Questions tagged [optimization]

Mathematical techniques for the selection of a best element (with respect to some criteria) from the set of available alternatives.

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When can one drop time subscripts? Example from Angrist and Kugler (2003)

Not the first time I am asking myself, but in this paper they actually start with a time dependent maximisation problem and then drop all time subscripts. Background: They have profit maximisation ...
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Arrow-Debreu Theorem of Existence: Non satiation

Let $n$ be the number of consumers and $m$ be the number of commodities. The Arrow-Debreu theorem requires closed and convex consumption sets $X_i \subset \mathbb{R}^m$ for all buyers $i \in [n]$. ...
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Solving for parameter value

I have the following maximization function - $\max_{x \in (0,1)} (((p_1e_1x^2)^{r} + (p_2e_2(1-x)^2)^{r})/2)^{1/r}$ where, $p_1$ and $p_2$ are drawn from uniform distribution [0,1] and are considered ...
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Lagrangian multiplier and optimal bundle

I would like to know where I am wrong (if I am) and why I am wrong here please: If a consumer has an income of 600 euros to spend for good x (Px = 10 euros) and good y (Py = 5 euros). What is the ...
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I have to maximize the following function - $\max_{x \in (0,1)} (((p_1x)^{2r} + (p_2(1-x))^{2r})/2)^{1/r}$ where, $p_1$ and $p_2$ are drawn from uniform distribution [0,1] and are considered to be ...
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Comparing 2 equilibrium values (competitive vs centralized): can I compare only 1st derivative of objective function?

I have a rather complex model where analytical solutions do not seem achievable (I also tried symbolic solving in Matlab and Python and could not find any) so that I cannot get an explicit expression ...
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Conic optimization in economics

Are there any mainstream economic models that rely on conic optimization to solve for decision variables? Conic optimization is a type of convex optimization problem, different from linear and ...
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Is a binding ZLB a binding constraint?

Usually, in an optimisation problem, a binding constraint is one at which the optimal solution holds at the constraint with equality, i.e. it's a boundary solution. However, in many articles, for ...
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Practice question on Correspondences and maximization

We're learning about Theory of the Maximum. I tend to struggle with correspondences in this context, so I'm trying to work through some practice questions. I will start with some general notation of a ...
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How can you interpret one of the parameters of optimal consumption at the Merton portfolio problem?

Statement: Let the dynamics of wealth of the agent satisfy $$dX_{t} = \pi_tX_t\Big(\mu dt+\sigma dB_{t}\Big)- c_t X_t dt, \qquad \textrm{with}\quad X_0=x_0 \in \mathbb{R},$$ where $(\pi,c)$ is an ...
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How do you formulate a distance constraint and a budget constraint?

Everybody knows about budget constraints and how they are represented: but what if I want to represent a distance constrain from the shop you buy the goods? How can I build that?
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Find the utility maximizing bundle [Sundaram, P.169, Q.7 (Kuhn-Tucker Theorem) ]

A consumer with a utility function given by $u(x_1, x_2) = \sqrt{x_1} + x_1x_2$ has an income of $100$. The unit prices of $x_1$ and $x_2$ are $4$ and $5$, respectively. (a) Compute the utility-...
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How can this be proved? (Convex optimization)

Consider the following maximization problems: $\max_{x} x -\gamma p(x)$ subject to $x \in \Omega_1$ $\max_{x} x-\gamma (p(x) + q(x) )+K$ subject to $x \in \Omega_2$ where $\Omega_1$ and $\Omega_2$...
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When the global optimal is outside of the constraint set, what will be the demand?

$u:\mathbb R^n\to\mathbb R$ is a quasi-concave utility function so the indifference curves are convex. $a,b\in\mathbb R^n$ are two points. Our budget set is the (one-dimensional) segment $[a,b]$ that ...
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Simplex Lp interpretation of dual problem´s solution

I am wondering whether my interpretation of my simplex dual problem result is correct. The primal problem is: ...
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Solving a HJB with additional constraints on control and state variables

I am trying to solve a Hamiltonian-Jacobi-Bellman equation with additional constraints on the state and control variables, but I am a bit confused on how to do that. In Intrilligator 2002, it is ...
I have the utility function: $U(x_1,...,x_n)=a_0+\sum_{i=1}^{n}a_ix_i\;\;\;\;\;\;\;\;\;a_j\in\mathbb{R}_+ \;\;\forall j=\{0,...,n\}$ (maybe $a_0$ could be zero) $\sum_{i=1}^{n}a_i\in (0,K)\;\;\;$ ...
I am trying to solve the problem of a firm facing the possibility of a future tax, in continuous time. The firm maximizes $V(k)=\int_{t=0}^{\infty}e^{-rt} \pi_t dt$ with $\pi_t=f(k_t)-i_t$ and \$\dot{k}...