RDP 2018-08: Econometric Perspectives on Economic Measurement Equation (33)

\begin{array}{l} \Rightarrow f^{- 1} (\frac{1}{U_{t v}} \sum_{u} f (\frac{p_{t u v}}{q u a l i t y_{t v}})) q u a l i t y_{t v} = p_{t \bar{u} v} & \forall t, v \end{array}