The parallel replacement problem under economies of scale (PRES) determines minimum cost replacement policies for each asset in a group of assets that operate in parallel and are subject to fixed and variable purchase costs. We study the mixed-integer programming formulation of PRES under technological change by incorporating capacity gains into the model such that newer, technologically advanced assets have higher capacity than assets purchased earlier. We provide optimal solution characteristics and insights about the economics of the problem and derive associated cutting planes for optimising the problem. Computational experiments illustrate that the inequalities are quite effective in solving PRES under technological change instances.