Question

ABC Corp produces widgets with labour as the only variable input. Its production function is y = z2, where y is output and z is labour input. The maximum output possible with its plant is 100 units of output. Denote the price of output by p > 0 and the wage rate by w > 0. Does the Extreme Value Theorem guarantee an answer to ABC’s profit maximization problem? Defend your answer.

Answer 1

The extreme value theorem states that if a function is continuous in a given interval it will have an extreme value of either maximum or minimum or both within that interval.

The profit function is given as

The maximum output occurs at z=10. Then the set for this firm is

The set is closed and bounded. The profit function is twice differentiable at this interval as

Then EVT guarantees a maximum at z=10.