A competitive firm produces a single output using several inputs. The price of o

Question

A competitive firm produces a single output using several inputs. The price of output rises by $3 per unit. The price of one of the inputs increases by $6 and the quantity of this input that the firm uses increases by 12 units. The prices of all other inputs stay unchanged. From the weak axiom of pro t maximization we can tell that:
(a) the output of the good must have increased by at least 24 units.
(b) the inputs of the other factors must have stayed constant.
(c) the output of the good must have decreased by at least 12 units.
(d) the inputs of at least one of the other factors must have decreased by at least 12 units.
(e) the inputs of at least one of the other factors must have increased by at least 12 units.

(Please show work or explain. I already have the answer. just need to know how to solve it.)

Explanation / Answer

(a) the output of the good must have increased by at least 24 units.

For profit max: Increase in revenue > Increase in costs

Increase in revenue = increase in output * increase in price of output = 3 *  increase in output

Increase in costs = increase in input * increase in price of input = 12 * 6 = $72

Increase in revenue > Increase in costs

=> 3 *  increase in output > 72

=> increase in output > 72/3

=> increase in output > 24

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