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Question 1:
The production function is q= 2L2/3k1/3. This tells us the maximum volume of output
a firm can produce with its quantities of inputs. There are 2 inputs: labor (L) and
capital (k). The volume of the output is represented by q.
In this production function, the labor is raised to the 2/3 powers and capital to the
1/3 power, representing two positive values. The production function therefore,
exhibits a constant return as long as the labor and capital remain constant to scale. If
l and k represent the same value x, then L2/3t1/3 or x2/3x1/3 = x. Therefore, whatever
value is replaced by x is considered separate situation and will represent the ratio or
increase.
For example, if labor (L) = 8 and capital (k) = 8, q = 2 (82/3)(81/3)= 2 x 8 = 16
If labor (l) = 64 and capital (k) = 64, q = 2 (64) 2/3(64) 1/3=2 x 64 = 128.
The labor and capital both increased by 8 times and so did ...
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