Question: (a) A competitive firm receives a price p for each unit of its output, and pays a price w for each unit of its only variable input. It also incurs set-up costs of F. Its output from using x units of variable input is f(x) = √x. Determine the firm's revenue, cost, and profit functions.
(b) Write the first-order condition for profit maximization, and give it an economic interpretation. Check whether profit really is maximized at a point satisfying the first-order condition.