Question

Suppose that worker hours (L) and machine hours (K) are fixed proportion inputs in the production of widgets (Q). Moreover, to produce an additional widget, the firm needs to use exactly 50 worker hours AND 10 machine hours. Which of the following correctly represents the production of widgets? a. ?(?,?) = min(50?, 10?) b. ?(?,?) = min(10?, 50?) c. ?(?,?) = min(0.02?, 0.1?) d. ?(?,?) = min(0.1?, 0.05?)

Answer 1

The fixed proportion production function shows that at the kink both inputs used in the fixed proportion so that output is equal to the minimum of both the proportions.

L= 50

K= 10

For (a) Q= min (50L ,10K)

= min [(50)(50) , (10)(10) ]

= min (2500 ,100) . These two are not equal , so this does not correctly represents the production function.

For (c) Q= min (0.02L , 0.1K)

= min [(0,02)(50) , (0.1)(10)]

= min (1,1) .These two are equal ,and Q=1 from this ,which correctly describe the given condition in the question . That is , to produce an additional widget ,the firm needs to use exactly 50 worker hours and 10 machine hours.

Hence,option(C) i.e Q= min(0.02L, 0.1K ) is correct.