# Ricardian Model: Trade pattern rules (ch. 3 Krugman's book)

I'm reading chapter three of International Economics by Paul Krugman et al. I have two questions that are somewhat related.

Question 1: Let $$P_{c}$$ = price of cheese, $$P_{w}$$ = price of wine, $$a_{Lc}$$ = unit labor requirement to produce cheese, $$a_{Lw}$$ = unit labor requirement to produce wine.

How does $$\dfrac{P_{c}}{P_{w}}=\dfrac{a_{Lc}}{a_{Lw}}$$ produce the flat portion of the world relative supply curve? I know the textbook says it is because the home country is willing to produce either good. Still, how does that translate to a flat portion of the world relative supply curve?

Question 2: Also, in chapter three Krugman talks about how to determine patterns of trade by looking at relative productivities. Take the variable definitions I gave in question one and let $$a^{*}_{Lc}$$ = unit labor requirement to produce cheese in the foreign nation and $$a^{*}_{Lw}$$ = unit labor requirement to produce wine in the foreign nation. Krugman says that one should order the goods $$i$$ to $$N$$ so that the lower the number $$i$$, the lower the ratio $$\dfrac{a_{Li}}{a^{*}_{Li}}$$. That is, we order the goods in such a way that

$$\dfrac{a_{L1}}{a^{*}_{L1}} < \dfrac{a_{L2}}{a^{*}_{L2}} < \cdots < \dfrac{a_{LN}}{a^{*}_{LN}}$$

He says that the relative wage $$\dfrac{w}{w^{*}}$$ fits somewhere in that chain of $$\dfrac{a_{Li}}{a^{*}_{Li}}$$'s. He says that any goods left of the relative wage will be produced at home and any goods to the right of the relative wage will be produced in the foreign nation. But then he says something that I think contradicts what he has already laid out. He says that a good will be produced at home if $$\dfrac{a^{*}_{Li}}{a_{Li}} > \dfrac{w}{w^{*}}$$. It seems that these two rules can contradict each other right? Is this a typo or is there something that I'm not understanding?