Questions about course content for Econ 441, Fall 2008

Dec 15
Hi. I'm just wondering why the answer to number 1, part e is neither. Isn't 
country A at a higher utility curve? 

A:
The question asks about welfare "per person."  Country A has added to its 
consumption exactly in proportion to its added number of people.

Dec 7
Hi. I forgot to ask one question. In lecture, you talked one day about tax 
on imports vs tax on exports and showed that they result in the same price 
ratio (using algebra). I understand the derivation but I'm not sure why 
exactly a tax on imports implies Pc = (1+t)Pc* and a tax on exports implies 
Pf = Pf*/(1+t). I assume a tax on imports is a tarrif, but what exactly is 
a tax on exports? Which of the two goods is home importing in this example?

A:
The country here is exporting good F and importing good C.  The tax on 
imports is a tariff on imports of C, and it requires purchasers to pay a 
domestic price that is t% above the world price; that is, they pay Pc* to 
the foreign exporters plus tPc* to their own government, so Pc = (1+t)Pc*.  
The tax on exports is a tax on foreigners buying our exports of F.  Thus 
the foreigners pay Pf to our sellers plus tPf to our government:  Pf* = 
(1+t)Pf.  Divide this equation by (1+t) and you get Pf = Pf*/(1+t).

Dec 7
Hi. I was doing practice final number 1, and have a question about problem 5. 

In part a, it says that for a large country the tax is necessarily better. 
I drew a partial equilibrium diagram and, using the usual letters for 
welfare, came up with this:

for the tariff, it the country gains or loses   -(b+d) + e

for the subsidy, the country loses -(b)

I figure based on this that the results depend on the values of 'd' and 'e'. 

Did I do these calculations wrong?

A:
No, you did it right.  But you compared to a subsidy to production, not a 
subsidy on imports.  A subsidy on imports will move everything in the 
opposite direction, an necessarily reduce welfare, while an "optimal" tax 
on imports will improve welfare in a large country.

Q:
For part b, I don't understand how Home can provide a subsidy to a foreign firm. Is it paying that firm?

A:
Yes, that's the idea.  I'm not saying it happens.  But we can ask about the effects of doing it.

Dec 6
What is Non-distorting Transfers?
This word comes out in the past exam number 2. but I am not quiet sure what 
that is.

A:
A non-distorting transfer is a payment from one entity to another that does 
not introduce inefficiencies.  This means mainly that it does not provide 
an incentive to change production or consumption choices.  Thus if we 
transfer income from one group to another by, say, taxing the income of the 
first and paying to the second in proportion to their incomes, then this 
would be a distorting transfer, since it provides an incentive for both 
groups to minimize their incomes.  

A non-distorting transfer is often stated as a "lump-sum transfer," in 
which the government simply takes a lump sum (a set amount of money) from 
one group and gives it to another, without it depending at all on what 
either group does.  That way there is no incentive for them to alter their 
behavior.  Unfortunately, it may well be that non-distorting transfers are 
impossible to do, in practice.

Dec 4
I have a question about PS6. 

Do you think you could provide me with an explanation of how you get the 
result in part B or problem 3? How do you figure that a tariff of 3 would 
raise the price only to 9? I'm also having a bit of trouble understanding 
why the Sm curve is upward sloping for the ED graph in a market with a 
large country. Why is the free trade price given by the point where this 
intersects the Dm curve... what does this point represent? What is the area 
between the Sm curve and the Dm curve? I'm thinking the quantity between 
the intersection point and 0 is the quantity of imports...?

A:
The definition of a large country is one that can influence the world price 
by the quantity that it imports.  That means that it faces a supply curve 
for what it imports that is upward sloping, rather than horizontal (as we 
assume for a small country when we take the world price as given).  We find 
the equilibrium in the world market by equating supply and demand.  In this 
case, that means equating the rest-of-world's supply of imports to the 
country's demand for imports.  That is why the free trade price is given 
where those two curves intersect.

With a tariff, the buyers of imports pay a price that exceeds the price 
received by sellers by the amount of the tariff.  So in this case we look 
for a domestic price that is $3 higher than a foreign price.  But both 
prices must also be selected so that the quantity supplied equals the 
quantity demanded.  And that's what identifies the equilibrium in the 
figure here.  In particular, it gives a foreign price of 6 and a domestic 
price of 9.  There are no other prices that yield the same quantities 
supplied and demanded and also differ by exactly $3.

Dec 4
I have a question for you on a part from your lecture on Nov. 17th. We 
talked about trade policy in the context of imperfect competition and drew 
a graph for a domestic monopoly in a small country and explained why the 
country would want to protect a monopolist.

We started with free trade and added two different tariffs. Could you 
explain the effects of the second tariff. More specifically where the 
quantity produced will be and how this permits a monopolist to begin 
charging a monopoly price?

A:
I'm not sure which of several diagrams I drew that day you are referring 
to.  According to my notes (which I might have departed from, but I don't 
think so), I first looked at the effects of four different tariff levels, 
not just two, in a small country whose domestic market has only a single 
firm.  The message was that the firm can charge up to the world price plus 
the tariff, but not above that.  For small tariffs, it will produce out to 
where that price equals its marginal cost, which as I drew it is less than 
domestic demand.  For higher tariffs, however, it produces only out to the 
demand curve.  In the first case, a rise in the tariff causes it to produce 
more, as it moves up its MC curve.  In the second case, a rise in the 
tariff causes it to produce less, as it moves up the demand curve.  The 
border between the two cases is where the MC curve crosses the demand 
curve.

If this is the figure you are asking about, then I guess you need more 
explanation of the second case.  In both cases, it is the tariff that 
permits the firm to charge higher than the world price.  In the second 
case, this price is high enough that it cannot sell all that it would most 
like to produce (given by the MC curve), since to do so it would have to 
lower its price to move down along the demand curve.  So it limits output 
to the lower amount demanded.

By the way, none of this was saying why a country would "want to protect a 
monopolist."  The country loses by doing this.

Nov 2
In PS#3 Q3.  Based on the result that a shift from A0 to A1 causes w/r to 
fall I must assume that Clothing is the capital intensive industry in this 
case?  Doesn't that break the convention explained in the text that X is 
generally the labor-intensive good (the one on the bottom left of the 
edgeworth box). Does the fact that the contract curve bows upward (in 
relation to a linear CC between the two origins) as opposed to downward as 
shown the text give us enough information to determine that C is capital 
intensive?

A:
Yes, I wasn't aware (or had forgotten) that the text has any convention as 
to which good is labor intensive.  Certainly in this problem you know 
immediately that good C is capital intensive compared to good F, since the 
ratio of capital to labor in C at point A0 is higher than the ratio of 
capital to labor in good F there, and the tangency of the isoquants means 
that they are facing the same relative factor prices.

Q:
I also had trouble with part e. (showing k=K/L is a weighted average of the 
ratios in the two sectors using full employment conditions) Is this 
something we should know for the exam?  I got minimal points trying to 
prove gains from trade using equations on the last exam which was pretty 
unexpected and a bit frustrating.  I'd like to be better prepared this 
time, but the equations give me trouble.  Any advise?

A:
The proof of the gains from trade on the last exam came directly out of 
lecture, for which you are certainly responsible.  This derivation was 
something that I thought you should be able to figure out, but it was not 
in lecture.  I do ask questions that I expect you to figure out, so it's 
probably a good idea to at least understand the answer to this one.

Nov 2
Just wondering if there is a difference between homogeneous and homothetic 
preferences.  I understand that identical and homothetic tells us that 
consumption will depend on relative prices only and that good will be 
consumed in the same proportion regardless of income level.  Specifically, 
what does the assumption of identical and homogeneous preferences in the HO 
model tell us.  Also, what would homothetic mean without the "identical" 
qualification.

A:
The words homogeneous and homothetic do have different meanings, slightly.  
Homogeneous implies homothetic, but homothetic does not imply homogeneous.  
Homothetic is about the shapes of indifference curves but not their 
numbering, while homogeneous adds a restriction on numbering.  We don't 
usually refer to preferences as being homogeneous, because the numbering of 
indifference curves (the level of utility to which they correspond) does 
not matter for behavior and is not well defined. However, for the same 
reason it would be harmless to assume that they are homogeneous rather than 
homothetic.

When we say that preferences are identical, we are referring to comparisons 
across consumers or across countries.  Thus in the HO model, identical and 
homothetic preferences means that, within each country preferences are 
homothetic (and thus ratios demanded depend only on relative price, not 
income), while across the countries they are identical (so that if the 
countries face the same prices, they will demand the goods in the same 
proportions).

Oct 30
I have a question about the solution posted for problem set 3,
question 5, part B. On the diagram, it shows that lowering p_c0 to
p_c1 shifts the unit value isoquant (which I understand), but this
makes tilde-k_c and tilde-k_f steeper. I don't understand why it does
that. Aren't those the factor intensities of producing C and F,
respectively?

A:
They are indeed the factor ratios employed in producing C and F, but these 
ratios change when factor prices change.  They would not change if the 
isoquants were L-shaped, but with curved isoquants, as we usually assume 
and draw, then factor proportions respond to changes in relative factor 
prices, and that's what's happening here.

Q:
Also, how can you tell from the diagram that the line
with intercept at 1/r2 (parallel to the unit-isocost line) shows that
r2 went down by an equal amount to the fall in p_c?

A:
From the geometry.  Look at the triangles formed by the tilde-k_C line, the 
vertical axis, and these two lines.  They are similar triangles, and 
therefore the proportional change in 1/r is the same as the proportional 
change in the sides of the triangles along tilde-k_C, which is the price 
change.

Q:
Similarly, for
part C, I can't understand how you know that tilde-k_c slants down
after the shift in the unit-value isoquant for cloth.

A:
Same answers.  As the factor price line gets flatter, the industry will 
operate at a point on the isoquant that is also flatter, in order to be 
tangent to it.

Oct 9
In today's lecture you mention that for the FPE to hold, both have to be 
inside the cone and both have to be diversified, by that do you mean that 
endowments have to be inside the cone and productions have to be 
diversified?

A:
Yes.  Of course these two are the same condition:  If both endowments are 
inside the cone, then necessarily production in both will be diversified, 
and vice versa.

Oct 8
I was going over the Exam answers, but I don't understand part of the 
answers on the answer key for question 7b.

With homothetic preferences, the ratios of consumption of goods X and Y 
stays fixed over different income levels.  With the trade prices changing 
to favor X, this represents an increase in income for the country.  well, 
wouldn't this necessarily cause higher consumption of both X and Y?  In 
other words, if we are assuming homothetic preferences, I don't understand 
how consumption in Y can increase without requiring consumption in X to 
rise as well (and thus causing total exports, which consist only of X, to 
necessarily fall.)

A:
Homothetic preferences only means that ratios of consumption stay the same 
if income changes and prices don't.  It doesn't mean that indifference 
curves are L-shaped, which is what you you are saying when you hold the 
ratios constant even when prices change.  In other words, in 7b, the 
indifference curves would normally be curved, as drawn, and therefore 
prices have a substitution effect as well as an income effect.  It is the 
substitution effect that leads to the ambiguity.

Oct 6
Comparing figures 7.2 and 7.3, I think the very left end of the flat
side of 7.3 corresponds to producing X exactly where H' is on 7.2 (all
the X possible, so that you are exporting as much as you can). I would
imagine the distance H'O from 7.3 to be the horizontal distance
between Ah and H' in 7.2 (not the diagonal, but the horizontal
component, ie the excess production of X). Now when I increase the
slope of pa to p1*, I produce at H' still (max X, as by the Ricardian
model) and consume at C1. Now, I figure that there is less amount of
exports being done here since the horizontal component of C1H' (ie the
amount of excess X which is exported by consuming at C1 and producing
at H') is smaller than it was between Ah and H'. However, there is
more excess supply shown in 7.3 for this point than for the point
corresponding to the left end of the flat area. Why does excess supply
at this point increase? Doesn't the higher world price for X allow
Home to buy more Y by selling less X, and to therefore require less
exports of X? Is this the "backwards bend" that you at some point
mentioned? Or am I totally lost and confused and have no idea what I'm
talking about? =)

A:
You are absolutely right.  The authors drew these poorly.  In Figure 7.2 
exports are shown as being smaller at the higher price than the maximum 
export at the autarky price.  In Figure 7.3 just the opposite is shown.  
To get Figure 7.3, they should have drawn the indifference curve in Figure 
7.2 less tightly curved, so that the tangency C1 would be to the left of 
(and thus much higher than) Ah.

Oct 6
 I found part d of problem 1 on Problem set 1 a little confusing.  At the 
end you get rK + wL = k p X.    You then go on to say that if k = 1 the 
equality holds, but if k > 1 , the value of inputs is GREATER than output.  
I thought the right side of the equation was the value of outputs (ie. 
(price of x "p") times (qty of X) times (k) if k > 1 The output side of the 
equation becomes greater than the inputs, yet the answer says the opposite 
is true. (ie inputs costs are greater than value of the output.   Please try 
to clarify this.

A:
The value of output is just pX.  If k>1, then kpX>px.  So the equation says 
that the value of inputs (the left side) is greater than the value of 
output, pX.

Q:
I also found it a little confusing where the equations were coming from.  
For instance, F(K,L) gives the quantity of X produced?   is F subscript K 
the MP of capital?  Some definitions of terms would be helpful.  I could 
follow reasonably well from my notes, but I got lost as far as what is being 
held constant and which are variables in the equation.

A:
Yes, you're right.  I should have explained that the subscripts K and L 
represent partial derivatives with respect to the first and second arguments 
of the function.

Q:
    Lastly could you describe in a few sentences what exactly diferentiating 
with respect to (the greek symbol) actually means for the production 
function.  The rate of change of the output of function F with respect to 
the change in ratio of the input factors?

A:
Differentiating with respect to lambda means, in this case, the (small) 
change in output per unit percentage change in both inputs together, holding 
their ratio constant.  However, we are not doing this because we really want 
to know what that change is.  Rather, we are doing it because we (I) happen 
to know that doing so will be a convenient way of getting a relationship 
between values of inputs and outputs.

Oct 5
I have a question to ask you about "Stolper Samuelson Theorem"

What I understood about the theorem is that as the price of good x 
increases, the real return of the factor that used intensively in the 
product x increases as well.

I remember in your lecture, you told us about how the trade helps abundant 
factors and hurts scare factors. In my notes, this is under "Stolper 
Samuelson Theorem".

Are they related ? or am I understanding wrong?

A:
Yes, they are two different forms of the same proposition, which we will 
explore further in the next few lectures.  You don't need to worry about 
that now, though.  The only reason I mentioned it already was to point out 
that there are losers from trade.

Sep 30
I was wondering what the ppfs look like for increasing, constant, and 
decreasing returns to scale.  I under stand the concepts as far as factors 
of production, but how do they affect the PPF.

A:
If there is only one factor, as in the Ricardian Model, the increasing 
returns to scale would cause the PPF to be convex to the origin while the 
decreasing returns to scale would cause it to be concave.  With constant 
returns to scale, it is linear, as you know.

With two or more factors, then differences in factor intensity cause the 
PPF to be concave to the origin when there is constant returns to scale.  
Decreasing returns to scale would make it even more concave.  Increasing 
returns to scale would make it less concave, and could make it convex.  It 
depends on both the strength of the increasing returns and how different 
are the factor intensities of the two industries.

Sep 19
I understand that we are talking about the U.S. bc perhaps we have a 
better understanding of its resources and scarcities. I know we talked 
about unskilled labor as being very scarce and therefore losing once the 
market for a certain good is open for trade. I remember you mentioning 
that in the case of an developing nation it would perhaps be the other 
way around bc for them, unskilled labor might actually be abundant.

So, lets say we are observing two developing countries, both abundant in 
unskilled labor and they have completely different resources, so that 
opening up trade and trading with each other is beneficial in terms of 
being able to acquire other resources not available in their own country. 
Would there be any losses in this case, would the gains outweigh the 
losses?

Does a country benefit in proportion to the losses it takes? Say for 
example in the case of the U.S, yes unskilled labor takes a loss bc their 
wage will be decreased, but does the benefit of being able to bring in 
other resources make up for it, or does this merely depend on the 
specific market that we are looking at?

A:
First, what I showed in class and we will see repeatedly in our standard 
models, is that no countries lose from trade in the aggregate.  That is, 
even though certain groups within them almost always lose, others within 
them gain even more.  So in the US, where unskilled labor is our scarce 
factor, other factors -- capital, human capital -- gain even more than 
unskilled labor loses.  In other countries, where unskilled labor may be 
abundant, those workers gain from trade more than others (owners of 
capital, perhaps) lose.

You ask about two developing countries that both have abundant unskilled 
labor but that also have two different resources on the basis of which 
they trade.  That is plausible, but that means that it is one of the 
resources that each country really has in abundance, and it is the owners 
of that resource that will gain the most from trade.  The owners of the 
other resource -- what each has little of -- will lose, while the 
unskilled workers may gain or lose.  But what we do know, again, is that 
each of the countries as a whole will gain from the trade.

Sep 16
Could you please explain once again how the value of output in free
trade (that is, (P*x)(Xfp)+(P*y)(Yfp)) must be either large or equal to 
value of output in autarky situation (that is, (P*x)(Xap)+(P*y)(Yap))?
How does assumption of maximizing the value of output play a role in 
this?

A:
The first is the value of the free-trade output at free-trade prices.  
The second is the value of autarky output at free-trade prices.  Since a 
competitive economy maximizes the value of output at the prices that it 
faces, it follows that the value of any output that is produced at some 
prices is greater than the value of any other feasible output at those 
same prices.  Thus, since free-trade output is produced at free-trade 
prices, and since autarky output is clearly feasible, it must be true 
that the value of free-trade output at free-trade prices is greater than 
the value of autarky output at free-trade prices.

Q:
And why is it that in autarky situation, P* was used instead of Pa?

A:
For two reasons.  First, if we'd used autarky prices, this inequality 
would not hold.  And second, it wouldn't be useful, since it wouldn't 
allow us to conclude anything about the relative desirabilities of the 
two consumption bundles.

Sep 15
Given the market clearing condition and competitive price condition, is it 
necessarily true that autarky economy will always create an equilibrium 
where total consumption of community equal total production of community?

A:
Yes, if you include the additional condition that expenditure equals 
income, which in our model with consumers as the only demanders, is simply 
their budget constraint.  Without that -- if consumers have the option of 
saving or dis-saving (which would require the presence of some asset in 
which they can store their wealth -- then total consumption need not equal 
total production. But then you will have instead a comparable condition 
that holds across all markets for both goods and assets.

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