* *

a. FALSE. Again, the Phillips Curve, p_{t} - p^{e }=
– a(u_{ t} - u_{ n)}, gives a relationship between
unemployment relative to the natural rate and inflation relative to expected
inflation. Since we know that expected
inflation will adapt and will equal actual inflation in the medium run,
unemployment must equal the natural rate in the medium run. Therefore, we cannot maintain as low a rate
of unemployment as we want – we will go back to the natural unemployment
rate. *If you answered with the above equation, plugged in lagged inflation
for expected inflation, and said the question was true, you missed the key
facet of this question: expectations of inflation change over time. Also, if you used lagged inflation, you
should have noted that keeping unemployment less than the natural rate would
lead to accelerating inflation, not just high inflation. *

- TRUE. We know that in the medium/long run, p
^{ }= g_{ M}- g_{ Y}. Since g_{ Y}is either zero (because Y= Y_{N}is the medium run) or small relative to g_{ M}(Dr. Caballero’s argument in class), to decrease inflation we must eventually have a decrease in the growth of the money supply. - FALSE. An increase in government spending shifts the IS curve and the AD curve initially. Note that the LM curve also moves: the AS curve is unaffected, so the shift out of the AD curve increases prices, reducing the real money supply, shifting the LM curve to the left.
- FALSE. While it is true that the usual reason for a downward sloping AD curve is no longer true (i.e. that the price level affects the real money supply and hence the interest rate, which affects demand through investment), there is a new channel: net exports. Higher prices will lower the real exchange rate, decreasing the demand for net exports. Thus higher prices are associated with lower equilibrium output in the goods/financial markets.
- FALSE. A monetary expansion does decrease nominal interest rates in the short run, but in the medium run nominal rates return to their original level (or rise, if the growth rate of money has increased.) In the short run, if M rises (or g(m) rises), the LM curve shifts out, moving along the IS curve and lowering interest rates. This shifts the AD curve to the right, moving along the AS curve and leading to lower prices and higher output. However, this is only the short run effect.

If there is a one-time level increase in M, you can see the medium run effects in the AS-AD diagram. Since the shock to AD raised Y above its natural level, it means prices were higher than expected prices. In the next period, expected prices rise, shifting the AS curve left. This raises prices, which shifts the LM curve back in. Eventually, we will return to the natural rate of output, and the LM will have moved back to its original level, with interest rates unchanged. This is why monetary policy is neutral in the medium run – only prices change.

If the growth of money has
risen in the medium run, the underlying logic is the same, but the explanation
is a bit different. We know from the
money market equilibrium condition that g(y) + p = g(m). We also know in the medium run that p = p^{e.} The Fisher equation gives us a relationship
between inflation and interest rates: i = r + p^{ e.} Finally, in the medium run, r = r_{n }because
we are at the natural rate of output.
Putting all this information together, we can back out the fact that
since g(m) has risen, inflation has risen, and therefore nominal interest rates
have risen in the medium run.

*To
get full credit, either one of these explanations is acceptable, but you must
have listed each of the steps given above.*

* *

**QUESTION 2: OPEN ECONOMY AS-AD**

** **

a. (5
points) The AS curve is an upward
sloping line in P-Y space; the AD curve is downward sloping. The reason the AS curve slopes upward is
because higher output implies lower unemployment. Lower unemployment means that workers have more bargaining power,
etc. and demand higher nominal wages.
Since the real wage is constant, higher nominal wages lead to higher
prices. The AD curve slopes downward
because it is a function of the real exchange rate, not real balances – because
this is a fixed exchange rate open economy, i = i*** **as long as exchange rates remain credible, so real balances are
effectively fixed. The real exchange
rate, EP*/P, is in the AD curve, however, and rising prices mean lower real
exchange rates, lower net exports, and lower output.

*In order to receive full credit on this question, you needed to give
complete explanations of the slopes, as above.
Simply saying that P and Y were positively or negatively related is not
an explanation. Also, using the real
balances channel (M/P) as the reason for the AD slope is not acceptable here –
this channel is NOT the mechanism behind the AD curve in the credible
fixed-exchange rate world.*

* *

b. (7
points) If people expect a devaluation,
this means that E^{e }> E – financial markets think that next
period’s exchange rate will be higher than today’s. Since this crisis is on the financial side of the economy, it
immediately affects the interest parity condition, i = i* + (E^{e }– E)/E. The second term on the right-hand side is
positive, so to keep arbitrage in balance, interest rates in the small (home)
country must rise. This happens
automatically as bondholders sell domestic currency and reduce the money
supply, or as the Central Bank contracts the money supply through OMOs.

Reducing M shifts the LM curve to the left. This shifts the AD curve to the left as well – it is a contractionary demand-side shock. This means prices fall and output falls. The fall in prices has two effects: first, it moves the LM curve a little back to the right, and second, it raises the real exchange rate (devalues the currency), raises NX, and shifts the IS curve to the right. These 2 short run effects dampen the immediate shock – negative price and output effects – of the currency crisis. Because this is a demand-side shock, the natural rate of output does not change.

*To get full credit on this question, you needed to mention all of the
points listed above. Many of you did
not read the question carefully, and assumed we were asking what an actual
devaluation would do to the country. An
actual (credible) devaluation) would raise E, and leave i = i*. This shifts out the IS and LM curves: the IS
moves because higher real exchange rates raise NX, and the LM moves out to
accommodate the goods market expansion and keep the interest rate fixed. This shifts the AD curve to the right,
raising prices and output, the opposite effect from the above case. Again, the price change mitigates the effect
a bit, pulling both the IS and LM back in.
If you answered the question correctly this way, we gave some partial
credit. Note that the question gives you
the fact that we are at the natural rate of output already, so a devaluation is
an odd policy to consider. In addition,
many students chose to change P ^{e} as an answer to this question. While there is some potential economic
justification for changing P^{e}, (a) you still should have changed the
expected exchange rate and (b) the justification is OUTSIDE our model, and thus
had to be logically explained before you received any credit. Just assuming an expected devaluation
changes P^{e }is not correct. P^{e
}is a supply side variable, and the expected exchange rate affects the
demand side of the economy. *

c. (4 points) The real exchange rate is (EP*)/P. From (b), you should have found that prices fell when expected
exchange rates changed. This means that
the real exchange rate rises – this effect will increase NX, and shift the IS
curve out. However, it does not move
the AD curve – P is on the axis in AS-AD, and changes in P do not shift the
curves. _{}

*To receive full credit, you needed to show the definition of the real
exchange rate. If you assumed (b) was
asking about an actual devaluation, then you should have found higher
prices. If you did, and therefore said
that the real exchange rate fell in (c), you still received some credit. Note that P ^{e }does not appear
anywhere in the real exchange rate. *

d. (5
points) In the medium run, the economy
continues to adjust after the currency crisis hits. The negative aggregate demand shock has lowered prices and
output. However, since in the next
period the economy has P < P^{e}, people adapt (lower) their price
expectations. This shifts out (right)
the AS curve, further lowering prices but raising output. This means P < P^{e }again next
period, and the AS curve continues to shift out until P = P^{e }and the
economy is back at the natural rate of output.
When this happens, if E^{e }>
E still, the country will have lower investment (from higher interest rates)
and higher NX (from a higher real exchange rate) that exactly offset each
other.

This process, however, is
time consuming, particularly because lowering the price level is more difficult
than raising it. This means the country
may spend a long time in a recession, with Y less than the natural rate. If they devalue, however, they will shift
the AD curve back up immediately, and can return to the original equilibrium
and natural rate of output. (See (b) for an explanation of a devaluation). Note also that it is difficult to hit Y_{n}
precisely with a devaluation, and that the j-curve means that NX may initially
fall with a devaluation. It is also
possible that the country will have to devalue in the short run if they have so
few reserves that they are unable to maintain i > i*, or if they dislike the
idea of lower investment due to higher interest rates. Finally, it is reasonable to assume that a
medium run equilibrium with E^{e }>
E is not sensible, and that expected exchange rates may shift over time.

*Note that if you answered (b) with an actual devaluation, this question
does not make sense! However, if you
talked about medium run dynamics – the changing price expectations that shift
the AS curve until you are back at the natural Y – and mentioned the
costs/benefits of the devaluation, you received some partial credit. You should
also note that, if an economy is in equilibrium to begin with and there are no
other shocks, a devaluation is inflationary.*

* *

* *

**QUESTION 3: AGGREGATE SUPPLY
AND DEMAND**

** **

a. (4 points) Using Y=C+I+G and all the information given one finds:

Y=(5/2)[72-(4/5)I]=180-2i

b. (4
points) To find money market equilibrium,
equate the *real* money supply to the *real* money demand, i.e. M/P=Y-i so
i=Y-60/P

c. (4 points) IS is downward sloping and LM is upward sloping in i-Y space; Y = 100.

d. (6 points) To find the AD curve, eliminate i in the goods market equilibrium equation using the money market equilibrium equation:

Y=180-2(Y-60/P) so Y=60+40/P

e. (6
points) Wage setting: W=P^{e}(90-180u)=
P^{e} 90(1-2u); for the price setting equation, you had to remember
that productivity is a component of the equation. This, and not the setup of the question, is what led a majority
of the students to find the algebra extremely messy: P=(1+ m)W/A=2W/120=W/60. To find the AS curve, eliminate W from the
price setting equation using the wage setting equation, first noting that
u=1-N/L and Y=AN=120N so u=1-Y/120.

P= P^{e}
90(1-2(1-Y/120))/60 = P^{e}
(3/2)(Y/60-1) = P^{e}(Y-60)/40.

To get full credit for explaining in words the sign of the slope, you had to give the economic reasoning for the sign of the slope, not the algebraic reasoning: higher output means lower unemployment, which gives workers more bargaining power and increases the nominal wage, which leads firms to raise prices.

f.
(4 points) The natural
rate of unemployment is the rate of unemployment consistent with prices and
expected prices being equal. Using the
price setting equation and the wage setting equation with unemployment in it:
60P=P90(1-2u), so u_{n}=1/6.

g. (4
points) When P^{e} =4, the AS
curve is P=(Y-60)/10 and the AD curve is Y=60+40/P. Rearranging the AD we find P=40/(Y-60). Eliminating P gives us: (Y-60)^{2}=400 so Y=80 or
40. From the AS curve, we see that Y=40
yields negative prices, hence the correct answer is Y=80. At Y=80, P=2.

h. (4
points) In the absence of intervention,
price expectations will adjust downwards (note that currently price is not
equal to expected price), causing the AS curve to shift down along the AD
curve. Prices will continue to fall
until output has risen to the natural level of output at which point prices and
expected prices are equal. Since u_{n}
is 1/6 and u=1-Y/120, we know that Y_{n}=100. The AD curve implies that at Y=100, P=1.

i. (8 points) The question was quite specific in that you must name two AD policies and two AS policies. Note that the economy is currently below the natural level of output, so expansionary policies should be used. AD policies include an increase in G, a decrease in T, and an increase in M. AS could include many different interventions into the labour market. In terms of the model, this could include policies that decrease z and m, although it should be noted that these change the natural level of output if they are permanent.

j.
(4 points) Given current price expectations, at Y=Y_{n}=100,
the AS curve implies that P=(100-60)/10=4 (which is what we expect: P= P^{e}
at Y_{n}). The IS curve tells us
that when Y=100, i can be found from 100=180-2i, i.e., i=40. Then from the LM curve, when Y=100, i=40,
and P=4: M/4=100-40 so M=240. M should
increase by 180. (There is an easier
way to come to the same conclusion: in (h) we found that at the natural rate
with M=60 we had P=1. Since the real
money supply is constant at the natural rate, if P=4 we need M/4=60, so M=240.)

k. (4
points) If people raise their price
expectations when M increases, the AS shifts up. Since the AD curve crosses the old AS curve at Y_{n}, the
new AS curve will cross the AD curve a point where Y<Y_{n} and
P>4.

l. (2 points) We now have many models that depend on expectations: of prices, inflation, and exchange rates. Your answer should incorporate the fact that the way people form these expectations plays a crucial role in determining the output and price levels in the economy. Any policy the government considers must take these expectations into account.

* *