Suppose a single-input production function has initially increasing but eventually decreasing marginal product -- and suppose we know that an interior solution is profit maximizing.In this case, the first order condition for the profit maximization problem
A)is necessary for identifying the profit maximizing production plan.
B)is sufficient for identifying the profit maximizing production plan.
C)is both necessary and sufficient for identifying the profit maximizing production plan.
D)is neither necessary nor sufficient for identifying the profit maximizing production plan.

Question

Quizplus · Accepted Answer

The first order condition (FOC) is necessary for identifying the profit maximizing production plan because it helps determine the level of input at which the marginal profit is zero, indicating a maximum or minimum. However, it is not sufficient on its own because we also need to check the second order condition (SOC) to ensure that the solution indeed corresponds to a maximum (i.e., the marginal product is decreasing at the optimum).

Suppose a Single-Input Production Function Has Initially Increasing but Eventually