RDP 2018-08: Econometric Perspectives on Economic Measurement Equation (35)

\begin{array}{l} \frac{1}{U_{t v}} \sum_{u} p_{t u v} = \frac{1}{S q_{t v}} \sum_{n} S p_{t n v} = \frac{1}{q_{t v}} \sum_{n} p_{t n v} & \forall t, v \end{array}