MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
A firm sells a product with demand equation p=90−0.5q, where p is the price per unit (dollars) and q is the quantity demanded. Its cost function is C(q)=25q+F, where F>0 is a fixed cost. The firm chooses q to maximize profit. How does an increase in F affect the optimal production quantity and the optimal price?
(a) The optimal quantity decreases and the optimal price increases.
(b) Both the optimal quantity and the optimal price remain unchanged.
(c) The optimal quantity remains unchanged, but the optimal price increases.
(d) The optimal quantity increases and the optimal price decreases.