Etymology

chase pennies with dollars

Today it means: To expend more money or effort in gaining something (especially, a cost reduction or revenue addition) than it is worth. Full definition →

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The story

References the foolhardy nature of spending more money, resources, or time, in order to earn or save lesser amounts. Chiefly used within the United States, in business and finance settings and media.

Etymology from Wiktionary, CC BY-SA 4.0.