# 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.
• 15.9k
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### First Order Condition for Profit Maximization in Gambling Industry

The expression in question is in footnote $11$ of the referenced article. Reading the paper, we see that the decision variable here is "the payout rate", which is the reciprocal of $P$. So ...
• 31.8k

### References to learn continuous-time dynamic programming

For continuous-time stochastic dynamic programming, the small, nontechnical Art of Smooth Pasting by Dixit is a wonderful option. It does a very effective job of conveying the basic intuition. Stokey'...
• 3,682
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 ...
• 26.1k
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### 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 ...
• 3,247

### 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 ...
• 3,721
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### 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 ...
• 26.1k

### 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 ...
• 9,435
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### 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 ...
• 2,021
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### 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 ...
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### References to learn continuous-time dynamic programming

Dynamic Programming & Optimal Control by Bertsekas Introduction to Modern Economic Growth by Acemoglu The Acemoglu book, even though it specializes in growth theory, does a very good job ...
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### Is there a way to link Berge's theorem of maximum to Envelope theorem?

They are related and usually fall into the same discussion, but as @Alecos mentions in the comments, the two theorems show different things. I suppose the connection that you're after is the fact ...
• 9,107
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• 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 ...
• 16.6k
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• 5,090
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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-...
• 2,559
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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 ...
• 41.6k
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### 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 ...
• 3,247