrium condition  S^d =  I^d, we arrive at:
	300 + 175r = 500 - 250r
so 	         r = 0.47

see graph 4b.



Q5.
a) The idea behind the twin deficits is that the government budget deficit
is thaought by some economists to be the primary cause of the current
account deficit.  Not all economists agree that this is true.

Theoretically, if the government budget deficit is increased there will be
a decrease in savings demand, and the current account will decrease (i.e.
increased current account deficit).  Here we must assume that the
increased budget deficit has the following effects:  first, that it
directly reduces savings demand and therefore the current account
(domestic residents reduce the amount they demand abroad at the real world
interest rate and also wish to consume a greater part of output at home),
second,  that the increase in the deficit is caused by a decrease in taxes
(where Ricardian equilvalence is assumed not to hold), and third,  that
tax treatment of investment is unchanged (so invesment demand is not
affected).  
The scenario would therefore be that government budget deficit rises
because T has been reduced.  If Ricardian equivalence does not hold, then
the reduction in T will cause an increase in C^d, which implies
S^d decreases.  Since CA = S^d-I^d, a decrease in S^d will cause a decrease in the CA,
all else being equal.
Note: if Ricardian equivalence does hold, then it will not effect savings
demand and therefore will not effect the current account.  


b) For country 1:

S^d 	= Y - C^d - G
	= Y - 430 - 0.5Y + 0.5T +150r^w - 100
  	= 320 + 150r^w	


CA 	= S^d-I^d
	= 320 + 150r^w -210 + 160r^w
	= 110 + 310r^w


For country 2:

S^d 	= Y - C^d - G
	= Y - 380 - 0.5Y + 0.5T +225r^w - 325
	= 420 + 225r^w	


CA 	= S^d-I^d
	= 420 + 225r^w -550 + 200r^w
	= -130 + 425r^w

The world equilibrium condition is     CA₁ = -CA₂
    			       110 + 310r^w = 130 - 425r^w 
				        r^w = 20/735   =  0.027

So, for country 1:

S^d = 320 + 150(0.027) = 324.05
I ^d = 210 - 160(0.027) = 205.68
C^d = 430 + 0.5(Y-T) - 150(0.027) = 1180 - 150(0.027) = 1175.95
CA = 110 + 310(0.027) = 118.4


for country 2:

S^d = 420 + 225(0.027) = 426.08
I ^d = 550 - 200(0.027) = 544.60
C^d = 380 + 0.5(Y-T) - 225(0.027) = 1255 - 225(0.027) = 1248.93
CA = -130 + 425(0.027) = -118.5



c) The new equilibrium values are below:


S^d 	= Y - C^d - G
	= Y - 430 - 0.5Y + 0.5T +150r^w - 150
	= 280 + 150r^w	


CA 	= S^d-I^d
	= 280 + 150r^w -210 + 160r^w
	= 70 + 310r^w

Recall: for country 2:

CA 	= -130 + 425r^w


The world equilibrium condition is     CA₁ = -CA₂
			        70 + 310r^w = 130 - 425r^w 
				        r^w = 60/735   =  0.082

So, for country 1:

S^d = 280 + 150(0.082) = 292.3
I ^d = 210 - 160(0.082) = 196.88
C^d = 430 + 0.5(Y-T) - 150(0..082)= 1182.3
CA = 70 + 310(0.082) = 95


for country 2:

S^d = 420 + 225(0.082) = 438.45
I ^d = 550 - 200(0.082) = 533.60
C^d = 380 + 0.5(Y-T) - 225(0.082) = 1255 - 225(0.082) = 1236.55
CA = -130 + 425(0.082) = -95

See diagram 5



 diagram 3a  now available HERE 
 diagram 3b now available HERE 
 diagram 3c now available HERE 
 diagram 3d now available HERE 
 diagram 5 now available HERE