# Questions tagged [lagrangian]

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### Why do we optimize utility from X1 according to itself?

In lecturer's notes we have a utility function $U_i = X_i^A * (1-L_i)^{1-a},$ $0< a< 1$, $i = 1,2$ $MP_1 = w_1$ $MP_2 = w_2$ $X_1 + X_2 = w_1 * L_1 + w_2 * L_2$ And we need to form a ...
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### Solving for the efficient subsidy amount with an externality

I am dealing with a problem that is set up as follows: Actors A and B get utility from consumption ($c_i$) and disutility from safety measures ($s_i$), however their chance of getting sick is reduced ...
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### How does this imply that a Pareto optimum maximizes a weighted average of utility functions?

I'm reading a passage from Asset Pricing and Portfolio Choice Theory by Kerry Back, and I don't understand some of it. I would appreciate any help anyone could provide me. In the passage, Back is ...
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### Calculate hicksian demand with utility function (with restriction)

$U(x_1, x_2) = 1/2 * x_1$ I am trying to calculate the Hicksian demand when when $U(x_1, x_2) = 2$ and the value of the minimum expenditure when $p_1 = 9$ and $p_2 = 16$ For the hicksian demand I ...
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