Suppose that a cost minimizing firm with two inputs, capital K and labour L rece

Question

Suppose that a cost minimizing firm with two inputs, capital K and labour L recently increased the quantity of each inputs by 10%. As a result, output has increased from 1,000 to 1,200 units. For each of the following statement, indicate whether it is true, false, or uncertain and explain your answer.

a) When output is 1,000 units, there are increasing returns to scale.

b) When output is 1,000 units, long-run average cost is downward sloping.

c) When output is 1,000 units, long-run marginal cost exceeds long-run average cost.
d) When output is 1,000 units, long-run marginal cost is downward sloping.

e) If the firm had increased the quantity of each input by 5%, output would increase from 1,000 to 1100 units.

Explanation / Answer

Here output is increased by 20% by 10% increase in input. That is output is doubled. When output is at 1200 then firm enjoys increasing return to scale.

Statement in a is false as 1000 unit of output is not doubled by 1 unit change in input.

Statement b is true as this is a cost minimizing firm. By increase in input, output is doubled. So long run average cost is downword sloping

Statement in c is false as LRMC is below the LRAC at 1000 output. Firm can double its output by increase its input in long run

Statement in d is true as LRAC is downward sloping so LRMC is downward sloping

As firm increase output 20% by 10% increase in input. So by 5% increase in input it can increase its output by 10%. So the statement in e is true.

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