Profit Maximization and the Threshold Price

Abstract

If the output market is perfectly competitive and the firm’s production function is not concave, an increase in the output price may lead to an explosive increase in firm’s profits at some point. We explore the properties of this point, called a threshold price. We derive the formula for the threshold price under very general conditions and show how it helps to study correctness of the profit maximization problem, without explicit assumptions about returns to scale or convexity/concavity of the production function.threshold price; profit maximization; production function; cost function; Cobb-Douglas function; returns to scale