7. Consider the following short-run production function (where L = variable inpu

Question

7. Consider the following short-run production function (where L = variable input, Q = output): Q=6L2-0.3L3. Does output always increase with input use? If so, prove it. If not, find the maximum output possible.

8. Use the following two statements to answer this question:

I.    The average total cost of a given level of output is the slope of the line from the origin to the total cost curve at that level of output.

II.   The marginal cost of a given level of output is the slope of the line that is tangent to the variable cost curve at that level of output.

A) Both I and II are true.

B) I is true, and II is false.

C) I is false, and II is true.

D) Both I and II are false.

(Please provide the reason why you pick that option not others)

Explanation / Answer

(7)

Q = 6L2 - 0.3L3

Let us use following data table.

It is seen that output increases with increase with input upto the input level of 13 units (when output reaches a maximum of 354.9 units), the starts falling with 14th unit of input and more. This is known as the law of diminishing returns to scale, which comes into effect from 14th unit of input.

NOTE: As per Chegg Answering Policy, first question is answered.

L Q 0 0 1 5.7 2 21.6 3 45.9 4 76.8 5 112.5 6 151.2 7 191.1 8 230.4 9 267.3 10 300 11 326.7 12 345.6 13 354.9 14 352.8 15 337.5 16 307.2 17 260.1 18 194.4 19 108.3 20 0 21 -132.3 22 -290.4 23 -476.1 24 -691.2 25 -937.5

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