Linear equation deduction enigma

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Linear equation deduction enigma

Postby jon80 » Sat Sep 29, 2012 8:51 am

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?

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Re: Linear equation deduction enigma

Postby stapel_eliz » Sat Sep 29, 2012 11:30 am

I have fixed the link in your post. For further information on posting, please review the FAQ for these forums.

The image at the link is very faint. Would it be possible to scan the images with "brightness" perhaps set a little lower and with greater contrast? Thank you! :wink:

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Re: Linear equation deduction enigma

Postby strumbore » Fri Jan 11, 2013 2:08 am

No one's gonna look at this, and I don't know if this helps, but from a Production standpoint in EconA:

Skilled Labor produces y more effectively
Unskilled Labor produces x more effectively

EconA producing soly x or y is double the output of that of that in EconB. Graph all 3 lines on the same plane. These are the equations:

EconA, Skilled: Y= -2x + 400
EconA, Unskilled: Y=(-1/2)x + 200
EconB, Unskilled: Y= -x + 200

Solving the system for EconA,Skilled and EconA, Unskilled yields the equilibrium point at (x,y)=(133 1/3, 133,1/3) (which is sloppy to me because fractions are meaningless in this context).

Looking at the graph, you can see that from that point of intersection, the difference of production of BOTH products x and y between Economy A and B is at its highest (a deficit of 66 2/3 units).


I don't know if any of this information is useful.

But this is:
  • In Economy A, Skilled Labor produces twice as much Product Y than Unskilled Labor in either economy.
  • Skilled Labor *COULD* produce some Product X, but it stands to reason that Unskilled Labor in Economy A can do it cheaper at the same output, and Economy B can do it even cheaper than Economy A at the same output.
  • Consumers in dirt-poor Economy B won't generally want to buy the same product at the same output at a higher price from Economy A. Most consumers in Economy A won't know or care if Product X comes from North Korea.
It stands to reason that Economy A *SHOULD*, in fact, produce only Product Y.

Unless I missed something

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