When I get a question from a student, I'll post the answer here.

Question: I'm confused. How do I get the bond demand for a given income? And is wealth ever used in any of the equations?

Answer: The household's problem is to take its given financial wealth, W, and allocate it between M and B. In class we discussed the transactions demand for money, according to which Md (money demand) is a function of Y, P and i. We wrote that function like this, Md=P*Y*L(i). This implies that the demand for bonds, Bd, is Bd=W-P*Y*L(i). Wealth is never used in any of our equations. We only include Y and T in the equation that determines consumption. Certainly, it would make sense to also include W in this equation. However, that should not change our analysis of the short and medium run. That's because W does not change much over that sort of horizon. So, there's no point in including it literally. It also does not appear in the investment equation, and that probably does make sense.

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Question: I know that wealth is supposed to be fixed at any given time. But if there is an increase in money demand, then does that cause wealth to go up since money demand plus bond demand equals wealth? I would figure that an increase in income would lead to an increase in wealth, which is why I don't quite understand what the book means when it says that wealth does not change. Please explain! Thank you!

Answer: when money demand goes up, then people seek to hold a larger fraction of their wealth in the form of money balances. A rise in money demand implies an equal fall in bond demand, since the two must add up to wealth, and that does not change much over the short and medium run. An increase in income will lead eventually an increase in wealth, to the extent that the increase leads to more saving. However, this takes time. It's like when you increase the flow of water into a bath tub. The water level doesn't jump immediately. You have to wait before you see significant effects.

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Question .... I know that for drop in spending, the change in y is change in g/(1-c1) as opposed to [c1*change in t]/(1-c1) for tax increase, but I wasn't clear on what the implications are..

Answer: the implications aren't particularly earth shattering. It's just that a $1 drop in G has a bigger effect than a $1 dollar rise in T. The reason is that T does not enter the aggregate demand curve directly. It has to go via its impact on planned consumption.

Question: I went over my class notes of today and have a question in regards of the LM-curve. It says that Money demand goes up, and the LM-curve shifts up. (interest goes up).

my question is why is LM moving up? Does that mean that the shift in the LM curve is due to increase in the interest rate. and from your previous notes you have said that LM curve shifts up due to cut in MS.

Answer: The LM curve is the (i,Y) combinations where Ms=Md. When L(i) in the money demand curve shifts up (is larger for each i), then a higher interest rate is needed to clear the money market for each value of Y. This is equivalent to the statement that the LM curve shifts up.

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**Question: **A reduction in Ms shifts the LM curve up. This is because, for fixed Y, with
a cut in Ms a higher i is needed to clear the money market. I have a question on
the equilibrium in the labor market in the short run. In class, you said that as
output increases, prices increase, which is why the total change in output in
the AS/AD model is less than in the IS/LM model for a demand shift (like an
increase in G). I have in my notes that prices increase because wages
increased due to the fall in unemployment. But how can that be true in the short
run? Aren't wages fixed, since they are negotiated for a certain period of time?
And if the production function is Y=N, rising marginal costs of production can't
be increasing prices as Y increases, so I don't understand why prices change in
the short run. Also, is there a way to show the short run on the WS/PS graph? Is
it the same as the medium run, but u is just not the natural rate of
unemployment? Thanks for your help!

**Answer**: Individual wages might well be fixed over a period of time,
like a year. However, they are not all negotiated simultaneously. Instead, there
are some being renegotiated all the time, and for different periods of time. The
ones being negotiated during any period will reflect the effects of changes in
labor market conditions like the unemployment rate. In this way, wages as a
whole are only affected slowly by changes in labor market conditions, with a
small number of wages being affected initially, and more being affected over
time as more wages come up for renegotiation.

The marginal cost of production is the marginal cost of a unit of labor (the wage) divided by the marginal product of labor (unity). So, marginal cost is not constant because the wage is not constant.

To see this better, here is a simple algebraic argument. The marginal cost of labor, n, can be written dC/dn, dC being the change in cost and dn being the change in labor. The marginal product of labor is dY/dn, where dY means the change in output and dn is the change in labor. Then, take the ratio of marginal cost of labor to the marginal product of labor and you see the dn's cancel, leaving dC/dY, i.e., the change in cost associated with the change in output. This is the marginal cost of production.

Now, the basic idea is that firms set price as a fixed markup over marginal cost. As output rises, say because AD shifts right, workers successfully negotiate a higher wage, and this drives up marginal costs, with is what induces firms to post a higher price. That's the story in the AS curve.

The short run applies to a period as long as a few years. So, the process by which wages rise with a rise in output is not something that happens overnight. In class, we made the assumption that if the economy finds itself off the AS curve (say because it just shifted), then the price level will move in a vertical directly SLOWLY until it hits the AS curve.

You could incorporate these things into the WS/PS graph. Keep the pricing curve unchanged. Here is what you do for the wage-setting curve. That curve is W=Pe*F(1-Y/L,z). Divide both sides by P, to get W/P = (Pe/P)*F(1-Y/L,z). In the medium run, the Pe/P term is just unity and so it disappears. But, in the short run it is not unity, and so deviations between Pe and P shift the curve.

**Questions: **

1. when you say something is neutral in the MR, does the word "neutral" encompass Y, i, both, or does the variables considered need to be explicitly stated for us to know? what is the difference between "money is neutral in MR" and "monetary policy is neutral in MR?" if in the case of fiscal policy, for example the effects of tax increase in the MR, the economy returns to the original level of output Yn, but P and i are lower than before the shock, is fiscal policy simply neutral in the MR, or is it neutral on Y, or is it money that's neutral?

2. to my understanding, the economy takes on a new natural rate of unemployment with a change in z or m. if there is a change in u itself (for example a change in the labor force because the government changed the method of measuring unemployment), does WS shift in the standard way (ie right or left), or is it a steepness change?

3. what types of changes would induce a change in the expected price, would an announcement of a monetary policy? how does the change in expected price appear in the AD-AS model, as an AS shift? does it appear in the IS-LM as a shift in LM (because the higher expected price posts higher wages, and thus higher P, so a higher M/P) - is this correct? is the y-axis on the AD-AS model expected price??

**Answers:**

**Question 1**

**The word, 'neutral', suggests that something has NO effect. Literally,
that does not apply in the context of the AD-AS model. The adjective is used,
nevertheless, because some shocks have a very small effect in the medium run (MR).**

**In the case of money, we find in the AD-AS model that money has no effect
on consumption, investment employment output in the MR. It does have an effect
on the level of prices. Although there is some effect (namely, on the price
leve), people nevertheless characterize this feature of the model by saying
that 'money is neutral'.**

**Now, when government spending rises, there are more effects in the MR. In
particular, the composition of output devoted to investment changes. This does
matter, and so it is inappropriate to say that government spending is neutral
in the MR. Still, government spending does NOT have an impact on the overall
level of output and employment (hence, unemployment too), and people want some
sort of way of characterizing this feature. They do that by saying that the
impact of government spending on output and employment is neutral in the MR.**

**Question 2**

**In our setup, a change in the labor force does not change the natural
rate of unemployment. What it does is to change the level of the natural rate
of output. Remember the relation, u=1-Y/L. It is u that enters the bargaining
equation. So, un gets determined as the intersection of the wage setting
equation and the price setting equation when Pe=P. Then, Yn is determined by
un=1-Yn/L, or, Yn=(1-un)L.**

**Changes in the labor force don't typically occur in the short run or the
medium run. They do occur sometimes....eg the migration of Russian Jews from
Russia to Israel, return of soldiers after WWII, return of Portuguese from the
colonies after decolonization, reduced population of Europe after the Black
Death, etc.**

**Changes in the measurement of u don't matter in our bargaining model.
What enters there is the actual rate of unemployment, something that is only
imperfectly measured by the government, and even then it is only measured with
a lag.**

**Question 3**

**The primary thing that will change the expected price, in our analysis,
is a situation where the actual price level differs from the expected price
level.**

**But, another thing that could raise Pe is a general perception that
monetary policy is going to be expansionary in the future.**

**Pe appears in the AS curve, and only there. It enters the model through
the wage setting equation W=PexF(u,z), or, W=PexF(1-Y/L,z), when unemployment
is written in terms of Y. The price level is P=(1+mu)xW. This is what defines
the AS curve. From this, you can see that, for fixed Y and z, a jump in Pe
raises P. That shows up geometrically as a shift up in the AS curve. So, a rise
in Pe shifts up the AS curve. That's the only curve Pe enters, so it does not
shift up any other curve. (Of course, a shift in Pe may set of a chain of
events that leads some other variable to change, like P, and that variable may
shift a curve. But, that is another story.)**

**The y-axis on the AD-AS model is the actual price.**

1. According to my lecture notes, Sgr=alpha. Why is that so? I don't understand how that is derived.

In long run equilibrium, s*f(k)=delta*k. With our production function, this implies s=delta*(k^(1-alpha)). This is one equation in one unknown, k, which can be solved uniquely for the unknown. By choosing different values of s, the policy authority can steer the economy towards different long-run equilibrium values of k.

In the golden rule, the marginal product of capital is equated to the depreciation rate on capital, delta. You can see this visually, simply by finding the value of k where the vertical distance between the depreciation line and income, f(k), is maximized. So, at the golden rule,

MP(k)=delta. With our production function, MP(k) is just alpha*(k^(alpha-1)), so that, at the golden rule, alpha=delta*(k^(1-alpha)). There is a unique value of the capital stock that satisfies this equation, and this kgr, the golden rule value of the capital stock. What value of s will cause the long-run equilibrium value of the capital stock to coincide with kgr? You can see this just by comparing the equation for the long run equilibrium and the equation for the golden rule. This comparison shows that if you set s=alpha, then the long run equilibrium k will be kgr.

2. Also, why is MP(K)=delta at Kgr?

you can see it in a graph, as explained above. The key thing to remember is that different saving rates produce different long run equilibrium levels of k, and each such k has a level of consumption associated with it. The golden rule level of k is the longrun equilibrium k where the long run equilibrium level of c is the highest.

3. F(K,L)=K^(1/3)*L^(2/3) Under the neoclassical theory, what is the share of total income going to labor. It is (w/p)*L/Y where w/p=dF/dL. I don't seem to get a number from this though.

In the neoclassical theory of distribution, MPL=w/p. Grind through the algebra, and you'll see that MPL*L/Y=(1-2/3) in this case.

4. What role does the assumption of perfect competition play? All I can think of is that it makes firms take w and r as given (i.e. price-takers). Is there anything besides that?

plus, they equate w and r to the relevant marginal products.

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Question: I thought that the format of the first and second midterms were very different-the first midterm was very technical and more mathematical while the second midterm was not that technical, but more about application of key concepts. Will the format of the final be a combination of both styles? I had a lot of difficult with the first midterm and did very well on the second midterm. How would you suggest I approach my studying given my difficulty with the more technical side of the class?

Answer: The style of the final should be closer to that of the second midterm. Larry

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Question: On the final, should we model technological progress as part of labor (so it's effective labor) as in the book and on the 97 final, or as a coefficient in front of K and L, as in class?

Answer: Technological change should be handled as I did it in class. There I did it in a less technically complicated way than it is done in the book.

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Question: Hi, I'm very confused about something... for queation 3 in Blanchard P.414 (of homework #8), the sloution posted on the web says that in the SR, IS and AD curves shift right. Then domestic prices rise and in the MR, the AS curve shifts up and the IS curve shifts left back to its original position. But since prices increase, shouldn't this cause a shift in the LM curve in the MR, instead of the IS curve?

And when exchange rates are fixed, does that mean the domestic interest rate can change in the SR but will always return to its original value in the MR/LR?

Answer: About the LM curve. Remember that under a fixed exchange rate regime the monetary authority shifts that around so that the domestic rate of interest equals whatever the foreign rate of interest is. The LM curve no longer plays a front seat role in the analysis. It's in the back seat, along for the ride.

The increase in government spending causes a rise in output (because firms see inventories falling, so they respond with an increase in production). In terms of graphs, it shifts IS and AD to the right. The rise in output leads to a rise in the price level as the economy moves up the AS curve and Pe is fixed (in the short run). The higher P causes a real appreciation (epsilon FALLS). Foreigners respond by buying less domestic stuff and domestic residents buy more foreign stuff, so net exports fall (the Marshall-Lerner condition was used here). This offsets somewhat, though not entirely, the rise in output due to the rise in G. That's the short run.

In the medium run, people wake up and see that the price level is higher than they expected. So the AS curve starts to shift up. This continues the rise in P until the economy gets back to the natural rate of output, which is where I assumed it started before the rise in G.

At this point, the rise in G has been met by an exactly equal decline in net exports. We know this is true because in both the old and new equilibrium, Y=C+I+G+NX. G rose, and C, I did not fall (Y is the same, and so is i). So, given that Y did not change, the rise in G must be met, one-for-one with a reduction in NX.

All this follows from shifting the graphs around and applying the disequilibrium dynamics discussed in class.

What about the LM curve, which has been very quiet, riding in the back seat? When the IS curve initially shifted right, in the SR, the LM curve had to be shifted right in order to keep the interest rate unchanged. Then, in the medium run, as the IS curve started to shift left again because of the rise in P, the LM curve had to be shifted left again. Again, under the fixed exchange rate regime the position of the LM curve is passively adjusted so that the current rate of interest always equals the domestic rate of interest.

When the exchange rate is fixed, the domestic rate of interest MUST always be identical to the foreign rate of interest.

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