dual_analysis

# Differences

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 dual_analysis [2020/03/26 10:43]matsz dual_analysis [2020/04/10 11:59] (current)matsz [Constrained optimisation background] 2020/04/10 11:59 matsz [Constrained optimisation background] 2020/03/26 10:43 matsz 2020/04/10 11:59 matsz [Constrained optimisation background] 2020/03/26 10:43 matsz Line 37: Line 37: The functions //f// and //g// depend on some parameters, e.g. prices and technical i/o coefficients respectively that were not shown in the exposition above in order to reduce the size of the expressions. By changing such parameters, we introduce shocks to the model. Assume that in a reference scenario, we have prices $p^0$ and technology $a^0$ resulting in the solution $(x_1^0,​…,​x_n^0,​λ_1^0,​…,​λ_m^0,​π_1^0,​…,​π_n^0 )$. In another simulation, we have other prices $p^*$ and technology $a^*$ resulting in the alternative solution $(x_1^*,​…,​x_n^*,​λ_1^*,​…,​λ_m^*,​π_1^*,​…,​π_n^* )$. The functions //f// and //g// depend on some parameters, e.g. prices and technical i/o coefficients respectively that were not shown in the exposition above in order to reduce the size of the expressions. By changing such parameters, we introduce shocks to the model. Assume that in a reference scenario, we have prices $p^0$ and technology $a^0$ resulting in the solution $(x_1^0,​…,​x_n^0,​λ_1^0,​…,​λ_m^0,​π_1^0,​…,​π_n^0 )$. In another simulation, we have other prices $p^*$ and technology $a^*$ resulting in the alternative solution $(x_1^*,​…,​x_n^*,​λ_1^*,​…,​λ_m^*,​π_1^*,​…,​π_n^* )$. - In this simulation we now would like to know more about why some particular activity $x_i$ reacts as it does, i.e. why $x_i^*$ is different from $x_i^0$. We then compute each term in the first order conditions, and compare the two simulation. To be slightly more explicit, we can assume that the resources are //​j//​={"​land"​ ,"​fodder"​ ,"​young animals"​ }. We can then do a comparison such as the following:​ + In this simulation we now would like to know more about why some particular activity $x_i$ reacts as it does, i.e. why $x_i^*$ is different from $x_i^0$. We then compute each term in the first order conditions, and compare the two simulation. To be slightly more explicit, we can assume that the resources are //​j//​={"​land"​ ,"​fodder"​ ,"​young animals"​ }. We can then do a comparison such as the following: + FIXME \begin{align} \begin{align} \begin{split} \begin{split}