# Tag Info

Accepted

### Karush-Kuhn-Tucker for series

Yes, Bachir et al. (2021) extend the Karush-Kuhn-Tucker theorem under mild hypotheses, for an infinite number of variables (their Corollary 4.1). I give hereafter a weaker version of the ...
• 191

### Real Life Examples of Optimization in Economics

Optimization problems Some of the problems you mention do not seem that simple to me, e.g., "farmers choosing between different crops to grow based on expected harvest and market price" can ...
• 29.6k

### Minimisation problem turned into Maximisation

The Lagrangian is not really symmetric; something that is easier to see if you formulate it without the calculus implementation. First-order conditions for maxima and minima might look similar, but ...
• 13.5k
Accepted

### Cost Minimization and Karush-Kuhn-Tucker

The term $\lambda_2(x_1-1)$ in your Lagrangian is incorrect; it treats the second constraint as an equality rather than an inequality. To allow for the constraint being an inequality you can include a ...
• 8,584
Accepted

### Two-Stage Utility Maximization Problem

Consider the Wikipedia definition (take from Hal Varian's book) of a quasi-linear utility function $$u(w,x_1,...,x_n) = w + h(x_1,...,x_n),$$ where $h$ is strictly concave. The example in this ...
• 3,798
Accepted

### Why do we need Complementary Slackness Condition for Karush-Kuhn-Tucker Conditions

Solving a non-linear programming (with inequality constraints) is about trial and error. You don't know a priori if a constraint is active. You consider all the possible cases satisfying your ...
• 1,262

### Applications of Optimal Transport in Economics

Optimal transport methods are very much still in use in economics. The show up in two-sided matching with side-payments, contract theory, hedonic pricing, partial identification in econometrics, and a ...
• 13.5k
Accepted

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

Because "adjustment costs are linear and there is no aggregate uncertainty", the FOC for $N_t$ is $$f'\theta g_N(N_{t}, I_{t}) - w_N = \phi \lambda C_N$$. Notice that this is exactly the ...
• 2,506
Accepted

### Regression Optimization problem under constraints

The situation is given in the following picture The black line is the true conditional mean $E(y|x)$. If we truncate the data, all observations above the truncation $Y^A$ are not observed. For low ...
• 12.5k

### Complementary slackness conditions (Kuhn-Tucker)

It is possible to have $$g(x^*) = b\; {\rm and}\; \lambda^* = 0$$. When the multiplier is zero and the constraint is equal to zero, then a) The constraint does not really "bind" b) That's ...
• 33.9k
Accepted

• 3,798
Accepted

### Constrained Optimization with Multiple Constraints: Do multiple strictly positive multipliers imply a solution at a vertex?

If by $\lambda_i$ you mean the multiplier belonging to constraint ($i$), then $\lambda_i$ and $\lambda_j$ being positive do mean that these constraints are active/effective/realized as equalities. Now ...
• 29.6k