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Consider an economy where two goods, x and y can be produced usingmachines, k, or workers, l. There are a total of 100 workers and120 machines in the economy (L ¯ = 100, K ¯ = 120). Good x can beproduced by using both 2 workers and 1 machine (lx = 2, kx = 1).Good y can be produced by using both 1 worker and 4 machines (lx =1, kx = 4).

The resource costraints for this economy are thus:
lxx+lyy = L ¯ ? 2x+y=100
kxx+kyy = K ¯ ? x+4y=120


Question:

Suppose that we wanted to have equal production of both goods. Findthe quantities of good x and y produced and the total number ofmachines and workers used. Are all of the resources used?

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Kelleb Mloyi
Kelleb MloyiLv2
28 Sep 2019

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