# 14.02 QUIZ THREE CONFLICT SOLUTIONS, FALL 2000

## QUESTION 1:TRUE/ FALSE(5 points each)

a.            FALSE.  Again, the Phillips Curve, pt  - pe  =   – 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.

1. TRUE.  We know that in the medium/long run, p  =  g M -  g Y.  Since g Y is either zero (because Y= YN 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.
2. 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.
3. 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.
4. 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 = pe.  The Fisher equation gives us a relationship between inflation and interest rates: i = r + p e.  Finally, in the medium run, r = rn 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.

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 Ee > 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* +  (Ee – 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 Pe as an answer to this question.   While there is some potential economic justification for changing Pe, (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 Pe is not correct.  Pe 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 Pe 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 < Pe, people adapt (lower) their price expectations.  This shifts out (right) the AS curve, further lowering prices but raising output.  This means P < Pe again next period, and the AS curve continues to shift out until P = Pe and the economy is back at the natural rate of output.  When this happens, if Ee  > 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 Yn 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 Ee  > 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=Pe(90-180u)= Pe 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= Pe 90(1-2(1-Y/120))/60 =  Pe (3/2)(Y/60-1) = Pe(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 un=1/6.

g.       (4 points)  When Pe =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 un is 1/6 and u=1-Y/120, we know that Yn=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=Yn=100, the AS curve implies that P=(100-60)/10=4 (which is what we expect: P= Pe at Yn).  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 Yn, the new AS curve will cross the AD curve a point where Y<Yn 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.