Growth, Expansion, Productivity, and Prices under Utility-Dollar Normalization

We develop a unit-consistent accounting framework that separates nominal measurement from real economic dynamics and links relative prices to productivity in a transparent way. Real output is measured in utilities (units of the base-year GDP basket) and real input in contributions (units of the base-year GDI/factor basket), yielding three core aggregates: output growth, input expansion, and aggregate productivity (Π = G/E). To make intertemporal comparisons invariant to purely nominal rescalings, we introduce a standard utility basket (SUB) and use it to define the utility-dollar unit of account; in this normalization the GDP deflator is the nominal price of SUB. Within this unit system, we provide quantity-first definitions of good and factor productivity and deduce real-price representations that decompose good and factor price changes into aggregate productivity and sector-specific components. An illustrative example demonstrates the accounting. Empirically, we validate the framework using BLS private nonfarm business series: productivity computed from published output and combined-input indexes reproduces published MFP, and reduced-basket proxies track MFP growth closely. A lightweight pseudo real-time exercise using quarterly nonfarm series illustrates how representative baskets support near-term attribution of nominal movements into price versus quantity components.