Let us think about the simple setup with a usual Cobb–Douglas production function with only one factor (labor) F(A, L) with a modification that a planner can choose an elasticity of population growth to income per capita at the start of the planning excercise. It still can be only negative ie more money always should mean slower growth.
We can have two types of planners following two utilitarian traditions.
A Benthamine planner wishes to maximize the total national income.
A Millian planner wishes to maximize the average national income.
The exogenous parameter in the model is returns to scale of L.
We obviously can have usual examples with decreasing, constant and increasing returns to scale.
Decreasing returns: Millian wants minimum population (most negative elasticity), Benthamite wants maximum (least negative).
Constant returns: Millian is indifferent, Benthamite wants maximum.
Increasing returns: Both want maximum population (least negative elasticity).
In the increasing returns case, both planners' objectives converge, as maximizing population increases both total and per capita income.