Consider the cost function of a firm, defined asc(y) =cv(y) +F; wherec'(y)>0 andF0. Show that

(a) At any pointy, the average cost function is decreasing if the marginal cost is lower than the average cost;

(b) At any pointy, the average variable cost function is decreasing if the marginal cost is lower than the average variable cost;

(c) The average cost function is decreasing everywhere if the marginal cost is decreasing everywhere.