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Digital advertising budget allocation remains dominated by a single aggregate metric: return on ad spend (ROAS), computed as total revenue divided by total expenditure.Industry surveys confirm that the majority of advertisers treat ROAS targets as the primary criterion for scaling or contracting media budgets [1].This practice, while operationally convenient, conflates average and marginal returns and can produce allocation decisions that systematically deviate from profit-maximizing optima.The present work formalizes this divergence, derives the conditions under which average-based and marginal-based decision rules yield opposing recommendations, and demonstrates the magnitude of the resulting profit gap through a numerical scenario grounded in standard microeconomic theory [2].The analytical foundation rests on the concave response function.As expenditure increases, a channel first reaches its most responsive audience segments; subsequent increments target progressively less responsive populations, producing diminishing marginal returns [3].Following Ivitskiy [4], the revenue-expenditure relationship is modeled as () = , where () is revenue from expenditure , is a scale parameter, and is the elasticity parameter satisfying 0 < < 1.The constraint on ensures strict concavity.This specification aligns with functional forms in Bayesian media mix models [5] and the classical Dorfman-Steiner theorem on optimal advertising intensity [6].Differentiating the revenue function yields marginal revenue () = , strictly decreasing in .Profit is () = () - - , where denotes fixed costs.The first-order optimality condition requires ( * ) = ( * ) , where () is the marginal cost of advertising.Under constant marginal cost , the profitmaximizing expenditure is * = ( / )^(1/(1 -)).The second-order condition / = ( -1) < 0 holds for all < 1, confirming * as a global maximum [4].Optimal allocation is thus uniquely determined by channel elasticity, scale, and marginal cost, not by any threshold imposed on the average return ratio.A numerical illustration clarifies practical consequences.Scenario A allocates $10,000 and generates $50,000 in revenue (ROAS = 5.0).Scenario B allocates $25,000