Answer to opportunity cost question

Since in order to produce one more unit of good Y we need 1/10 unit of labor -- the production function of Y is Qy = 10 Ly, so labor productivity is 10 and the activity requirement is 1/10 -- we must take that 1/10 unit of labor away from the production of good X.

The production function of good X is Qx = 5 Lx, and Lx decreases by 1/10. We will therefore have:

dQx = 5 dLx = 5 (- 1/10) = - (5/10) = - (1/2)

The difference (d) in Qx is 1/2 unit.

It should not be surprising that the opportunity cost of Y is the reciprocal of the opportunity cost of X -- to produce one more unit of X you give up two units of Y; to produce one more unit of Y you give up one-half unit of X.

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