Allocating river water

A town gets its drinking water from a nearby river. The marginal cost of the water is zero and the town’s demand is given by: W2Pd = 2200 – 2*Qd. Five hundred (500) local residents also use the river for recreation (swimming, fishing and boating). Each one receives the following marginal benefits from Qs units of water left in the stream: MBi = 2 – (1/250)*Qs. The quantity of water in the river is initially 1200 units. Water taken out of the river for drinking does not return to it, and cannot be used for recreation.

1. Please calculate the efficient allocation of water to the two uses.
2. Please calculate the net deadweight loss (inefficiency) that would occur if the river is common property and the town ignores recreation when deciding on Qd.

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