What is the relative importance of BOTH gross profit and contribution margin?

Gross margin is what is left after deducting cost of goods sold, which includes material, labor and overhead, both fixed and variable. Contribution margin is what is left after deducting variable cost. Therefore, contribution margin includes fixed costs.

The contribution margin is the proportion of the price made up by fixed cost and profit. Its importance in the calculation is that it is lost as revenue when sales fall in response to the contemplated price rise.