W(x_{t}^{n}, y_{t}^{n}) = g(y_{t}^{n} + (p_{t} + ε_{t})x_{t}^{n}) – k(x_{t}^{n})^{2} —– (1)

subject to the budget constraint

y_{t}^{n} + p_{t}x_{t}^{n} = 0 —– (2)

x_{t}^{n} = γε_{t}, γ = g/2k > 0 —– (3)

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