Etymology
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expense (n.)

also formerly expence, late 14c., "action of spending or giving away, a laying out or expending," also "funds provided for expenses, expense money; damage or loss from any cause," from Anglo-French expense, Old French espense "money provided for expenses," from Late Latin expensa "disbursement, outlay, expense," noun use of neuter plural past participle of Latin expendere "weigh out money, pay down," from ex "out, out of" (see ex-) + pendere "to hang, cause to hang; weigh; pay" (from PIE root *(s)pen- "to draw, stretch, spin"). For the financial sense of the Latin verb, see pound (n.1). 

Latin spensa also yielded Medieval Latin spe(n)sa, the sense of which specialized to "outlay for provisions," then "provisions, food" before it was borrowed into Old High German as spisa and became the root of German Speise "food," now mostly meaning prepared food, and speisen "to eat." Expense account is from 1872.

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expense (v.)

"offset (an expenditure) against an income," 1909, from expense (n.). Related: Expensed; expensing.

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expenses (n.)

"charges incurred in the discharge of duty," late 14c. See expense (n.).

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expensive (adj.)

1620s, "given to profuse expenditure," from expense (n.) + -ive. Meaning "costly, requiring profuse expenditure" is from 1630s. Earlier was expenseful (c. 1600). Expenseless was in use mid-17c.-18c., but there seems now nothing notable to which it applies, and the dictionaries label it "obsolete." Related: Expensively; expensiveness.

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*(s)pen- 

Proto-Indo-European root meaning "to draw, stretch, spin."

It forms all or part of: append; appendix; avoirdupois; compendium; compensate; compensation; counterpoise; depend; dispense; equipoise; expend; expense; expensive; hydroponics; impend; painter (n.2) "rope or chain that holds an anchor to a ship's side;" pansy; penchant; pend; pendant; pendentive; pending; pendular; pendulous; pendulum; pension; pensive; penthouse; perpendicular; peso; poise; ponder; ponderous; pound (n.1) "measure of weight;" prepend; prepense; preponderate; propensity; recompense; span (n.1) "distance between two objects;" span (n.2) "two animals driven together;" spangle; spanner; spend; spider; spin; spindle; spinner; spinster; stipend; suspend; suspension.

It is the hypothetical source of/evidence for its existence is provided by: Latin pendere "to hang, to cause to hang," pondus "weight" (perhaps the notion is the weight of a thing measured by how much it stretches a cord), pensare "to weigh, consider;" Greek ponos "toil," ponein "to toil;" Lithuanian spendžiu, spęsti "lay a snare;" Old Church Slavonic peti "stretch, strain," pato "fetter," pina "I span;" Old English spinnan "to spin," spannan "to join, fasten; stretch, span;" Armenian henum "I weave;" Greek patos "garment," literally "that which is spun;" Lithuanian pinu "I plait, braid," spandau "I spin;" Middle Welsh cy-ffiniden "spider;" Old English spinnan "draw out and twist fibers into thread," spiðra "spider," literally "spinner."

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sumptuary (adj.)

"pertaining to expense," c. 1600, from Latin sumptuarius "relating to expenses," from sumptus "expense, cost," from sumere "to borrow, buy, spend, eat, drink, consume, employ, take, take up," contraction of *sub-emere, from sub "under" (see sub-) + emere "to take, buy" (from PIE root *em- "to take, distribute").

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low-budget (adj.)

1939, originally of motion pictures, "made with little expense;" from low (adj.) + budget (n.). Usually with a suggestion of low quality as a result.

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parasitism (n.)

"a habitual living on or at the expense of another," 1610s, from parasite + -ism. Biological sense of "vital relation of a parasite to a host" is by 1840.

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costly (adj.)

"of great price, occasioning great expense," late 14c., from cost (n.) + -ly (1). Earlier formation with the same sense were costful (mid-13c.), costious (mid-14c.). Related: Costliness.

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poorhouse (n.)

"establishment in which persons receiving public charity are lodged and cared for," 1781, from poor (n.) + house (n.). Poor-farm "farm maintained at public expense for the housing and support of paupers" is by 1834, American English.

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