Variability and average profits - does Oi's result generalize?

Average profits of a price taker are increasing in the variability of the output price (Oi, 1961). We show that, for the same reason, average profits of the price taker are increasing in the variability of the price of inputs. We proceed to establish that the same holds for a firm with a downward sloping demand curve. Unless the inverse demand curve of the firm with market power is very convex, the profit function of the price taker forms an upper limit for the convexity of profit (assuming constant curvature of costs).