# Questions tagged [lagrangian]

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### Technology Parameter In Converted Minimisation Problem

Question: I want to understand what's going on with respect to the technology parameter $A$ when i convert this minimisation problem into a maximisation problem. The issue is only revealed when i use ...
62 views

### Minimisation problem turned into Maximisation

My course always converts minimisation problems into maximisation. They given the following reason as outlined in the problem below. $Min\; P_xx + P_yy \; s.t. \; u(x,y) \le x^{\frac{1}{2}} + y$ &...
124 views

### Arguments for Concavity or Quasi-concavity

I'm faced with questions that want me to show that a utility or production function is either concave, or if not then quasi-concave so that we can apply the KKT conditions. For example the production ...
1 vote
51 views

### Logarithmic Utility function Algebra

Question: I'm told the following (by an exam mark scheme): Using $a + b =1$ $a[ln(\frac{am}{p_1})] + b[ln(\frac{bm}{p_2})] = ln(m) - aln(p_1) - bln(p_2)$ I can't get this to hold without the ...
28 views

### Envelope Theorem and Factor Mix Intuition

Brief Summary of question: I'm frustrated with the intuition of the envelope theorem that when input costs change, our envelope theorem tells us we do not need to re-optimise demand levels. Context: I ...
57 views

### Inappropriate use of Calculus in estimating ΔCost?

I have the following model, and i solve for my optimised conditional factor demands, and minimised cost functions $C$. (Note: I have turned a minimisation problem into a maximisation problem). Let's ...
271 views

### Lagrange Multiplier Dual Meaning?

Is the Lagrange multiplier: The marginal cost of the constraint? The marginal benefit of relaxing the constraint? Through duality, both interpretations imply the other? If anyone were so kind, I ...
1 vote
102 views

When we take our Lagrangian and we include non-negativity constraints. If a variable $x = 0$ do we take FOC first or set $x=0$ first? E.g. $Max \; L(x, y, λ) = f(x,y) - λ_1(g(x,y) - k) - λ_x(-x) - λ_y(... 0 votes 1 answer 59 views ### Finding the constraints for a profit maximization program in Acemoglu et al, 2016 I have been reading the paper of Acemoglu et al., 2016 [Networks and the macroeconomy : an empirical exploration], and I have been struggling with a maximization ... 0 votes 0 answers 32 views ### Max and Min with$\leq$and$=$constraints. General questions I wrote this question on Maths.stackexchange but perhaps this community suits better (?) I need to ask you for this question, which is a rather general one, in order to understand how to behave when ... 1 vote 1 answer 81 views ### Supply function of a price-taking firm with a quadratic production function For a firm with the production function $$Q = 40L-L^2$$ where$L$is labor and wage$w = 20$find supply function of a price-taking firm under perfect competition. Fixed costs equal$10$. Following ... 2 votes 0 answers 37 views ### Does local non-satiation hold for this problem? I am getting some confusing results solving this problem:$max_{c_0\geq0, c_1\geq0} \bigg\{EU = R(1-c_0) [p t_1 + (1-p) c_1^{-2} t_2] \bigg\} ~ s.t. ~c_0+c_1 \leq 1$where$p$is the probability of$...
Under what conditions constraints start to bind and how to find it I was trying the following optimization problem: $$\mathscr{L} = x_1 x_2 + x_2 + \lambda(M-P_1 x_1-P_2 x_2) + \mu x_1$$ The thing is,...