# Questions tagged [lagrangian]

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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 $[... 0answers 26 views ### Solving for the efficient subsidy amount with an externality I am dealing with a problem that is set up as follows: Actors A and B get utility from consumption ($c_i$) and disutility from safety measures ($s_i$), however their chance of getting sick is reduced ... 1answer 54 views ### How does this imply that a Pareto optimum maximizes a weighted average of utility functions? I'm reading a passage from Asset Pricing and Portfolio Choice Theory by Kerry Back, and I don't understand some of it. I would appreciate any help anyone could provide me. In the passage, Back is ... 1answer 63 views ### Calculate hicksian demand with utility function (with restriction)$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$For the hicksian demand I ... 0answers 39 views ### FOC for stochastic Ak Model (Note: the other posts do not cover this part of the derivation) I have tried to compute the FOC of$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$...
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{*} ...