The productivity growth slowdown started in the U.S. in the 1970s and lasted several decades, which presents a challenge to Kaldor's growth facts and the one-sector growth model. We ask, What is the simplest modification of the one-sector growth model that can generate a prolonged productivity growth slowdown? We show that the answer is a two-sector version in which productivity growth in the consumption sector slows down and real GDP is measured with the Fisher index used to construct the NIPA. We also show that the Fisher index of real GDP is a welfare measure in the two-sector model.