Questions tagged [lagrangian]

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What is the meaning of lagrange multiplier (especially in ramsey problem)

Consider lagrange function for ramsey problem: $L=E_0 \sum_{t=0}^{\infty} \beta^t \{u(c,l)+\gamma_t (s^t)[E_0 \sum_{j=0}^{\infty} \beta^j u_c (s^{t+j}) z(s^{t+j}) -u_c (s^t) b_t(s^{t+1})] \}$ where $[...
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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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49 views

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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56 views

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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39 views

FOC for stochastic Ak Model

(Note: the other posts do not cover this part of the derivation) I have tried to compute the FOC of $k_{t+1}(s^t)$. I get that $0 = -\lambda_t(s^t)$; I can't see why the sigma remains for the FOC of $...
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39 views

How to derive consumer expenditures in EMEA 14.2.5

I am working on a problem 14.2.5 from EMEA by Sydsaeter, Hammond and Strom. Consider the consumer demand problem: $$ \max_{x,y} U(x,y) = \alpha \ln(x-a) + \beta \ln(y-b) \text{ s.t. } px+qy=m \tag{*} ...