Suppose the price of a firm's fixed input rises

The statement is false.

Explanation:

The production level of the firm can be maintained even if the fixed cost rises. This will increase the average total cost. But the cost will be high in the long run as compared to the short run. The costs can be reduced in future using various methods like reducing other costs, reducing profit margin and others. The change in fixed costs affects the total cost in both the short and long run. In long run, other factors also affect the cost of production.