RDP 2018-08: Econometric Perspectives on Economic Measurement Equation (F9)

\begin{array}{l} \sum_{v} q_{t v} {\hat{λ}}_{v} (\frac{p_{t v}}{{\hat{λ}}_{v}} - {\hat{α}}_{t}) = 0 & \forall t & \Rightarrow & {\hat{α}}_{t} = \frac{\sum_{v} p_{t v} q_{t v}}{\sum_{v} q_{t v} {\hat{λ}}_{v}} & \forall t \end{array}