# 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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### Constrainted optimization: merge two constraints into one

Consider the following problem \begin{align} &\max_u F(x,u)\\ \text{s.t. }& u \in [0,\bar u]. \end{align} Any idea how to merge the two constraints $u \geq 0$ and $\bar u - u \geq 0$ into one ...
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### Overlaping jurisdictions Model: Proof of Lemma 1; The Size of Nations

I've been reading the book 'The Size of Nations' by Alberto Alesina and Enrico Spolaore (can be found on the net if you know where to look) and I'm having trouble following their "proof" of the first ...
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### Transformation Function

In Mas-Colell microeconomics textbook I have found that profit maximization problem (as well as many further optimization tasks) could be represented with application of some transformation function (...
237 views

### Price Optimization from Data

How can I find the optimal price that maximizes profits, given past sales data? I thought I could do this, but I've been running into problems. Data: ...
192 views

### Find Indifference curve/s and Marginal Rate/s of Substitution given only one point

Arka likes fries. She wants to consume as much as possible. She consumes either regular (1 oz) or large sizes (5 oz). Draw her indifference curve through $(x_R, x_L) = (10,0)$ and her indifference ...
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### Does this conditional increase in income affect a budget line in the same way as an unconditional increase in income would?

It's been awhile since I've taken introductory microeconomics. I remember increases in income move budget line outward. What if the increases have some condition? The problem: Jill has $I$ to ...
282 views

### Can budget lines be discontinuous?

It's been awhile since I've taken introductory microeconomics. I read budget lines can be discontinuous awhile ago but am suspicious as to such a concept being discussed in intro micro classes ...
96 views

### Dynamic programming: verification principle

Consider the Gale cake problem with $u(c) = log(c)$, so that the problem becomes:$$\max_{x}\sum_{t=0}^{\infty} \beta^{t}log(x_t-x_{t+1})\: sub\: 0<x_{t+1}\leq x_t,\: x_0>0\ given$$ It is ...
I've been trying to figure out how the author came up with the constraints for this liquidity model in a textbook I'm reading. details: http://imgur.com/TpVjg4w $U = \pi_1u(C_1) + \pi_2u(C_2)$ where ...