This document discusses and compares short run and long run cost functions. In the short run, average total costs and average variable costs are U-shaped, and marginal cost intersects them at their lowest point from below. In the long run, firms can adjust all factors of production, and long run average cost forms an envelope of the short run cost functions. The key difference is that short run cost functions impact input quantity decisions in the short term, while long run cost functions influence expansion decisions.