Consider one farmer using an aquifer. The volume of water in the aquifer is described by X_t+1 = X_t - Y_t + Q_t where X_t is the volume of water in period t, Y_t is the extraction of water in period t and Q_t is precipitation. The marginal net benefits of the farmer in each period are described by

MNB_t = 20 - Y_t

There are two periods. The amount of water in the first period is X₀ = 7 and Q₀ = 1.5. The farmer cannot use more water than available at the beginning of each period such that Y_t X_t. With a discount rate of 10%, what is the efficient water use in the first period?

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