The phrase trickle-down theory designates the theory that granting concessions such as tax cuts to the rich will benefit all levels of society by stimulating the economy: wealth, it is alleged, will gradually benefit the poorest as a result of the increasing wealth of the richest.

All things considered, this phrase is a mere euphemistic rewording of the earlier crumbs from a rich man’s table, denoting an unjustly small share of something in contrast to a large share taken by someone else.

The latter phrase alludes to the parable of the rich man and Lazarus in the gospel of Luke, 16:19-31:

(King James Bible – 1611)
19 There was a certaine rich man, which was clothed in purple and fine linnen, and fared sumptuously euery day.
20 And there was a certaine begger named Lazarus, which was laid at his gate full of sores,
21 And desiring to be fed with the crummes which fell from the rich mans table: moreouer the dogs came and licked his sores.
22 And it came to passe that the begger died, and was caried by the Angels into Abrahams bosome: the rich man also died, and was buried.
23 And in hell he lift vp his eyes being in torments, and seeth Abraham afarre off, and Lazarus in his bosome:
24 And he cried, and said, Father Abraham, haue mercie on me, and send Lazarus, that he may dip the tip of his finger in water, and coole my tongue, for I am tormented in this flame.
25 But Abraham said, Sonne, remember that thou in thy life time receiuedst thy good things, & likewise Lazarus euil things: but now he is comforted, and thou art tormented.
26 And besides all this, betweene vs and you there is a great gulfe fixed, so that they which would passe frō hence to you, cannot, neither can they passe to vs, that would come from thence.
27 Then he said, I pray thee therefore father, that thou wouldest send him to my fathers house:
28 For I have fiue brethren, that he may testifie vnto them, lest they also come into this place of tormnt.
29 Abraham saith vnto him, They haue Moses and the Prophets, let them heare them.
30 And hee said, Nay, father Abraham: but if one went vnto them from the dead, they will repent.
31 And hee said vnto him, If they heare not Moses and the Prophets, neither will they be perswaded, though one rose from the dead.

The earliest instance of crumbs from a rich man’s table that I have found is from a letter, published in The Stamford Mercury (Stamford, Lincolnshire, England) of Thursday 9^th December 1779, in which a person signing themself ‘a sportsman’ argued for “a tax upon dogs”:

How many favourite lap-dogs, and spaniels are pampered with more delicate viands than ever regaled the palate of the industrious husbandman! And the poor half-starved beggar is refused even the crumbs from the rich man’s table, while Jockey and Jowler are glutting themselves around the hearth, with the fragments that remain.

The second-earliest occurrence that I have found is from The Massachusetts Centinel (Boston, Massachusetts, USA) of Saturday 16^th December 1786:

The week is now expired, which has in a particular manner called on the affluent, while floating in the full tide of overflowing plenty, to think on the distress which a great part of their fellow creatures feel, and to stretch forth the bountiful hand to their relief, by bestowing on them a part of that abundance with which “the Lord of all,” hath blessed them—the season, united with the occasion, have rendered the language of penurious complaint, strikingly pathetick, and it is believed in most instances, irresistable—the citizens of this metropolis, celebrated for their munificence on this period of annual festivity, in general felt the necessity of charity, and bestowed it accordingly—The example of its first characters, stimulated others less wealthy, who waited therefor, to throw in their mite towards the relief of the necessitous—the mansion for the distressed resounded with the songs of joy on once more partaking of the delicacies of life—happy in tasting of the “crumbs which fall from the rich man’s table”—the cries of want were hushed—and those who have long felt the cold ice of poverty quenching in their bosoms the latent fire of devotion, “sacrificed the sacrifice of thanksgiving, and declared the works of the Lord with rejoicing.”—Say, ye whose frozen bosoms never yet felt the glow of sympathy animating them, do ye not envy the pleasures ye know the bountiful enjoy, in reflecting on the happiness their benevolence has diffused?—But ye shall taste them not—while on them the blessings that attend the charitable shall unceasingly be poured. A winter is now before us, which from present appearances will be tedious, and which will call loudly on the charitable, and well-disposed, to lay up to themselves more treasures in reversion, by bearing in mind, “the poor and needy,”—That they will, we have no doubt—and we assure them——
“The heart that feels for other’s woes,
“Shall find each selfish sorrow less,
“His breast, who happiness bestows,
“Reflected happiness shall bless.”