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Approximate quadratic-linear optimization problem

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Approximate quadratic-linear optimization problem

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    1. Approximate quadratic-linear optimization problem Based on Pierpaolo Benigno and Michael Woodford

    2. The Quadratic Approximation to the Utility Function Consider the problem

    3. The first-order condition

    4. The second-order approximation to the utility function

    5. The second-order approximation to the constraint

    6. Substitute the second-order approximation to the constraint into the linear term of the second-order approximation to the utility function, using the FOC, yields a quadratic objective function

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