Transitional Economy

China shifted from a Soviet style economy to a market-style economy.

Why is China different?

• more gradual, via family outlets
• no simultaneous political transition
• began at a lower-level of economic development
• thus, China started in agriculture

East Asian Development Model

We see this in Singapore, HK, Japan, Korea, Taiwan, China.

• land to the tiller: moving land away from landlords and giving it to producers
• export orientation: moving from low-end products to high end export
• financial repression: low interest rates (promote exports + make imports more expensive + allow lending), undervalue currency, capital controls on cross-border flows

Unlike Japan, etc., China had to import technology + expertise because their work is way behind; therefore they were interested in foreign direct investment

Suppose \(f\) is convex on \(\mathbb{R}^{n}\), with domain \(\text{dom } f\). We can make an extended-value extension:

\begin{equation} \tilde{f} \qty(x) = \begin{cases} f\qty(x), x \in \text{dom }f \\ \infty, \text{ otherwise } \end{cases} \end{equation}

This could simplify notation .

Key Sequence

Notation

New Concepts

• Euclidian Geometry Crash Course
  • perspective function
  • linear-fractional function
  • generalized inequality
• convex function
• extended-value extension

Important Results / Claims

• operations that preserve convexity
• seperating hyperplane theorem
• supporting hyperplane theorem
• some convex functions
• some concave fuctions
• convexity preserve line restriction

Questions

Interesting Factoids

\(f: \mathbb{R}^{n} \to \mathbb{R}\) is convex IFF the function \(g: \mathbb{R} \to \mathbb{R}\) is convex:

\begin{equation} g\qty(t) = f\qty(x + tv), \text{dom } g = \qty {t \mid x + tv \in \text{dom }f} \end{equation}

is convex in \(t \in \mathbb{R}\) for any \(x \in \text{dom } f\), \(v \in \mathbb{R}^{n}\).

\begin{equation} f\qty(X) = \log \text{det} X \end{equation}