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# Tag Info

Accepted

### Marshallian Demand for Cobb-Douglas

Since $a + b=1$ the equations are exactly the same. Substituting in for $a+b$ with $1$ in the third and fourth equations gives the first and second equations.
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 ...

### 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 ...
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 ...
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 ...

### Marshallian Demand for Cobb-Douglas

This is how you get from your first equation to your second. your utility function is $u(x_1, x_2)=x_1^a x_2^b$ since $a+b=1$ I'll change it slightly to a and (1-a) In order to optimise these two ...
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### Monetary policy optimization

You are unfortunately mistaken. DSGE models are at the heart of monetary policy and the most widely used class of models in this field. To work in monetary there is no real way around learning DSGE. ...

### Interpretation of lagrange multiplier

As mentioned in the other answer, the Lagrange multiplier is the marginal effect on the value (optimized) function, when the constrained is "relaxed" marginally. In your case then it should be ...
Accepted

### How do you formulate a distance constraint and a budget constraint?

Because you are talking about constraints, it appears you do not consider the case of inserting such "access costs" (because this is what they are) in the utility function. It implies that ...
Your Lagrangian would be $$L = (ax+by)+\lambda (I−p_x x−p_y y) +\mu_x(x−0)+\mu_y(y-0),$$ where the final two terms represent the restriction that $x,y\geq0$. You then arrive at conditions $$\frac{\... 5 votes Accepted ### setting of Lagrangian function It's a matter of choice how one writes the Lagrangian in the context of Lagrange/KKT. Depending on how it's written, the gradients of the objective and constraint functions are either parallel or anti-... 5 votes Accepted ### Contradictory FOC and maximizing solution As alluded to by Bertrand in his +1 comments this is because FOCs do not tell you where maximum or minimum occurs. This is common misconception among some students but it simply does not hold. FOCs ... 5 votes Accepted ### How do I find the socially optimum and equilibrium value? You need to think about what the total costs are and what the marginal costs are. The social optimum is where marginal costs are equal to the outside option which is riding the bus. The story goes ... 5 votes ### Real Life Examples of Optimization in Economics One could use simple games of resource management, this way the scope is fairly finite. I do research in digital games and economics, which students tend to be interested in. Some relevant papers are ... 5 votes ### Real Life Examples of Optimization in Economics So one thing to keep in mind is that the "simple" examples you're looking at are very much real-world. Any particular optimization decision needs to be simple enough for the people making ... 5 votes ### Real Life Examples of Optimization in Economics The NFL uses optimization when scheduling. In 2013, the NFL began using Gurobi’s mathematical optimization solver to tackle this incredibly complex scheduling problem. With mathematical optimization, ... 5 votes Accepted ### Calculating cost-minimizing inputs with 3 inputs in production function The production function$$F(x) = x_1^{\alpha_1}x_2^{\alpha_2}x_3^{\alpha_3},$$has the derivative with respect to x_j where for sake of example I choose j=1$$\frac{\partial F(x)}{\partial x_1} = \...
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 ...