RDP 2018-08: Econometric Perspectives on Economic Measurement Equation (37)

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