Class note from Price Theory course. Consider an individual looks to buy $m$ goods. Let there be nice assumptions: Continuous: that consumption can be expressed as $x\in \R^m$. (Strictly?) concave utilities. Linear budget: $p\cdot x \le \texttt{Budget}$. Back of (a big) envelope Let $\mathbf x^H(p, u), \mathbf x^M(p, I)$ be the Hicksian and Marshallian demand functions. If we focus on one single good $i\in [m]$, and with a tiny abuse of notation, we can write $$ \begin{align*} & x_i^{H(\bar U, p_{-i})}(p_i) :=x_i^H(p_i, p_{-i}, \bar U)\cr & x_i^{M(I, p_{-i})}(p_i) :=x_i^M(p_i, p_{-i}, I) \end{align*} $$ When economists scribble a downward sloping demand curve on a 2D plane, we are basically holding $(\bar U, p_{-i})$ (or $(I, p_{-i})$) fixed and drawing the Hicksian demand curve $D^H:\lbrace (x_i^H(p_i), p_i)\rbrace$ or Marshallian demand curve: $D^M:\lbrace(x_i^M(p_i), p_i)\rbrace$....

The TV series Etoile (2025) ends with a solo modern ballet choreographed by Christopher Wheeldon, to the music by Sparks, singing, “I married myself, I’m very happy together. Candlelight, dinner’s home, lovely times…” Seems a bit absurd a first sight, but It’s a very very beatiful and deep concept explored here. “To marry oneself means to fully accept one’s own flaws, either by looking past them or taking the necessary steps to improve....

Today the U of Chicago Symphony Orchestra rehearses Tchaikovsky’s 5th Symphony. Nooooooo. The French horn solo at the beginning of the 2nd movement is one of Tchaikovsky ’s most beautiful melody passages. This pure beauty pushed beyond imagination, in my opinion, it is love.

Professor Aumann’s most highly cited paper “AGREEING TO DISAGREE” only has four pages… Slay. Here’s how I understand Aumann’s common knowledge: Let the state of the world be a finite set $ \Omega $. Each agent $ i $ has an information structure represented by a partition $ \mathcal{P}_i $ over $ \Omega $. For each state $ w \in \Omega $, let $ P_i(w) \in \mathcal{P}_i $ be the element of the partition that contains $ w $....

The Chicago Price Theory (2019) Chapter 8 Location Choice features the following model: $$ \begin{align*} \max_{C, L, t} & \ U(C, L)\cr s.t.&\ C =\alpha + w(24 - L - t) - R(t)\cr & L, t\in [0, 24], C\ge 0. \end{align*} $$ where, $C$ is consumption (think of it as money), $L$ is leisure time, and $t$ is travel time, $R(t)$ is the rent function, assume it be decreasing. $w$ is individual’s wages....

the Economist’s Money Talks has the episode about how the money works for broadway shows: TL;DR: broadway revenue on shows. Each show is like an investment — you put in millions of dollars to put it on stage, with a small probability it becomes a hit and earns huge return. However, post-pandemic the return distribution has shifted a little so that this business model becomes less sustainable.x The episode focus on economic of broadway, but at the end it shed light on a really insightful problem: for general art products with huge positive externality but low investment incentives, how should government subsidize them?...

The night started with Kodály’s Dances of Galánta, then Hadelich joined for Dvořák Violin Concerto, lastly Brahms’s Symphony No. 2. The digital program book which contains full, detailed, amazingly written notes can be found here. My friend says that someone said that unpaid intern hold those pens. I’m not violin nor Brahms expert. But it was definitely a splendid night that even the 48-minute super long Brahms symphony failed to bore me....

The Grande Pas Classique is one of the most academic and technically challenging piece among the bellet repertoire. [The choreographer, Victor Gzovsky] was born in Russia and studied ballet in St Petersburg under the famous Mariinsky ballerina Evgenia Sokolova. In 1925, he left for Berlin, but later moved to France and after WWII he even held a post of the ballet master at the Paris Opera. In the 1950s – 1970s, Gsovsky worked in Munich, Dusseldorf and Hamburg, where he staged a number of productions....

The U of C Symphony Orchestra is rehearsing Ouvertüre zur Fledermaus for Halloween these days. I play piccolo for this piece. It saves a lot of practice time (piccolo can easily play fast). Though the piece sounds easy, the rubato of the piece takes a lot of rehearsals to align everyone on track. Fledermaus overture is such a ubiquitous piece for all music festivals that it’s yelling for parody. Tom and Jerry has one episode dedicated to it — doesn’t the background look like the Schönbrunn Palace?...

Here’s my own class note from first two weeks of Professor Kamenica’s Topics in Informational Economics course. Math Prelims: Comparing Two Distributions Second-Order Stochastic Dominance (SOSD) Definition. Given $\mathbf{X}, \mathbf{Y} \in \mathcal{X}^n$, we say that $\mathbf{X}$ second-order stochastically dominates $\mathbf{Y}$, written as $\mathbf{X} \ge_{sosd} \mathbf{Y}$, , if for every increasing and concave function $u : \mathbb{R}^n \to \mathbb{R}$, $$ \int u(x), dF_{\mathbf{X}}(x) \ge \int u(x), dF_{\mathbf{Y}}(x). $$ Mean-Preserving Spread (MPS) Definition....