In economy A there are two types of labour (say, skilled and unskilled). The economy produces two goods (x and y) which can be produced either by skilled labour or unskilled one. Skilled labour can produce either 400 units of y or 200 units of x (or any linear combination of the two). Unskilled labour can produce either 200 units of y or 400 units of x (or any linear combination of the two). Economy B, on the other hand, has only unskilled labour which can produce either 200 units of y or 200 units of x (or any linear combination of the two). If the countries traded at all, it would necessarily mean that country A should fully specialise in the production of x. True or false, explain.

My handwritten workings are available here.

In order to answer the question I have to estimate the linear equation for skilled and unskilled labour for economy A and economy B. Do you know of any economy which has only unskilled labour available btw?

In order to find the economic implications of full specialization in either good x or good y, my tutor recommends working it out by deducting the production resources available assuming self sufficiency i.e. what would be the production if each economy were to produce enough for its own internal consumption. Secondly there is the implication of whether it would be worth for economy A to trade in (buy) enough of good y for its internal consumption (self sufficiency level). Self sufficency is deduced from the linear equation of the above, however, I think I have done a mistake in calculating the linear equation, because when I try the following linear equation within Graphing software, the graphical solution is nowhere near to that I have scribbled (see the link above).

Economy A

Skilled labour (Ls) = 0.5x + 200 based on the assumption that f(x) = mx + c, is the gradient (change in y / change in x) and adding the constant where x = 0.

Unskilled labour (Lus) = -2x + 400 based on a similar assumption as the above.

Where am I mistaken, please?