At 11:38 AM 1/11/2005, you wrote:

Professor here are my 2 questions:

1) When we went over the paradox of thrift, we said that private saving + government saving equals
investment. You then went on to write the equateion :

-Co + (1-C1)(Y-T) + T(bar) + G(bar) = I(bar). My question is how you derived this equation. I
understand the T(bar) G(bar) and I(bar) parts but im not quite sure where the first part came from.

Answer:  The national income identity is Y=C+I+G, or, after rearranging, Y-T-C = I + G-T, which says that private saving, Y-T-C, must equal borrowing by business to finance investment plus borrowing by the government. This must always be true, whether in equilibrium or not. In equilibrium, the national income identity holds with all variables equal to their planned values. Private saving, given our consumption function, is -c0 + (1-c1)*(Y-T(bar)), where T(bar) is the assumed value of taxes. Also, planned investment is I(bar) and planned government spending is G(bar). This is where the equation you cite in your question comes from. That equation only holds in equilibrium, because I is equal to I(bar) only in equilibrium. Outside of equilibrium, I is I(bar) plus unintended inventory accumulation.

2) When we talked about  the financial markets, we talked about what would happen if consumption
went from 80 to 75. And I think what happens is that when C goes down by 5, that means people are
buying 5 less shirts so that means firms have left over inventory of 5, which means that investment
goes up by 5, so to finance this extra investment they have to borrow this amount from the
financial markets, but this all works out because since C goes down by 5, households are depositing
an extra 5 in the financial markets?

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Question:  Hi,

I do not understand the accelerator effect.  Could you please explain it in detail?

Hi:

In our discussion of the IS-LM model, we made planned investment a negative function of the interest rate:
I = I(bar) - b*i,
where i is the interest rate. I spent some time motivating this negative relationship.

In class, I discussed the fact that some people think investment is usefully thought of as being a function of aggregate economic activity, Y, too (see, for example, the book, on page 106). Why might investment be a function of the general level of economic activity? To see why, it is useful to go back to my discussion of why investment is a negative function of the interest rate. Each potential investment project has associated with it an 'internal rate of return'....the amount of extra revenues the investment project is expected to generate in the future, per dollar spent today. An example I gave in class was that of a restaurant contemplating investing in a new pizza oven. That oven cost some amount of dollars today (say \$100), and was expected to produce an addition to revenues in the future of (say) \$5. In this case, the internal rate of return is 5%. The pizza oven will be invested in if the interest rate is 5% or less. But, think about those extra \$5 in revenues the oven is expected to produce. Obviously, that expectation incorporates some assumption about how many people out there will come in to buy pizzas. If more than expected come in for pizzas, then the internal rate of return could be higher, as the restaurant sells more pizza. If fewer customers show up, then the internal rate of return could be lower. The idea is that the demand a restaurant (or any other firm) can expect is related to what total economic activity, Y, is. When current Y is high, individual firms deduce that a lot of demand will show up at their doorstep, and this leads them to revise upward their assessment of the internal rate of return on investment projects. The result is a right-shift in the investment demand equation (the down-sloped graph with i on the vertical axis and investment on the horizontal). Similarly, when Y is low investment demand shifts left. This is summarized in the equation,

I = I(bar) + b1*Y - b2*i, b1, b2>0.

So what does all this have to do with an accelerator? To see this, notice that with b2>0, there are now two things in aggregate planned spending that respond positively to income: household consumption and business investment. That is, the slope of planned spending is now c1+b1 (here, c1 is the marginal propensity to consume). The Keynesian Cross multiplier is just

1/(1-slope of ZZ curve) = 1/(1-c1-b1).

Notice that this multiplier is BIGGER than the Keynesian Cross multiplier. For example, if c1=.75 and b1=.1 then the multiplier is not the number 4 that it is when b1=0, but a bigger number, 1/(1-.85)=6.67. So, with b1>0 equilibrium output rises by more (potentially, a lot more if b1 is big) in the Keynesian Cross model. In addition, since the Keynesian Cross multiplier is the amount by which the IS curve shifts right in the IS-LM model, b1>0 also increases the multiplier in that model.

The fact that the effect of an exogenous shock on equilibrium output is bigger when b1 > 0 is why it is said that setting b1 > 0 in the investment equation introduces an 'accelerator' effect into the model. For example, if there is a rise in G of \$1, the rise in equilibrium output with b1 = 0 is \$4. When there is an accelerator effect on investment, then the rise in equilibrium output is \$6.6. Setting b1 > 0 in effect added some juice to the multiplier.

What's the intuition for all this? It's just a continuation of the intuition underlying the multiplier itself. That is, when there is an exogenous shift up in spending (say a rise in G), then output increases by more than just that increase in spending. The reason is that the initial increase in spending triggers additional increases in spending by households (due to c1 > 0) and now, by firms. This extra spending by firms acts in the same way on the economy as if households simply had a higher marginal propensity to consume.
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Question:

At 08:35 PM 1/22/2005, you wrote:

Hey Professor,

I just had a quick question.  Why does an increase in taxes shift IS curve to the left?  I would think that with an increase, govt spending would increase to offset the decrease in consumer spending.  Therefore keeping it the same.  Thanks.

Hi:

In our model, government spending is a exogenous variable. This means that it does not shift, unless we specifically assume it does. So, when you say that taxes go up and you say nothing else, this implicitly says that none of the other exogenous variables (including G) moved.

You are referring to what is perhaps a more interesting model, a model that is different that the one we've discussed in class. In your model, G is a function of T. In that model, if you raise T, the contraction would be less severe, as you say, because the increase in G itself exerts a positive effect on output. Indeed, the contraction could actually turn into an expansion. For example, if when T rises by \$1, G rises by the same amount, then we get the balanced budget multiplier: in the KC model, equilibrium output would RISE by \$1 and in the IS-LM model the IS curve would shift RIGHT by \$1.

Larry

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11:54 AM 2/13/2005, my answers immediately follow the questions in this email:

Hi Professor Christiano,

I have some questions about the material I am studying for the midterm.

1) In the globalization graph, why does the decrease of "z", thus the decrease of workers'
bargaining power, lead to lower unemployment? I understand the graph, but not the intuition.

In our model, in the medium run, the outcome of worker bargaining must be consistent with the real wage implied by firms' price setting equation. The only endogenous variable, in the medium run, in the bargaining relationship that can accomplish this is the unemployment rate (other variables appear in z, but they are exogenous variables). A higher unemployment rate is associated with a worse outcome (i.e., a lower real wage) for workers. A lower unemployment rate is associated with a better outcome. So, if something happens (i.e., a shift in some exogenous variable in z) which reduces the bargaining power of workers, but does not change the price setting equation of firms, then the unemployment rate consistent with the unchanged real wage is lower.

2) In the oil shock example when government intervened and increased M to push the AD up, does this
push in AD occur after the first upward shift of the AS curve, or after the second upward shift of
the AS curve?

Most of the experiments that we have done involve a shift in just one exogenous variable. In the oil shock example, two exogenous variables were shifted. The whole analysis was done simultaneously, though perhaps with a small delay in M, because the move in M was viewed as a reaction to the recession produced by the oil shock. Still, in my analysis, the short run equilibrium involves a right-shift in the AD curve (due to the increase in M) as well as a left-shift in the AS curve (due to the oil shock). The short run equilibrium occurs at the intersection of these two new curves (holding Pe fixed). The medium run equilibrium occurs at the intersection of the AD curve (this does not shift any further after the short run) and the new Yn.

3) Is there some kind of rule about AD and AS moving up, down only, or left, right only? Like how
the LM curve moves up and down, and the IS curve moves left and right?

If the economy finds itself above the AS curve, we can expect the price level to rise. If below, P falls. These things happen fairly slowly because not everyone is renegotiating their wage at every moment. In many cases, wage negotiations only come up once a year or even less often. Similarly, price-setting decisions are not revised continuously by all firms. So, what we say is that when the economy finds itself off the AS curve, forces come into play that slowly move the price level to that curve. Analyses of the data suggest that P may respond more slowly to being off the AS curve than Y responds to being off the AD curve. But, the evidence is not particularly sharp on this. So, I'll just maintain that they both move slowly. In any case, note that how fast P, Y, i move when in disequilibrium has nothing to do with where the short run and medium equilibria are.

4) Is stagflation's definition: Price increases when output decreases? In this case, stagflation
doesn't only occur when government increases M in the oil shock, correct? Because with or without
government increasing M, an oil shock is can always decrease output and increase price?

The word stagflation means P going up when output falls (stag - stagnation, flation - inflation). This received a special word in the 1970s because observers at the time thought it was quite unusual.

5) Whenever there's a change in the AS relation, we find the new Yn' and then find the point where
Yn' intersects P, where P is Pe=P in the old MR equlibirum. And then we draw the new AS curve
through this point. Why does the new AS curve have to be on this point? What is the signficance of
the intersection between Yn' and P when Pe=P?

In algebraic terms, the AS curve is:

P = (1+mu)*Pe*F(1-Y/L,z),   (*)

where mu is the markup, Pe is the expected price level, Y is aggregate output, L is the labor force and z is a 'catch all' for other exogenous variables that impact on the labor market (examples we have discussed include globalization and the quality of the unemployment system). Here, the unemployment rate, u, corresponds to 1-Y/L, under the assumption that Y=N, where N is aggregate employment (when we discuss the effects of increased labor productivity, we set Y=aN and consider the effects of a change in a). Because F is decreasing in u (make sure you understand why this is so), it follows that F is increasing in Y. This is why the AS curve is positively sloped. Note that the precise location of the AS curve depends on the value of Pe as well as on the exogenous variables, mu and z.

We define the natural rate of unemployment, un, as the unemployment rate that occurs when the expected (i.e., Pe) and actual (i.e., P) price levels coincide. That is to say, un is defined by 1=(1+mu)*F(un,z). We define the natural rate of output, Yn, as the level of output that occurs when the actual and expected price levels coincide, i.e., 1=(1+mu)*F(1-Yn/L,z).

From the last relationship, you can see that if you take the AS curve and evaluate it at P = Pe, you get:

Pe = (1+mu)*Pe*F(1-Yn/L,z).

So, when you graph the AS curve and you look at the point on the vertical axis were the actual price level equals Pe, then the associated value of Y is Yn. This is so, because this is how we defined Yn.

Suppose now that we shift the AS curve for some reason, say by shifting z, or changing the value of mu. Then, the new value of Yn, call it Yn', solves the new equation: 1=(1+mu')*F(1-Yn'/L,z'). So, when you graph the new AS curve (holding Pe fixed at its old value), then when you look up Pe on the vertical axis, you find that the level of output it is associated with is Yn'. Again, this is because of the way Yn' is defined.

6) About the analysis of "a" increasing in u=1-Y/aL, I understand why u does not change in the W/P
vs. u graph, but I don't understand why AS(pe) shifts down. I am looking at the AS relation
function and I see that it is P=(1+mu) Pe*F (1-Y/aL, z). From what I understand, Y and a increase
by the same amount in order to keep u constant in u=1-Y/aL. Wouldn't this mean the proportion Y/aL
stays the same in the AS relation equation as well? Then wouldn't this mean the AS would stay
constant and not move down?

Let's first make sure we understand why the natural rate of unemployment, un, does not change with the change in a. The natural rate of unemployment solves 1=(1+mu)*F(un,z). This is an equation that does not involve a and this is why un does not respond to a. However, Yn is the solution to un=1-Yn/(a*L). This equation does involve a, and so Yn does change with a. Yn increases.

Consider the version of the AS curve that takes into account a. Appropriately modifying the logic that resulted in (*) above, we find that the AS curve is:

P = (1+mu)*Pe*F(1-Y/(aL),z).

From this, you can see that when a goes up, for given Y, Y/(aL) goes down and 1-Y/(aL) goes up. Because F is decreasing in u, it follows that an increase in a results in a lower value of  F(1-Y/(aL),z) for each value of Y. That is to say, the AS curve shifts down. The intuition for this is simple. At a given level of output, if a is higher, then employment is lower and so unemployment is higher. But, the higher unemployment reduces the bargaining power of workers and their wage outcomes deteriorate.

The preceding logic explains why the AS curve shifts DOWN, when we consider the vertical direction of shift (i.e., we hold fixed Y). It is also useful for us to think about the horizontal direction of shift. We can see this by considering the point on the vertical axis that corresponds to Pe, the expected price level that was used in the construction of the AS curve. For the reasons discussed above, this value of the price level is associated with the natural rate of output. I argued above that the natural rate of output increases with an increase in a (let Yn denote the old natural rate of output, and Yn'>Yn the new one). This means that if you draw a horizontal line emanating from the vertical axis at P=Pe, the new AS curve intersects that line at the point Yn' > Yn. That is to say, the AS curve shifts to the RIGHT.

In your question you note that Y/(aL) in the medium run remains unchanged with the change in a, and so perhaps the AS curve should not shift. You are right that Y/(aL) does not change in the medium run. However, this does imply a change in the AS curve, because for Y/(aL) not to change when a changes implies that Y changes. And, it is Y that appears on the horizontal axis.

7) I wrote down in my notes that AS shifts to the right because Y increases as a increases (but I
am still confused about what exactly moves AS, is it what I mentioned in #6 of is it just the Y
increasing?) If the increase in Y is what moves the AS curve outward, does this move the AS curve
to AS', where short run eq. is, or does this move the AS curve to AS'', where medium run is? If the
increase in Y is only responsible for one of these AS shifts, what is responsible for the other one?

Most of this was answered (I hope!) in the previous question. But, here is one thing to keep in mind. The movement of an object (like a curve) in a two-dimensional space is complicated. You can describe it as a move in the horizontal direction, the vertical direction or any combination of the two. In practice, it is convenient for us to think of movements in the vertical or horizontal direction. For example, it is easiest to think of the shift in the IS curve that occurs with an exogenous shock in the horizontal direction. That's because this corresponds to the Keynesian Cross multiplier, and we've spent a lot of time talking about this. In principle, you could think of the SAME shift in the IS curve in the vertical direction. With the LM curve, I find it most convenient to think of its response to an exogenous shock (e.g., to money supply or demand) in terms of the vertical dimension of the shift...i.e., the move in the interest rate. This seems natural when you think of the money demand/money supply graph that underlies the LM curve. However, you can also think of a shift in the LM curve in the vertical dimension.

Thank you so much for your time and help; I really appreciate it.

I hope this helps, Larry

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1. Why is there 100% Crowding out in the Medium Run? (I think that we used the scenario of decreasing government spending in class).

The medium run occurs as Pe moves to equality with P. The fact that the economy is on the AS curve implies that output is at its natural rate (for a discussion, see my response to question #5 in the 11:54 AM 2/13/2005 email). That is, Y = Yn (*). The fact that the economy is on the AD curve implies that the goods market (also the financial markets) is in equilibrium. That is, Y = Cp + Ip + Gp (**), where Cp, Ip and Gp are planned consumption, investment and government consumption, respectively. Here, Gp is exogenous in our model, and equal to G(bar). Putting (*) and (**) together, we conclude that Yn = Cp + Ip + Gp. Since Yn is the same in the new and old equilibria, Cp must also be the same in the new and old equilibria. But, Gp is higher in the new equilibrium, so Ip must be lower by the same amount. That is, in the medium run there is complete crowding out.

1. For globalization, I don’t quite understand why would F(u,z) go down? I know it affects z, but how do we know if it goes up or down? Does F(u,z) generally stands for the bargaining power of workers, so globalization would weaken the bargaining power and thus causing F(u,z) to shift downward?

You are exactly right. Globalization makes F(u,z) move down. Workers can't be so demanding when the number of workers they compete with goes up with globalization.

1. When a shock occurs, sometimes Yn changes and sometimes it doesn’t in the Medium Run. Is it true that the only time there will be a new Yn after the shock is if markup, labor productivity or natural rate of unemployment change?

Recall the equation that defines Yn: It is 1=(1+mu)*F(1-Yn/(aL),z) (for explanation, seem my response to the 11:54 AM 2/13/2005 email). If the variables we have lumped into z (i.e., unemployment insurance, globalization) or mu, or a, or L does not change, then Yn cannot change.

I hope this helps, Larry

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2/13/2005 email:

Question: In my notes, i have that the natural rate of unemployment is high in Europe b/c of high unemplooyment benefits. However, we have a graph that says the better benefits came before the increase in Un. I forgot the explanation for this. Could you possibly refresh my memory.

Answer: In class, in response to a very insightful question, I described the so-called 'ticking time bomb' theory of how high unemployment benefits in Europe may account for the high unemployment observed starting in the late 1970s. This theory is due to some work by Ljungqvist and Sargent.

The 'problem' with any theory that relates the high quality unemployment benefits in Europe to the higher unemployment rate starting in the late 1970s is that the unemployment system in most cases was instituted shortly after WWII. For decades afterward, unemployment in Europe was actually lower than what it was in the US. If the high quality unemployment system is the cause of the high unemployment in the 1970s, then why did the system take so long to have this effect?

One answer is that the system put in place after WWII was like a ticking time bomb. It needed the right circumstances to have its effect on the unemployment rate. The key feature of the system is the 'replacement ratio'. This is the fraction of the wages you earned in your previous job that the system replaces when you become unemployed. For example, if the replacement ratio is 70 percent, then when you lose your job, the unemployment benefits give you 70 percent of the wage you had before you lost your job.

The idea is that the nature of job turnover in the first few decades after WWII was very different from what it was starting in the late 1970s. The idea is that in the early period, people who lost their jobs typically could find another one (after some search) at roughly the same wage rate (e.g., you quit your job working at one gas station, and moved to another one across town where the pay was similar). Since the replacement ratio typically put you at a lower income than before you lost your job, unemployment was not particularly attractive. Then, in the 1970s job turnover increasingly was associated with people losing their jobs because of technological change. People who lose their jobs under these circumstances often find that their basic job skills have become redundant (examples are secretaries when the pc came in and people started doing their own typing). As a result, their next best job may involve a very substantial drop in wage. Under these circumstances, the replacement ratio in the unemployment system can look a lot more attractive. This is one (not uncontroversial) explanation of how the European unemployment system caused unemployment to rise in the 1970s.

Best,
Larry

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2/13/2005

Quick question about Investment. Say there is a decrease in Government spending and the AD curve shifts to the left and decreases price level and output, what happens to Investment in the short run and medium run? I figure it would be unclear because there is a decrease in interest rates as well as output.

Answer: You are right. When we include the accelerator effect on investment, then a fall in output produces a fall in investment. So, when there is a cut in government consumption and the interest rate rises and output falls, it is unclear what the net effect on investment is in the short run. Without the accelerator effect (i.e., with b=0) investment unambiguously rises because of the fall in i. However, with a big enough accelerator effect (i.e., with b positive and big enough to produce a really big KC multiplier) the fall in output could be so big that investment actually drops. So, in the short run the impact of a cut in G on I depends on the magnitude of the accelerator effect. In the medium run the accelerator effect is irrelevant because there is no impact of G on the natural rate of output. In the medium run I rises by the same amount as G falls.

Larry

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2/15/2005

Question: What is the fatal flaw in returning to the gold standard?  I'm not clear how you said it in class.  Thanks.

Answer: The phenomenon of interest is that after 1919 Britain dropped below the US and stayed there for many decades. This extends well beyond any notion of the short run. According to the AD-AS model, a monetary policy action (like return to the Gold Standard) can only have an effect in the short run, not the medium run.

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2/15/2005

Question:

In lecture on Feb. 2nd, at the end of class you were finishing the analysis of Governent spending
increasing leading to a decrease in unemployment, an increase in Money Supply, better wages, higher
Price...why does the higher G lead to a lower u? Why does Money supply increase?

I don't have my lecture notes here, so I'm not sure exactly what I did on February 2. However, the analysis you describe involves a movement in two variables that we have treated as exogenous, G and the Money supply. It's not until recently that I have talked about the effects of two exogenous shocks simultaneously. In my answer I'm going to assume that you meant Money demand, not money supply. Money demand is endogenous because it depends on three endogenous variables, the interest rate, output and the price level.

In our model (the AD-AS model), an increase in G shows up as a shift right in the AD curve. That's because at a given price level, a higher level of income is associated with equilibrium in the goods and financial markets. To see this, consider the IS-LM diagram. An increase in G shifts the IS curve right by the amount of the KC multiplier, and this leads to an increase in output that is somewhat less (because of the rise in the interest rate) than what is predicted by the KC multiplier. That is, the IS-LM multiplier is less than the KC multiplier. This analysis implies that the AD curve shifts right by the amount predicted by the IS-LM multiplier. So, the short run equilibrium, which occurs at the intersection of the AS curve and the new AD curve involves a higher price level and a higher level of output. In the medium run, output is back to where it was before (assuming, as we typically do, that we began in a long-run equilibrium), though the price level is now higher. The way this works is that as the short run turns into the long run, people notice that the price level is higher than the original value of Pe, and so Pe starts to rise, shifting the AS curve to the left. It stops shifting left when it intersects the vertical line above Yn at the point where the AD curve intersects that line. We are now in medium run equilibrium and the raw technical part of the analysis is complete.

The AD curve and the AS curve summarize a lot of economics in a concise way. Let's now 'unwrap' all that economics. What would an observer in this economy see? The initial rise in G would show up as an unintended drop in inventories of firms. The rise in G would start hitting actual production when those firms start to order more goods from producers and producers increase output and employment. In the AD-AS diagram, the economy is starting to move right from its original medium run equilibrium point (this is a point that is no longer an equilibrium, because the AD curve is now sitting to the right). Similarly, in the IS-LM diagram, the economy is moving from its initial position to the right (the original point is not an equilibrium because the IS curve shifted to the right). The expansion in output has an impact in two places: financial markets and labor markets. In financial markets, the rise in output leads to an increase in the demand for money, because the number of transactions is increasing. People in financial markets begin to react by trying to sell bonds. This drives their price up and the interest rate down. In terms of the IS-LM diagram, the economy rises to the LM curve to clear the financial market (in terms of the money demand equation - this is summarized in the LM equation - with real balances on the horizontal axis and the nominal interest rate on the vertical, the demand for money is shifting right with the increase in Y).  The expansion in output also impacts on the labor market, in the supply side of the economy. This is because the unemployment rate drops as employment is increased. The drop in unemployment increases the bargaining power of workers and so their wages rise. The rise in wages, because they reduce costs, leads firms to post higher prices. This connection from higher output to a higher price level is summarized in the upward-sloping AS curve. The increase in output and the increase in price level finally take us to the short run equilibrium point. There, the interest rate is higher, unemployment is lower and consumption is higher (this is because consumption depends on Y). We can't say for sure what happened to investment unless there is no accelerator effect (i.e., q=0). When q=0, we know investment is lower because of the higher interest rate. when q>0 investment might be higher, if the accelerator effect dominates the interest rate effect.

Question:

Another question I have is from my notes on globalization (02/09), I think I have a decent
understanding of globalization now, but I was confused as to what you meant in class when you said,
monopoly of firms leads natural rate of unemployment to decrease to nat. rate of unemp. prime...and
then monopoly of workers leads nat. rate of unemp. to shift to nat. rate of unemp. double
prime...what is the monopoly of workers and firms? I understand the graph and why in one case nat.
rate of unemp. would move to one point depending on what forces are affecting it, but I was
confused with the meaning of monopoly of firms and workers.

My answer is a little long, because I want to put it into proper context.

In class, I argued that globalization might show up in three places: (i) it would hurt workers' bargaining power relative to firms, because globalization expands the set of workers that the firm could potentially hire....as a result, a break-down in the bargaining process hurts the worker doing the bargaining more than it hurts the firm, since the firm can now more easily find another worker (say, by moving to Mexico, or India). In this sense, because workers now have to compete with more workers, globalization reduces the monopoly power of workers. We modeled this effect of globalization as a shift down in the F function. (ii) globalization also cuts into the monopoly power of firms. They now have to think twice about posting high prices. If they set prices too high it is more likely after globalization that they would lose their customers to another firm. We modeled this effect of globablization by a decrease in mu. (iii) globablization is also likely to increase the efficiency of firms. This would happen in two ways. First, inefficient firms are more likely to disappear with globalization because the competition is greater. Second, firms that do survive have a strong incentive to become more efficient - aggressively adopt more advanced technologies, maintain better discipline and accountability in their work force, etc. - with the increased competition from globalization. We captured this by thinking of an increase in a. (In class, I argued that an increase in a could also occur in the absence of globalization, when new technical discovers occur. Similarly, mu and F could shift for reasons other than globalization too.)

I hope this helps, Larry

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2/15/2005

Question:

Hello Professor,

I had a quick question about shocks to the AS curve.  I understand graphically what happens when a or L change, however, I'm having trouble understanding why unemployment doesn't change.  Un solves the equation 1=(1+mu)*F(un,z) and thus b/c a and L aren't in that equation, unemployment can't change.  But isn't Un also given by Un=1-Yn/(aL)?   Would it make more sense to say that b/c a or L go up, we are given a new natural rate of output and therefore, Un does goes up in the short run, due to aL increasing more than Y.  Not until the new MR, in which Yn has increased proportionally to aL, does Un return to it's previous MR value.  Is that correct?  Sorry for the repetition, I know you went over this with other students already, I was just having problems understanding exactly why unemployment would remain unchanged.
I was also wondering if questions 1 and 2 from your fall '97 midterm #2 were relevant.  You speak of NAIRU and I don't remember doing that as well as a time consistency problem which seems to be from Ch 8.

In terms of coverage of the exam, it will only cover material up until last Wednesday. We did not do time consistency or NAIRU. So, they aren't covered.

On the connection between un and a, L. We have two equations for output and unemployment in the medium run: (i) 1=(1+mu)*F(un,z) and (ii) un=1-Yn/(aL).  An analogy might be helpful. Consider the following two equations: (I) x=8 and (II) q*x+y = 10. Note that equation (I) determines x and that q has no impact on the value of x. Equation (II) takes the value of x determined by (I) as given and (II) then determines y. Equation (I) corresponds to (i) and equation (II) corresponds to (ii). This is why un is independent of a or L: un is determined by (i) and a and L just don’t appear there. (Actually, it would be odd for a or L to determine the unemployment rate. Both a and L have steadily increased over the past 200 years. We haven’t observed any corresponding trend in the unemployment rate.)

You suggest that un goes up in the short run. But, by definition, un is a medium run object. It's where the actual unemployment rate moves to in MR because of the nature of the assumptions we made about disequilibrium dynamics. After a change in a or L, there is no change in un (just like the value of x in the example doesn't change with a change in the value of q). What does change in the short run is the unemployment rate, u.
Larry

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2/15/2005

Question:

Say there is an increase in L and the AS curve shifts to the right, what happens to unemployment in the short and mediun run? I remember being told that it was the same in the MR and it increases in the short run, and that was because in the medium run the new and old natural rates of out are the same. I dont understand why this is so.

When in the first sentence you said that the AS curve shifts to the right, implicitly you were saying that the natural rate of output increases. But, in the second sentence you suggest that the natural rate of output may be the same in the initial and final medium run equilibria, without noting the contradiction.

Be careful to understand why it is that an increase in L shifts the AS curve to the right. It is the fact that the natural rate of output increases. In fact, if you consider the point on the horizontal axis where P = Pe, then the horizontal shift at that point in the AD curve corresponds exactly to the increase in Yn. To see this, look at the equation that corresponds to the AS curve:

P = Pe*(1+mu)*F(1-Y/(aL),z)

When P=Pe, then this equation reduces to

1 = (1+mu)*F(1-Y/(aL),z).

The value of Y that solves this equation is what we call the natural rate of output, Yn.

To see what happens to unemployment in the short run, shift the AS curve to the right, and note that because the AD curve is downward-sloping (recall the economic reasoning for this), output in short run equilibrium is less than the new natural rate of output. But, output would have to rise at least as much as the natural rate of output rises, in order to keep unemployment at the natural rate. Since in the short run output necessarily rises by less, if follows that unemployment rises in the short run.