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This paper attempts to show that an implicit consideration, using the utilitarian paradigm of maximizing the sum of agents' utilities, is insufficient.
An agent can be in one of three broad states and the sum of agents is equal to unity: they can be unemployed, in paid employment (by a large firm or a self-employed recruiter), or in self-employment.
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The number of antihypertensive agents used was expressed as the sum of antihypertensive agents such as thiazide diuretics, loop diuretics, aldosterone antagonists, alpha blockers, beta blockers, calcium channel blockers (CCBs), ACEIs, ARBs, renin inhibitors, and centrally-acting adrenergic drugs being used.
'Additive' antitumour activity was defined as an antitumour effect of the sum of both agents alone, 'synergy' as effects greater than the sum of both agents alone, and 'potentiation' as the effect of an itself nontoxic agent to increase the efficacy of the combined agent.
The sum of all agents in the economy is equal to unity.
A minor tax on total earnings improves the sum of the agents' and the principals' payoffs.
In many settings, the objective is to maximize the sum of the agents' utilities (taking payments into account).
It turns out that by allocating inefficiently, more payment can sometimes be redistributed, so that the net effect is an increase in the sum of the agents' utilities.
We then have the total number of agents, N, as the sum of ni from 1 to h.
(A synergistic reaction is one whereby the effect of combining two or more agents is greater than the simple sum of the individual agents).
Still with a complete asset market but with a more demanding utility function such as power utility, aggregation of marginal utilities is more complicated and does not involve just summing up consumption of agents.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com