Thread: Micro/Macro Economics - Comparative Analysis, Specialization, gains from trade HELP!

Please help! I'm so lost. My book isn't helping me understand how to figure out the gains from trade between two countries. So here's a sample problem that I'm working. Please give me step by step explanations on the parts that I can't figure out. And please don't waste effort explaining the parts that I DO get.

Production Possibilities for Slobovia
-------------------------------------
Product A B C D E F
cams 1500 1200 900 600 300 0
widgets 0 100 200 300 400 500

Production Possibilities for Utopia
-------------------------------------
Product A B C D E
cams 4000 3000 2000 1000 0
widgets 0 200 400 600 800

From this, I know how to decipher which country should specialize in which product. I'm not going to type out my work since this parts easy, but I know that:

Utopia should specialize in cam production
Slobovia should specialize in widget production

Let's say that, before specialization, Slobovia produces at alternative C and Utopia produces at alternative B.
So Slobovia produces 900 cams and 200 widgets.
And Utopia produces 3000 cams and 200 widgets.

After specialization:
Slobovia produces 500 widgets and 0 cams
Utopia produces 0 widgets and 4000 cams.


How do I find the rate of exchange each country should trade at? And how do I find the total amount of each product traded? Knowing these two pieces of information will allow me to calculate gains from trade.

Please please please help! My test is tomorrow and my book doesn't explain this clearly!

Slobovia
On its own, Slobovia must give up 100 widgets to make 300 cams.

equivalently, Slobovia must give up 0.333333333333333333 widgets to make 1 cam


So, Slobovia will gain from trade if it can buy a cam for less than 0.333333333333333333333 widgets


Utopia
On its own, utopia must give up 200 widgets to make 1000 cams. Equivalently, it must give up 5 cams to make 1 widget.

So, It will benefit from trade if it can get more than 1 widget for every 5 cams it produces.

It must sell cams for more than 0.2 widgets each.


Combined

For both countries to gain from trade, the price for cams must be

0.2 > p > 0.3333333

I did it differently and found my trade exchange to be

3 < cams < 5 = 1 widget

This turned out to be correct.

Now I'm desperately trying to figure out how to come up with the gains of trade, when I have no idea what amounts are being traded.

For the avoidance of confusion, there is no difference between:


0.2 widget < 1 cam < 0.333333333 widgets

and

3 cams < 1 widget < 5 cams
You have simply expressed your price in terms of cams instead of widgets.



To find the gains from trade, compare the total world output in each good before and after trade.

Before Trade:
3900 cams
400 widgets


After Trade
4000 cams
500 widgets


Gains from trade
100 cams (=4000-3900)
100 widgets (=500-400)

Ohhhhhhhh! I get it now. God, do I feel dumb. I spent hours trying to figure this out. Thank you so so so so much!!!!