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The question "how are the first order conditions" seems very unclear to me, and I am providing a set-up for finding and writing them out, while explaining the Kuhn-Tucker conditions that are easy to s …

I got some outside help for the ending of the proof I was attempting. I'll leave this question if by chance someone else finds it useful. So if we want to show $p_1x_1 + \cdots + p_{n−1}x_{n−1} = 0 \ …

One (perhaps flippant) answer is that Marxists have a lot of ideas about how prices "should" work or how the value of labor "should" be rewarded, that aren't in line with what we observe, because cent …

Hint: I will talk through a simpler case, and let you extend it to the generic case. Let's say there's only two bidders and only the top 1 bidders win. Whoever wins pays whatever the loser bid. This …

We know that if $u$ represents $\succeq$ on $X$, then for any strictly increasing function $f: \mathbb{R} \rightarrow \mathbb{R}$, then $v(x) = f(u(x))$ represents $\succeq$ on $X$ ($X$ in this case …

(Don't vote on this; this is just my comment which is too long) The Riemann-Zeta function, which is a general case for the Ramanujan sum, has many un-intuitive and baffling properties such as: havi …

Given $$\max_{x_2^h} \quad U^h(\phi(\bar z + y^h - x_2^h), x_2^h)$$ You have to find FOCs by taking the chain rule twice for the first argument. Denote the argument for function $\phi$ as $(\cdot)$. …

I will only set up the first part of your question. See if you can move on from there. If you try and set revenue as $p \cdot x$ immediately, you will get $$p \cdot x = p \cdot (\gamma ap + b + R(y) …

From what it looks like, you are literally trying to subtract $(2)$ from $(1)$, incorrectly as well (You didn't distribute the minus out correctly.) It is saying to use equations 1 through 2 to solve …

First, to give a little more background to 123's answer, a production set $Y$ is the set of all feasible production values. With $y \in Y$, $y$ is a vector in $\mathbb{R}^L$, where positive elements i …

Consider the standard utility maximization problem: $$\begin{align}\max_{\vec x} & \quad U(\vec x) \\ & \quad \vec p \cdot \vec x \leq Y \end{align}$$ Here utility is your objective function, and th …

I talked to my teacher to try and get a handle on the question. You are correct that usually $$\overline {f(x)} = \frac{1}{b-a}\int^b_a f(x) dx$$ But for the demand function there are two arguments …

A rough guideline: You already know the first case. At $q < q_c$ (competitive quantity), we have $$S(p) > S(p_c) = D(p_c) > D(p)$$ This is assuming you have "normal" (monotonic) assumptions on the …

Take an individual's maximization problem: $$\max_{x_i} = U(x_1,...,x_n) \quad \text{s.t.} \ \vec{p} \cdot \vec{x} = w$$ Where one of the goods $j$ is a riskless savings good (savings account, gover …

I don't think there's really a name for the type of ordering on preferences, and preferences are between vectors, which aren't necessarily ordered. It looks like because you have a finite number of al …