1. Consider a firm that has fixed costs. Its marginal cost curve must pass through the lowest point on the average cost curve. Also, it must pass through the lowest point on the average variable cost curve. 

2. If input prices for a firm are doubled, then the cost function must double for all levels of output.

 

3. Consider a firm that has fixed cost F. This firm will not change its output decision regardless of a change in F in the short run.