All Questions
Tagged with lagrangian utility
10 questions
4
votes
2
answers
184
views
Intuition of sign used for Lagrange multiplier and corresponding constraint function in constrained optimization
It seems that in many applications there may be some economic interpretation for the Lagrange multiplier and thus it might be beneficial to ensure it's value takes on a specific sign.
If the above is ...
- 53
5
votes
1
answer
228
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.
$Min\; P_xx + P_yy \; s.t. \; u(x,y) \le x^{\frac{1}{2}} + y$
&...
- 1,011
2
votes
1
answer
369
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 ...
- 1,011
1
vote
1
answer
195
views
Compensating Variation - Interpreting the formulae
Assume $U(x,y) = x^{1/2}y^{1/2}$ s.t. $P_xx + P_yy = m$
And a price increase from $P_x$ to $P'_x$:
$U_0 = \frac{M}{2(P_xP_y)^{1/2}}$
Compensation variation formulae is: $\frac{M + ∆M}{2(P_x'P_y)^{1/2}...
- 1,011
3
votes
1
answer
156
views
How can I solve a Utility Maximization problem using the Lagrangian method where the Utility formula has an exogenous constant $a$?
The utility function is given by: $$u(x, y) = 2x^{\frac{1}{2}} + 2ay^{\frac{1}{2}}.$$
The optimal bundle should be expressed as a function of $a$. Other variables are given by:
$$\begin{eqnarray*}\...
- 31
3
votes
2
answers
282
views
How to handle multiple lagrange multipliers in a maximization problem?
Let's assume a standard household maximization problem of the form:
\begin{align}
\underset{C_t}{max} \sum_{t=0}^{\infty} \beta^t U(C_t)
\end{align}
subject to a standard Budget constraint:
\begin{...
4
votes
1
answer
692
views
Concave utility functions solution example
In the following post an example is given of the corner solution for a concave utility function. I tried solving it but got stuck. I have no idea how these types of problems are solved so if you could ...
- 43
1
vote
1
answer
99
views
Lagrangian when ICs are tangent to the budget line
Suppose the graph below shows three Indifference Curves such that $t > s > r$, and the budget line $p_1x + p_2y = I$. I was wondering if we set the Lagrangian as $\mathcal{L}= U(x,y) - \lambda (...
- 244
2
votes
1
answer
534
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 ...
- 121
0
votes
1
answer
655
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 ...
- 13