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Misunderstandings in cross-cultural communication often arise from subtle differences in interpretation, but it is unclear whether these differences arise from the literal meanings assigned to words or from more general pragmatic factors such as norms around politeness and brevity. In this paper, we report three experiments examining how speakers of British and American English interpret intensifiers like "quite" and "very." To better understand these cross-cultural differences, we developed a computational cognitive model where listeners recursively reason about speakers who balance informativity, politeness, and utterance cost. Our model comparisons suggested that cross-cultural differences in intensifier interpretation stem from a combination of (1) different literal meanings, (2) different weights on utterance cost. These findings challenge accounts based purely on semantic variation or politeness norms, demonstrating that cross-cultural differences in interpretation emerge from an intricate interplay between the two.