# 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.
• 16.2k
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 ...
• 28k
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 ...
• 3,256
Accepted

### Why couldn't the Karush-Kuhn-Tucker optimization find the solution?

As @user32416 pointed out the first order stationarity conditions are not enough. Specifically it seems that you violate Slater's condition, which states that "the feasible region must have an ...
• 28k
Accepted

• 151

### Reverse auction formula

A first price standard and reverse auction are formally equivalent to each other, and the same method can be used to solve both: First Price Auction In a first price auction, $n$ bidders choose ...
• 16.8k
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• 5,170
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### 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-...
• 2,589
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### 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 ...
• 50.2k
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 ...
• 3,256

### 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 ...
• 3,422

### 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 ...
• 151
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} = \...