another possibly erroneous problem

[retaker]

Fall 2000, Course 2 #11

In the 80's a certain country was a net borrower on the international financial markets. Suppose that the preference of this country's citizens had shifted during this time from domestically produced automobiles to imported autos. Assume no change in fiscal policy. In a simple Keynesian model, determine the effect of this shift in preference.

Their answer: C) A decrease in net exports, thus increasing the gap between aggregate savings and investment.

Another choice:B) A decrease in net exports, thus decreasing " ".



I'll be the first to admit that I don't know a ___ thing about economics, but from a purely mathematical I think that I can show that there is not enough info given to determine C) as the correct answer.

I believe that whether there is an increase or decrease in the gap between aggregate savings and investment is dependent on several factors:

Here we go:

1) They say that "was a net borrower on the international financial
markets."
Seems to me that this means that: NR-INF < 0
I don't think this is even necessary to show my point, but let's assume
it for now.

Remember: NR - (X-M) - INF = I - (PS + BS +GS).

2) Assume |NR-INF|>|X-M|. This implies NR-INF-(X-M) < 0.
Now, if X-M<0 --> -(X-M)>0 --> as M increases, -(X-M)
becomes more positive --> NR-INF-(X-M) becomes less negative
and possibly even positive --> It is impossible to tell whether the gap
between savings and investment gets bigger or smaller.

3) Now assume, on the contrary, that |NR-INF|<|X-M|. This implies the
sign of NR-INF-(X-M) equals the sign of -(X-M).
If (X-M)>0 --> -(X-M)<0 --> as M increases, -(X-M)
becomes less negative and possibly positive --> NR-INF-(X-M)
becomes less negative and possibly even positive --> It is impossible
to tell whether the gap between savings and investment gets bigger or
smaller.

[PocketAces]

NR - (X-M) - INF = I - (PS + BS +GS)

If the quantity (X-M) gets smaller, as it does in this case, then the quantity I - (PS + BS + GS) must get larger. This is the quantity of interest. Answer C is correct.

[retaker]

Okay, but assume that NR-INF is more negative than X-M, and that X-M is in fact negative, so that NR - (X-M) - INF and hence I - (PS + BS +GS) is negative. The magnitude of it's "negativness" is the gap between investment (I) and aggregate savings (PS + BS +GS), no? In this case aggregate savings is greater than investment.

Now, by the assumption, as M increases, -(X-M), which is already positive, becomes even more positive so that the magnitude -(X-M) begins to "catch up" with the magnitude of NR-INF (but in the opposite direction, of course) and hence begins to cancel it out and possibly over take it.
Hence the difference, NR - (X-M) - INF, which we agreed was equal to the difference I - (PS + BS +GS) i.e. the gap between investment and savings, actually can become smaller.

[PocketAces]

Consider the condition that you don't think is necessary. It implies that
I-S>0

[PocketAces]

I think you also need to change the signs on INF and NR.

[retaker]

Which condition do I not think is necessary?
Doesn't being a net borrower mean that the interest you pay out to foreigners is greater than the interest you collect? Doesn't this mean that
NR-INF < 0 ?

There is a condition that implies that I- (BS +PS +GS) must be >0 ?

[PocketAces]

Try this:

I - (PS+BS+GS) = -NFI

[retaker]

Cool, thanks PocketAces:

Since they are a net borrower NFI <0 --> -NFI >0 --> I-(PS+BS+GS)>0

so that (NR-INF)-(X-M)>0

Still assuming that being a net borrower implies NR - INF<0, this requires that -(X-M)>0. So as M increases, -(X-M) gets more positive, hence
(NR-INF)-(X-M) gets larger, and (NR-INF)-(X-M) = I - (PS +GS+BS), so the gap, which was positive to start with, gets more positive. Okay.

Even if you don't require that NR-INF<0, it works out.

Thanks, Pocket Aces. Even though you b_tch slapped me earlier. I forgive you. :oops: