# Questions tagged [lagrangian]

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• 13
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### Assumption of interior solution in the Lagrangian method

Why do we need to assume an interior solution before using Lagrangian method for utility maximization problems?
1 vote
78 views

### Dealing with integrals in econ models

I am currently studying econ models, and trying to calculate the FOC for different kind of models. I use J.Gali "Monetary Policy, Inflation and the Business Cycle - An Introduction to the New ...
• 50
86 views

### Understanding Duality between Individual and Collective Maximization in Macroeconomic Models

I'm currently studying macroeconomic models, specifically from the book "Recursive Macroeconomic Theory." In Chapter Seven, it is mentioned that some economic models involving firms and ...
• 155
1 vote
21 views

### 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 ...
• 991
223 views

### Minimisation problem turned into Maximisation

My course always converts minimisation problems into maximisation. They give the following reason as outlined in the problem below. $Min\; P_xx + P_yy \; s.t. \; u(x,y) \le x^{\frac{1}{2}} + y$ &...
• 991
247 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 ...
• 991
1 vote
63 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 ...
• 991
60 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 ...
• 991
363 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 ...
• 991
1 vote
234 views

• 33
82 views

### Determine for which prices and income the constraint is binding

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,...
• 822
1 vote