The paper presents a problem statement and a preliminary study of the oscillatory behavior of total production capacity near balanced growth in a model with an endogenous production function and production capacities represented by capacity distributions across technologies. The mathematical framework employs a first-order delay differential equation with constant or periodic coefficients, subject to a constant initial condition. The paper seeks solutions to this equation both in quadrature form and via numerical methods implemented in Mathematica system. Solution profiles and their dependencies on varying parameters are constructed and systematically analyzed.